Cinnabun Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣈⡙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⣠⣴⣾⠿⠟⠛⣛⣛⡛⠻⠿⣿⣿⣍⠙⠛⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠏⠀⣠⣾⡿⠋⠀⣀⣴⣿⠿⠛⠋⠀⠀⠀⢹⣿⡆⠀⠀⣿⠹⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⣿⡟⣰⡟⣿⡿⠀⢠⡾⠙⣿⣧⣄⣀⣀⣀⣀⣤⣾⡿⢁⣴⠟⠁⠀⣿⣿⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢰⣿⡇⢿⡀⢿⣿⠀⠈⠛⠷⣌⠙⠛⠿⠿⠿⠛⠛⠉⣠⠟⠁⠀⠀⢠⣿⣿⡀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⢀⣴⠛⣿⡇⠘⣧⠈⢿⣷⣄⠀⠀⠘⠷⣤⣤⠶⠶⠶⠖⠛⠉⠀⢀⣠⣴⡿⠋⢸⡇⠀⠀⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠸⣧⠀⢻⣿⡄⠙⢶⣤⡙⠻⢿⣶⣤⣤⣀⣀⣀⣀⣀⣠⣤⣴⣾⡿⠟⠋⢀⣠⠟⠁⠀⣼⣿⠛⣿⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠘⣷⠀⠹⣿⣦⣀⠈⠻⣦⡀⠈⠉⠛⠛⠛⠛⠛⠛⢛⣫⡿⠶⠶⠶⠛⠋⠁⢀⣠⣾⡟⠁⣰⠟⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢹⡆⠀⠈⠙⢿⣷⣦⣌⡛⠛⠛⠛⠛⠳⠶⠶⠶⠛⠁⠀⠀⣀⣠⣤⣶⣾⠿⠛⠁⠀⣼⠏⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠙⠛⠿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡿⠿⠿⠛⠋⠉⠀⣀⣀⣀⣴⠏⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠈⠛⠛⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⣉⡉⠉⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠉⠉⠀⠀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡶⠟⠛⠉⠙⠛⠶⢦⣤⣤⣤⠾⠋⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣆⣀⡈⣀⣠⣿⠖⣲⣀⣀⡀
⠀⠀⠀⠀⢀⣤⠖⣨⡕⢹⣏⠡⠶⣏⠙⢯⡙⠲⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠉⠉⠉⢉⣤⣼⣿⡿⢃⣽⡄
⠀⠀⠀⣠⣼⣿⡀⢿⣷⣈⠙⠛⠻⠛⠀⣸⡿⠀⢈⣏⢷⢠⡀⠀⠀⠀⠀⠀⠀⢀⣀⢴⣯⣈⠀⠉⠛⠷⠶⠾⠿⠛⠛⣛⣉⣀⣾⣿⡇
⠀⠀⢠⣿⣦⡙⠳⣤⡙⠛⠿⠶⠶⠶⠚⠋⠀⢀⣾⠋⣼⠈⣿⣆⠀⠀⠀⠀⣰⡟⣿⢦⠈⠙⠷⣿⣧⣴⣦⣤⣶⣿⣿⣽⣿⣿⣿⠿⢩⣦⡀
⠀⢀⣼⣟⠿⣧⣄⡈⠉⠛⠒⠒⠤⠤⠤⠴⠚⢋⣠⣾⠏⠀⣿⣿⠀⠀⠀⢠⣿⣯⣝⠢⡛⣷⣦⡤⣈⠉⠉⠛⠛⠛⠋⠙⠉⣉⣠⣼⣿⣿⡇
⠀⢸⣷⡉⢷⣄⣉⠛⠻⠷⣶⣴⣶⣦⡴⠶⠶⠟⠉⠀⣀⣼⢿⡿⠀⠀⠀⠘⣿⣿⣉⡠⠐⢌⠻⣿⣦⡜⢋⡉⢸⠁⠈⠏⠛⠓⠠⢠⣿⣿⡇
⠀⠸⣿⡏⠠⠟⠛⠻⠷⢤⣤⣀⣀⡀⣀⣀⣠⣤⠴⠞⣋⣥⡾⠃⠀⠀⠀⠀⠙⢿⣿⣧⣷⣄⠙⠢⡙⣾⣟⣷⢋⡀⠄⢠⣤⣴⣼⣿⣿⡿⠁
⠀⠀⠈⠛⠿⣿⣷⣦⣤⣤⡀⡀⠈⠉⠉⢉⢀⣀⣶⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣤⣌⡪⣟⠿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡾⠀⠘⠃⠀⠀⢀⢀⠀⡴⣦⠀⡾⢻⢠⠏⡟⣸⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡾⠀⠀⠀⢀⠆⣼⣾⢁⡿⡟⢸⣡⣇⢸⡥⠏⠘⠞⠁⠁⠘⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠋⠀⠠⠴⢺⡇⠀⣠⠃⠼⠐⠇⢧⠘⠁⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢂⡛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡦⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⣛⣾⣲⣴⡦⣶⣴⠄⠀⠀⣀⣀⠴⠶⠟⠛⡂
⠀⠀⠀⠀⠀⠀⠀⣀⡨⢄⠙⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠛⠛⢉⣁⣀⠴⠾⠛⣋⣉⣀⣀⣠⣴⡥⠟⠁
⠀⠀⠀⢀⠄⡂⣤⡶⠅⠬⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡴⠞⠚⢋⠉⣠⣠⣴⡿⠿⠿⣿⣭⣛⠿⣶⣄
⠀⠀⠠⠀⠶⣟⡊⠀⠠⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⣿⣿⣿⣉⢁⣢⡽⠶⠚⠋⠉⠙⠻⣿⣲⣄⣴⣿⣟⠳⣶⣭⡛⢦⣌⣠⡄
⠀⠀⠀⠉⠁⠋⠨⠤⠀⠀⠀⠀⣀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡄⠙⠳⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠈⠉⠉

⠰⠂⠀⢀⡔⢮⣻⠭⠶⠛⣠⡼⡢⠀⠐⣶⠀⣰⠀⡤⠐⠀⡄⣶⠀⠀⠐⠀⠶⠤⠀⠤⠔⠀⠀⢰⠰⣾⣻
⣀⠀⠀⠠⠳⠦⠤⠤⠔⠚⠉⠀⢠⠇⠀⠁⠠⠘⠀⠀⣀⣔⣀⡟⠀⠀⢀⠔⠒⠒⠀⢤⡀⠀⠀⠈⠳⠤⠤
⢻⠰⠄⠀⠡⣀⡀⠀⠀⣀⠠⠀⠁⠀⠀⠀⠀⠴⠄⡴⠦⠛⠊⠀⠀⠐⠡⢲⠗⠀⠒⢽⣧⠲⡄⠀⢦⣀
⠈⡄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣠⣀⠀⠀⠀⠀⡄⠲⠿⠘⠛⢠⢞⢉⡄⠀⠀⠀⠀⠉
⠀⠀⠂⠀⠀⡄⢨⡀⠒⠆⠀⠀⠀⠀⠀⣼⣋⣻⠈⡨⣁⢶⠕⠀⠀⢻⡍⢖⣘⠓⢛⣤⠂⠠⠁⠀⢠⡄⢨
⠐⠁⠀⠀⣧⠙⠦⣀⠀⢀⠀⠁⠂⠀⢸⣻⢡⡰⣆⣼⠽⢀⠿⡇⠀⠀⠙⠲⢥⢄⠈⠤⠚⠁⠀⢰⡆⠻⢆
⢀⠀⠀⢘⣿⠈⣠⡀⣀⣔⣊⡞⡇⠀⠘⣯⡏⣻⠷⡷⣶⣿⢀⡇⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⢸⣿⢁⣄
⣤⠑⡄⠀⠻⣍⣻⣓⠃⢀⣽⣤⠗⠀⠀⠀⠙⠻⠾⠧⠴⠷⠞⠀⠀⠰⠁⣠⣖⣲⣖⡲⣌⠑⡀⠈⠿⣍⣛
⣾⡇⠃⠀⠀⠀⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⢸⣱⣿⡿⣿⣿⣾⠀⡇⠀⠀⠈⠉
⣸⠁⠂⠀⠀⠀⣤⣤⣶⣶⣤⣄⠀⠀⠀⣴⠃⠐⠒⠐⠂⠀⠀⠀⠀⡆⢸⡸⣿⠿⡿⢟⡽⠀⠀⠀⠀⢀⣤
⢀⠄⠀⠀⠠⣾⠿⣖⣯⠾⠋⣸⢇⠀⠰⣷⠀⢠⠒⣁⠢⠈⠂⣤⠀⠘⠠⢑⣬⣙⠛⢉⡠⠂⠀⢠⢰⡿⢾
⠀⠀⠀⢈⢧⣉⣉⣁⣠⠴⠚⠁⠉⡆⠀⠛⢀⠹⠀⠁⠀⣠⠁⡿⠀⠀⠀⣀⠄⠠⠄⣀⠀⠀⠀⠘⣦⣉⣉
⣿⢠⡀⠀⢄⠈⠉⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⣀⡀⣀⡎⣷⠝⠁⠀⠠⠊⣡⡆⠒⠤⣺⣇⣤⡀⠀⣄⠉⠁
⠸⠀⠑⠀⠈⠙⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⣀⢈⠁⠁⠀⠀⠀⠀⠀⣤⣾⢠⠶⠀⣭⠛⠀⠃⠀⠈⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠙⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠟⠁⢀⣶⠟⠋⢉⣩⣭⣭⣍⡉⠛⠿⣶⣄⡀⠈⠳⣖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢩⣿⠄⠀⠀⣾⠛⠀⠠⣿⣀⣦⣄⠈⣿⣦⠀⠹⢿⣿⡄⠀⠘⣷⠄⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⢸⣿⠀⠀⠘⢿⣗⣶⡄⢈⠛⠛⠋⢀⣴⣿⠀⢀⣼⣽⣇⠀⠌⡹⣧⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣇⡂⠘⣿⣧⣢⠀⠀⠙⠻⢿⣿⣬⣿⣾⣷⣿⠟⠀⢴⣷⣿⡇⠀⢆⣶⣿⡆⠀⡔⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢺⣿⣆⡀⠈⠻⣿⣶⣶⣄⠀⠀⢀⡉⢉⠋⢉⠀⣤⣠⣜⣿⠟⠀⠀⣞⣿⣿⡇⠀⠀⠐⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠻⣿⣦⣵⠄⠀⠉⠙⠻⠿⢿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠃⡀⠴⣿⣿⣿⣿⠇⠀⠠⡄⡀⢻⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢔⠄⠀⠙⣿⣿⣷⣾⣧⣀⡀⠀⠀⠀⠀⠈⠈⠉⢀⠀⠠⢠⠤⢫⣶⣿⣿⣿⠋⠀⠀⣙⢷⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⠀⢨⡑⠠⣀⠈⢻⢿⡿⣿⣿⣷⣷⣼⡦⣤⣼⣁⣤⣪⣾⣷⣿⣿⣿⡿⠋⠀⠐⠀⠀⣞⠌⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠁⠀⠀⠀⠈⠑⠂⠤⢀⠉⠙⠻⠛⠿⠿⢿⠿⠿⠿⠟⠛⠋⠁⠈⠀⠀⠀⢀⡀⡴⢿⠿⣁⠤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠤⠄⠀⠀⠀⠀⠀⠤⠄⡀⠡⠄⠀⢅⡬⢚⡅⠶⡠⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣔⡂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡁⡅⣊⣟⠿⢖⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⣗⣢⣀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣣⣠⣶⣻⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣥⣿⣣⢞⡂⠀⠀⢀⢀⣀⣀⡠⢀⠔⡘⣳⣟⣵⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠷⢶⣶⣾⣥⣬⣥⡾⠿⠟⠋⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⣾⣧⠀⠘⠢⠄⠀⠀⠐⠂⠀⠀⠀⢀⠏⠁⠀⡀
⠀⠀⠀⠀⠀⣀⡴⣶⢿⢻⡆⠈⠻⠈⠒⡤⠀⠀⠌⠠⡀⠀⠀⠹⠇⢠⠞⠀⢰
⠀⠀⠀⠀⡼⠁⠘⠁⠘⠇⢩⠇⢄⠀⠀⠒⠂⠤⠤⠠⠅⠄⠀⠐⠀⠀⡤⠔⠀⠀⢁⡖⢀
⠀⠀⠀⢸⣣⢶⡀⠀⠀⠀⠚⠅⠀⣉⠈⢆⠔⠂⠐⠒⣆⠄⠉⠂⠹⡜⠀⠀⠀⠀⠊⢀⡼
⠀⠀⠀⢹⡏⠈⢧⡀⢀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠒⠒⠂⠀⠈⠀⠉⠁⠀⠀⢁⡠⡄⡏⠀⢰
⠀⠀⠀⢿⣧⡀⢸⣷⠉⠙⠛⠛⠳⡄⠀⠀⣀⣄⡀⠀⠀⢀⣀⠀⠀⡾⠋⠙⠊⠀⠸⠇⠀⢸⣷⠄
⠀⠀⠀⠈⡿⣇⡀⠉⠀⠀⠀⠀⠀⣿⢠⠎⠀⠀⠙⠓⠈⠀⠀⢳⣀⠁⠀⠀⠀⠀⠀⣀⣴⡟⠁
⠀⠀⠀⠀⠀⠙⠳⢦⣠⡀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣄⣀⠀⠀⠀⢀⣀⣠⣀⣀⣤⣴⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣇⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠚⠉⢉⠁⠀⠀⠄⠈⠩⠟⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡅⠀⠀⣨⠶⠛⠛⠙⠻⢿⣦⡀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠙⣿⡿⠀⠀⢈⠿⣴⣤⣾⣿⡶⠀⢹⡇⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠠⠀⠂⠀⣰⡿⢁⠀⠃⠀⢀⡗⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⢠⠀⠀⠀⠀⠉⠛⠢⠤⠄⠶⠆⠓⠊⠁⠀⠀⠀⠀⢠⡼⠁⠈⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢿⣿⡗⡁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⡟⠀⡀⠀⠰⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠐⠀⠀⣌⠑⠻⠆⣲⡆⣀⠀⠀⠀⢀⠀⢀⠀⣠⡄⣼⠝⠉⠀⠀⠁⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⠘⠀⠈⠉⠛⠷⠾⠷⠾⠧⠿⠗⠛⠁⠀⠄⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠙⠀⠀⠀⠘⠀⠀⣄⠒⠀⢀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⢀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⢶⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣶⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣽⣇⣶⢴⡀⡄⢀⠀⠀⠀⠀⢀⢀⣠⣤⢦⡾⢧⣿⡿⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣾⣟⣱⣾⣾⣷⣢⢳⣾⣿⣷⣽⠿⠕⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⢀⣀⣀⣀⢀⣀⣀⣀⠀⠀⣀⣀⣀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⢶⢶⣶⣶⣶⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢹⣏⠲⣾⣹⣏⣏⣇⣧⣿⣧⣧⣧⣦⣼⣬⣾⣼⣼⣿⣴⣼⣏⣫⣇⣇⣼⠹⣿⠁
⠀⠀⠀⠀⠀⠀⣀⣛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡉⡛⢃
⠀⠀⢠⠀⡴⣶⡻⠿⢟⡿⢿⣶⢀⠀⠀⠀⠀⣶⠀⢢⡀⠉⠹⢂⠀⢠⠀⠀⠀⠀⢀⣴⣿⢩⡞⠜⠃⢴⣮⠗
⠀⠀⣿⠈⠷⣬⣉⣛⣯⣵⣿⠟⠘⡇⠀⢰⣇⠘⢷⣄⠁⠀⠀⢀⡀⠈⠰⠀⠀⠀⣾⢋⠛⡕⠀⡜⣰⢆⠘⣸⢿⣃
⠀⡀⠙⠷⣤⣀⡀⠀⠀⢀⣠⣤⡾⡃⠀⢰⣶⡔⠄⠈⠉⡁⠀⠩⠔⢠⣶⡆⠀⢸⣿⡿⠌⠴⣷⢸⣥⠾⠀⣼⡈⢽
⠀⢷⡀⠁⠀⠉⠉⠉⠉⠉⠉⠀⠈⣡⠄⠸⣿⣇⣠⣾⡆⢰⡞⠒⢶⡟⠀⣇⠀⢸⡌⡇⣸⢷⡞⣮⡅⣶⡾⣷⠑⣼⡇
⠀⠈⠛⠦⣀⡀⠀⠀⠀⠀⠀⡀⠴⠋⠀⠀⠙⢦⣤⣹⣍⣉⢀⣠⣾⣿⡶⠋⠀⠀⠹⢧⣿⣀⣟⡁⣽⣅⢉⣿⣤⠿⠁
⠀⠀⠀⠀⠀⣈⣉⣉⡉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠙⠛⠛⣛⡉⠁⠀⠀⠀⠀⠀⠀⠉⠙⣛⣛⣛⠛⠋⠁
⠀⠀⢀⡴⠋⢁⡠⢤⠀⠀⣹⣷⠄⠀⠀⠀⣰⠞⠉⢀⣀⣠⣤⣀⣐⠉⠢⡀⠀⠀⢀⣴⠀⢀⣉⠭⣁⡀
⠀⠠⠋⢠⢚⣟⠊⠉⠈⢃⢼⣿⡘⠷⡄⢰⠃⠁⡴⢛⣥⣶⣶⣦⣝⢷⡀⢹⠀⢠⡿⡀⠀⠀⠀⢀⠀⠈⠠⡀
⠀⢀⠀⣶⡜⡇⠼⣻⠇⢨⠴⡟⢁⠀⠁⢸⠀⢸⢣⣿⣟⡝⣯⢳⢹⡎⡇⠈⠀⠸⣼⠁⠀⡰⠊⢉⡉⢳⠀⢙⠀⣴
⠀⢸⣇⢢⢠⡁⢮⣢⢠⡟⠜⡡⠛⢀⠇⠘⠀⢸⡘⣿⢧⣟⣒⣻⡿⢡⡇⠀⠀⠰⠿⢀⠀⣷⠀⠙⠁⠊⠀⡼⠈⣿
⠀⠀⢻⣆⠑⢵⡦⠉⠅⣤⠾⠒⣀⠎⠀⠈⢇⠌⢷⡙⠷⣯⣭⣥⠶⠋⠀⡜⠀⠀⠰⠈⠧⡈⠀⠀⣀⡤⢞⡡⣴⠏
⠀⠀⠀⠉⠛⢶⣠⣬⣁⣀⠤⠞⠁⠀⠀⠀⠈⠢⠄⣉⣒⡤⠤⠄⠠⠴⠊⠀⠀⠀⠀⠀⠠⠦⣄⣠⣶⡆⠻⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡔⢨⡥⣠⠀⡩⣄⣀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡊⠀⢾⣷⣄⣸⠀⠈⠉⠛⠛⠁⢈⣿⣿⠆⠀⠱⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⣶⣄⠀⠀⠀⠈⠉⠛⠛⠛⠓⠲⠓⠚⠛⠉⠁⠀⠀⠀⣸⣷⠈⢧⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣿⣀⠈⠙⠻⠿⠶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠟⠛⢁⣀⡿⠁⣸⠇⢂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠛⠿⠶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⠶⠟⢋⣁⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣉⣉⣉⣉⣩⣭⠭⠤⠶⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⠤⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠤⠀⢀⠀⠀⠠⠤⠤⠄⠐⠒⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⢋⠉⢉⡛⢯⠉⠳⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢰⠞⠁⠀⠰⣎⣀⣂⣀⡼⡃⣠⠀⠀⠙⡌⠒⠶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠶⠋⠁⢀⡏⠀⠀⠀⠈⠳⠛⠯⠕⠶⠋⠁⠘⠁⢀⡟⠠⠀⠀⠙⠢⡈⢉⠓⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⣱⠋⠀⠀⡀⠘⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢩⡇⠀⠀⢀⠄⠀⠘⡄⠀⢁⠀⠉⠲⡄
⠀⠀⠀⠀⠀⡠⠞⣱⡟⠁⢰⠿⡄⠀⠄⠉⢀⠀⠙⠻⢯⣝⣓⡒⣒⣒⣛⣉⣡⡤⠔⠋⠀⠀⠀⢀⡀⠀⠀⣧⠀⠀⠀⠀⠀⠘⣦⣀
⠀⠀⠀⢠⠎⠀⢰⠃⡇⠁⠈⢧⠳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⣠⠞⢻⠄⠀⠈⠀⠀⢀⢿⡎⠳⡀
⠀⠀⢠⡏⠀⠀⢸⠀⡇⠀⠀⠀⠙⢮⡳⢤⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠒⠀⢀⣀⣀⡤⠴⠚⢁⡤⠋⠀⠀⠀⠀⣠⠎⣸⠁⠀⡇
⠀⠀⣼⠀⠀⢐⠘⡄⠘⢦⡀⠀⠁⠀⠙⠳⢬⣝⣓⠖⠶⠦⡤⠤⠤⠶⠶⠒⠛⠋⣉⣉⣁⣠⡤⠶⠚⠁⠀⠀⠄⠀⢀⠔⢁⡴⠁⢀⠼⡇
⠀⠀⢿⣧⠀⠈⠱⡘⢦⡀⠙⠢⡀⠀⠂⠀⢠⠀⠉⠉⠛⠓⠚⠒⠒⠚⠒⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⣠⠴⣋⡴⠋⢀⡴⠋⠀⣷
⠀⠀⠈⡏⠳⣄⠀⠀⠀⠙⠲⢤⣌⠑⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⢀⣀⣠⠴⢚⣥⠖⠉⢀⡴⠋⠀⠀⠀⡏
⠀⠀⠀⢣⠀⠈⠓⠦⣀⠀⠀⠀⠀⠉⠙⠓⠲⠬⣍⣉⠋⠐⠒⠒⠒⠒⠒⠖⠒⠒⠒⠚⠛⠉⠉⠉⣁⡤⠞⠋⢀⣠⠖⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠈⠇⠂⠀⠀⠀⠉⠲⣦⣄⡀⠀⠀⠀⠀⠀⠈⠁⠘⠒⠚⠶⠴⠦⠴⠤⠤⠤⠶⠖⠒⠛⣉⣁⣤⠴⠚⠉⠀⠀⠀⠀⠀⠐⡠⠋
⠀⠀⠀⠀⠐⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠤⠤⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⢀⠠⠂⠀⠀⠊
⠀⠀⠀⠀⠀⠈⠓⢤⡈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⣁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣈⠉⠒⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⢤⣄⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁




⣿⠿⠿⠿⠿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢀⢀⢤⢤⣤⢤⢄⡀⠀⠀⠀⠀⠀⢀⡆⣾⢱⡛⣿⣿⢆⢲⡄⠀⠀⠀⠀⠀⠀⡠⠦⠤⠼⣲⣤⣄
⠀⠀⠀⣴⢧⡻⣮⣛⣋⡸⠃⡽⣶⣄⠀⠀⣴⣾⣷⣜⠿⣿⣒⣫⡼⢠⡿⣦⠀⢀⣤⠶⣌⣙⠒⢒⣛⣻⣥⣿⡀
⠀⠀⣰⢿⡷⣭⣐⣂⣐⣒⣪⠵⢃⣿⠀⢸⣍⠿⣟⡻⢝⡒⠨⠶⢒⣋⣥⢿⠃⣾⡿⠕⢦⣍⣛⢛⡛⣛⣩⢵⣿
⠀⠀⠹⣧⣟⡳⠦⠭⠭⠭⠤⢒⡿⠟⠀⠀⠙⠷⣬⣉⠓⠶⠾⢿⣿⣿⠿⠋⠀⠙⢷⣴⡅⢹⣷⣟⣄⣠⣤⣾⡿
⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣠⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⢀⠀⣇⢠⣀⡄
⠀⠀⠀⢀⣴⠏⢻⠆⢠⣾⣦⡄⠀⡀⡀⠀⢀⠇⠈⠀⣴⠰⡆⠽⠨⠊⠒⠈⠃
⠀⠀⢀⡾⠈⠠⣽⠶⠿⠋⠀⣸⠢⡀⠀⠠⠈⠒⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢶⣶⣦⣴⣤⣀⣀⡤⠤⢦⡀
⠀⢰⡏⠁⠴⣴⣿⣥⣤⠶⠾⢋⣼⡇⠀⠀⠀⠀⠀⢀⡔⡞⠂⠀⡀⠀⠀⠀⠀⠀⣀⣀⡨⠥⣖⣉⣭⠷⣶⡾⢯⡁
⠀⠻⣴⣿⠀⣤⣞⣙⣳⣷⣮⣤⠟⠀⠀⠀⠀⠀⣶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠚⠉⠉⠈⠙⠳⣾⣿⡝⠯⣷⡦
⠀⠀⠀⠉⠙⠛⠛⠛⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢛⣟⣻⠿⣿⢻⡛⣿⢻⡟⣿⢿⢹⡏⣽⢹⡍⣟⢹⠉⡏⢹⠉⣿⣿⢐⡃⢿⠟⡟⢿⠉⣿⢹⡿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣌⣹⣽⣧⣿⣼⠷⠿⠾⠷⠿⠾⠿⠿⠿⠛⠿⠛⠛⠻⠿⠿⠿⠿⠿⠾⠷⠾⠶⢷⣿⣼⣧⣼⣧⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡉⢙⣀
⠀⠀⠀⢀⡤⢔⡨⣴⡞⣻⢻⡿⢿⡲⡲⣦⡀⠀⠀⠀⠀⠀⠀⢠⡦⠀⢸⠀⠁⠺⠉⣷⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⣴⣯⠞⣱⡶⣰⢿⢁⢂⣜⣳⠆
⠀⠀⡰⣿⠂⣾⣇⠿⢷⣤⣭⣴⡿⢃⣿⣾⡏⢲⣄⠀⠀⢀⡄⠘⣷⣄⠈⠳⠄⠁⠈⠀⠞⠁⢠⠇⢀⠀⠀⠀⠀⢠⣿⢧⣳⠆⡏⠄⢰⠆⣈⡘⠻⡇⣤⣠⣄
⠀⢠⡇⣿⡀⠈⠛⠷⠶⢶⣶⣶⣶⠿⠟⠋⠁⢸⡇⡆⠀⠸⠷⡄⠈⠻⢷⣀⡀⠀⠀⢀⣠⡤⠀⠀⠋⠀⡀⠀⢀⣿⣃⣄⢉⡼⠁⠠⠟⣴⠟⣰⠀⠡⡏⣿⣼⡄
⠀⢸⠁⠙⠿⣦⣀⣀⡀⠀⠀⠀⠀⠀⣀⣤⣴⡿⢃⠂⠀⢰⣿⣎⢳⠄⠀⣀⣉⡉⠀⢀⣠⠴⠋⣴⣷⡆⠀⠀⢸⣿⣿⢏⡌⢰⣿⣶⢰⣴⡆⡿⠀⣠⢿⠈⢼⡇
⠀⢈⡇⢨⡓⠀⠉⠙⠛⠛⠒⠚⠛⠛⠛⠉⠁⠚⠇⠀⠀⢸⣿⣿⠀⢀⣴⣦⠀⢠⣴⡶⢤⣤⣴⠟⠈⣟⠀⠀⢸⡈⣿⡀⣰⣷⣬⡝⣘⣛⢡⣴⣤⣿⣜⢠⣈⣷
⠀⠀⢿⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠘⣿⡝⠶⠾⢿⡿⣦⡽⠏⠀⠀⣨⣿⣇⣠⣿⠂⠀⠘⣷⣿⡇⣿⠋⠿⣼⡿⢿⣸⠛⢧⢿⣿⠀⣿⣿
⠀⠀⠀⠉⠛⠦⣤⣀⣀⠀⢀⡀⠀⢀⣀⡠⠴⠋⠀⠀⠀⠀⠈⠛⢷⣶⣤⣷⣤⣄⣀⣠⣶⣿⣿⡿⠟⠁⠀⠀⠀⠈⠻⣷⣿⣄⣴⣻⣄⣼⣿⣄⣀⣼⣿⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⢉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⢀⣤⡾⠋⠉⠉⠉⠉⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠉⠉⠀⠀⠀⠈⠉⢉⡒⢤⡀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠙⠯⠽⠛⠁⢀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠟⠁⣀⣤⣞⣉⣛⣉⣭⡳⢾⣿⡏⢠⣀⠀⠀⢀⡾⢫⠀⢀⣠⣶⠶⠞⠛⠳⠶⣦⣌⠁⠙⣦⠀⠀⠀⣠⡾⠋⠀⠴⠖⠚⠛⠓⠲⢄
⠀⠀⡜⠁⢠⡞⢩⣯⠋⠀⡀⠀⠈⣆⢿⣿⣿⠸⠟⢧⠀⢸⠃⠁⢠⡾⢋⣴⢾⣿⣿⣿⣷⣮⠻⣧⠀⢸⡆⠀⢰⡿⢃⠄⠀⠀⠀⠀⢀⡀⠀⠀⠐⣄⠀⠀⠐
⠀⠰⠃⠀⣬⣤⣿⡟⢠⡿⢽⡦⠀⢹⢰⡏⡟⠀⠆⢸⠀⣻⠀⠀⣾⢠⣿⣿⢋⡽⢭⡙⣧⢻⣇⢻⡄⠀⡇⠀⣾⣠⡏⢀⠀⢀⡴⠋⠉⡉⠙⣦⠀⠘⡇⠀⣠⡆
⠀⠀⣿⡄⣏⠛⠳⡇⢈⢜⠉⠀⣠⡿⢠⠇⢀⡶⠀⣸⠀⣹⠀⠀⣿⢸⡿⣿⡸⣧⣜⣵⣿⣼⡇⢸⠇⠀⡇⠀⢧⣿⡄⠀⠀⣾⠀⠀⢾⠛⠀⡘⠀⠀⡧⢰⡟⡇
⠀⠀⢻⣿⠘⢇⠲⣄⠘⢧⣟⡲⠾⠘⣁⠴⢢⠁⢠⠇⠀⢸⡀⠀⣿⡈⢿⣝⢿⣾⣯⣶⡿⠟⣠⡿⠀⢀⡇⠀⠈⠻⠁⢦⠀⢻⡄⠀⠀⠉⠉⠀⠀⣸⠃⠀⣿⠇
⠀⠀⠈⢿⣷⡈⠓⢬⣷⠤⠤⠤⢤⣾⠟⠚⠁⣠⠋⠀⠀⠈⣧⠢⠘⢿⣌⠛⢷⣶⣦⣶⣶⡾⠛⢁⠀⡼⠁⠀⠀⠘⠄⡘⢧⡀⠉⠀⠀⣀⣠⣤⠞⣡⡤⣾⠏
⠀⠀⠀⠀⠉⠻⢷⡦⠭⣀⣘⠃⠁⠀⣀⣶⠟⠁⠀⠀⠀⠀⠈⠷⣄⡀⠙⠳⢤⣀⣀⣀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠁⢀⣬⡀⠀⠀⣠⣤⡄⢾⣧⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠓⠒⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠓⠚⠃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⠞⢋⣩⡴⠶⢖⠶⠶⣭⡙⠻⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⣡⣴⠖⢛⣩⣭⣍⣙⠓⢦⣌⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⣰⣿⣏⠀⢾⣿⡀⠺⣿⣥⣴⠿⠋⣀⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⠏⠀⢸⣿⡁⠐⣿⣅⡐⠛⢛⣀⣼⡿⠀⡀⠉⢻⣿⣿⣿
⠀⠀⠀⣿⡏⠻⣦⣄⡙⠛⠳⠶⠶⠶⠶⠟⢛⣡⡾⢻⣿⠀⠀⠀⢸⣿⣿⣿⠀⣶⣄⠙⠿⣶⣤⣍⣉⣉⣉⣉⣥⡴⠞⢁⡄⠈⣿⣿⣿
⠀⠀⠀⢻⣧⡀⠈⠙⠛⠿⠶⠶⠶⠶⠶⠿⠛⠋⠀⣼⡏⠀⠀⠀⢸⣿⣿⣿⣆⠘⣿⣷⣦⣤⣀⣉⣉⣉⣉⣉⣁⣤⣶⣿⠃⣸⣿⣿⣿
⠀⠀⠀⠀⠙⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡈⠛⠻⠟⣿⣿⣿⣿⣿⣿⣿⠿⠟⣁⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠷⠶⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣬⣉⣉⣉⣩⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠄⠀⠀⠀⠄⠀⠀⣄⡙⠳⣦⣄⠰⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠀⣴⠃⠀⣞⣀⣠⡾⠂⠀⣸⣿⡆⢸⣿⡆⠘⣿⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡎⢀⣿⡇⠀⢿⣷⣤⣤⣥⣤⣤⣶⣾⡿⠋⢀⠜⢃⠀⢀⡿⠁⢹⠘⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⠉⠑⢄⠀⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠁⠀⠋⣠⠞⠁⠀⡆⢠⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠘⠁⢃⠀⠠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⢀⠜⢠⡞⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠞⠋⠁⠀⠀⢀⡴⢋⡴⠏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣥⠾⠛⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠾⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠶⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠦⠤⠤⠤⠤⠤⠴⠶⠶⠾⠿⠿⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠒⠒⠒⡒⠒⠒⠢⢄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠊⠉⠁⠀⠀⠐⠠⠬⠭⠥⠄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠁⠀⠀⠀⠱⠤⣄⣤⣒⣒⣒⢦⣀⠀⣀⣀⣀⠤⠀⠀⠀⠀⠀⢀⠆⠀⠙⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠠⣄⡀⠑⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⡀⠀⢀⡤⠖⠊⠁⠀⠀⠀⢀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡀⠠⢄⣀⠀⠉⠙⠒⠲⠶⠤⠭⠭⠍⠛⠙⠀⠠⠈⠉⠍⠉⠉⠀⠀⠀⠀⠀⢀⣠⠤⠒⠁⠀⠠⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⠀⠀⠀⣈⡉⠓⠒⠦⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠤⠐⠒⠉⠉⠀⠀⠀⢀⠀⠀⠀⢀⡴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠑⣤⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢳⡄⠀⡜⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠲⠶⣾⣶⣄⡞⠁⠀⠀⠀⠻⡄⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢀⡤⠶⠋⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢠⠿⡟⠀⢠⠞⠓⠊⠁⠉⠘⠷⢤⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⡇⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡀⢀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠆⠐⠚⠓⠤⠤⠔⠛⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣉⠰⢶⡆⢹⣿⣿⡙⠿⣭⢭⣝⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢫⠏⣼⣏⡛⠛⠛⠡⢛⣿⣿⠇⠰⣿⡇⠉⢳⣄⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣽⠁⣾⡀⢿⣾⣥⣤⣤⣴⡿⠿⠋⢀⣦⣿⠃⠀⢨⣿⡇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣿⡄⠸⣷⣄⠉⠙⠛⠋⠉⢠⣠⣾⣿⠟⠁⠀⢰⣿⣿⠃⠀⣼⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠘⢷⣄⠉⠙⠛⠳⠿⠿⠟⠛⠉⠁⠀⠀⢀⣄⣿⡿⠇⠀⢀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠄⠀⠙⠿⣶⣤⣀⡀⣀⡀⣀⣠⣰⣴⣾⡿⠟⠃⠀⠀⢀⠼⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠙⠂⡄⠀⠉⠙⠛⠿⠿⠿⠟⠛⠉⠁⠀⠀⠄⡀⣀⢗⢶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣆⣀⠀⠀⡀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣖⡒⢦⣤⡤⣤⠤⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⢿⡿⠶⠾⠟⢴⣿⡷⠈⣿⠙⢦⣙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠃⣾⠸⣿⣇⣠⣤⡿⠟⠁⣸⣿⠁⢈⣿⡆⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⠹⣧⣌⣉⣉⣁⣤⣴⠾⠛⠁⢀⣿⡿⠁⢰⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠙⢷⣄⣉⠉⠉⠉⠁⠀⣀⣠⣴⡾⠋⠁⢀⡞⣼⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠒⠀⠈⠛⠛⠷⠿⠿⠿⠛⠋⠉⠀⠀⠈⢯⣴⠃⠀⢀⢤⡶⠉⣴⠋⡭⠯⢭⡑⢶⣄⠙⣖⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠞⠁⠀⣠⡆⢸⡇⠐⢷⣆⣙⣛⣠⡿⢠⣿⠄⢸⡆⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢤⣤⣤⣤⣤⣤⡴⠾⠛⠉⠀⠀⠀⢸⠉⣷⡈⠻⢷⣤⣈⣉⣛⣋⣡⣼⠟⢀⣾⣿⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢷⣧⣤⣈⠉⡉⠛⠛⠙⢉⣠⣽⡿⠋⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢒⣋⡤⠤⠤⠤⠄⣀⣐⠂⣀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠙⠛⠿⠿⠿⠶⠿⠟⠛⠉⠀⢀⣼⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡟⠁⣴⠋⣠⠶⢚⣛⣓⠒⢦⡉⠳⣄⠙⢦⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢾⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡟⣼⠀⢸⣷⠀⢯⣤⣈⡙⢻⣷⠀⢻⠀⠻⣷⡈⢷⡀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣄⡀⠀⠀⠀⠀⡀⢤⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣆⠘⣿⡄⠈⠉⠛⠻⠛⠁⣰⣿⠀⠀⣿⡇⢘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠛⠚⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠘⣿⡄⠘⠿⣶⣶⣤⣤⣴⣶⡿⠃⡐⢴⣿⠃⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⠘⢿⣦⣄⡀⢉⠉⠉⠉⣁⢀⣺⣿⡿⢉⡰⢥⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣞⣥⣴⠿⠄⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠉⠛⠿⠿⠷⠾⠿⠿⠛⡛⢩⠐⠻⣾⣿⠃⠀⠀⠀⣴⣤⡷⢛⣋⣉⣩⣭⠭⠵⠒⠒⠚⠋⣉⣉⣁⣈⣥⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣔⣿⡿⠃⠀⠀⠀⠀⣿⣭⢉⣉⣉⣀⣤⣶⣴⡶⠖⠛⠛⠛⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⣤⣿⣼⣦⣾⡾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣹⡟⠛⠉⢀⣰⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣀⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠫⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣻⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣿⣿⣯⣯⣭⣿⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⠉⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠈⠉⠛⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⠃⣠⣶⣿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⢉⣛⣿⡷⠀⠀⢀⣼⡿⠿⣷⣦⣀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠁⠈⢿⣷⣿⡏⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣾⠿⠿⠛⠋⠀⣠⣴⡿⠋⠀⢀⣾⡟⢿⣧⣀
⠀⠀⠀⣠⣾⣿⣿⡟⢻⣿⡀⠀⠀⠙⢿⣷⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⡿⠟⠋⠀⠀⣠⣾⠟⠀⠈⣿⣿⣷⡀
⠀⠀⣴⡿⠋⣾⡟⠀⠀⠻⣷⣤⡀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⣰⣿⠃⢻⣷⡀
⠀⣼⣿⡇⠀⣿⣇⠀⠀⠀⠈⠛⠿⢷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⡿⠟⠋⠁⠀⠀⣠⣶⡿⠃⢀⣼⣿⣇
⢸⣿⢿⣧⠀⠘⣿⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⣀⣤⣶⡿⠟⠁⠀⢴⡿⠟⢹⣿
⣿⡏⠈⢿⣧⡀⠈⠻⢿⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⠿⠟⠋⠁⠀⣠⣤⣄⡀⠀⠀⠸⣿
⣿⡇⠀⠀⠻⠿⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⣀⣄⣀⠀⠀⠀⢻⣿⠛⣿⣆⠀⠀⣿
⠹⣿⡄⠀⠀⢀⣤⣤⡀⢠⣶⣤⣤⡀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣤⣄⡀⠀⠀⠀⣿⡟⢻⣷⡀⠀⢸⣿⠀⠘⣿⡆⠀⣿
⠀⢻⣷⠀⢀⣿⡏⢻⣷⠀⠈⠙⠛⠁⠀⣼⡿⢿⣷⡀⠈⠿⢻⣿⡿⠋⠉⠉⢻⣷⠀⠀⠀⣿⡇⠀⢿⣧⠀⠘⣿⡇⠀⣿⡇⠀⣿
⠀⢸⣿⠀⣼⡿⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⠃⠀⣿⡇⠀⢠⣿⠏⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⠇⠀⢸⣿⠀⠀⣿⡇⠀⣿⡇⢠⣿
⠀⣿⡏⠀⣿⡇⠀⣼⡿⠀⢀⣾⣿⣷⣾⠟⠀⢀⣿⡇⠀⣾⡟⠀⠀⠀⠀⠀⠘⣿⡆⠀⣾⡟⠀⠀⢸⣿⠀⠀⣿⡇⠀⣿⣇⣸⣿
⢀⣿⡁⢸⣿⠁⠀⣿⡇⠀⢸⣿⠀⠙⠉⠀⠀⢿⣿⡇⠀⣿⡇⢠⣶⡄⠀⠀⠀⣿⡇⠀⣿⡅⠀⠀⣸⡿⠀⠀⣿⡇⠀⢸⣿⠟⠋
⠀⢿⣧⣼⣿⠀⠀⢻⣷⣤⣼⡿⠀⠀⣴⡄⠀⢸⣿⠁⢰⣿⡇⠀⠉⠀⠀⠀⠀⣿⣇⠀⣿⡿⠂⠀⣿⡇⠀⠀⣿⣇⣴⣿⠋
⠀⠈⠙⠋⠻⢿⣦⣄⡉⠉⠙⠟⠀⠀⠈⠁⠀⣼⡟⠀⢸⣿⠟⠀⠀⠠⣾⠆⠀⢻⣿⠀⣿⣷⠀⠀⢻⣷⠀⣰⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣦⣶⣄⣀⡀⠀⣿⡇⠀⢸⣿⠀⢀⣀⠀⠀⠀⠀⢺⣿⢀⣿⣧⣤⣴⣾⡿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣷⣤⣾⣿⣶⣾⣿⣷⣶⣾⡿⠿⢿⣿⠟⠛⠉⠉
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⢶⣶⣶⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡙⠶⣟⢻⣹⣙⣇⣇⣿⣧⣧⣴⣼⣼⣼⣼⣤⣧⣿⣇⣧⣹⣹⣹⣇⡇⣿⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢛⡛⢂
⠀⠀⢀⡄⣠⣤⡞⢽⣿⢳⡶⣲⣄⠀⠀⠀⠀⠀⣴⠀⢨⠀⠘⠉⠆⠀⠀⡄⠀⠀⠀⠀⢀⣴⡶⢊⡶⠱⠟⡀⣼⡳
⠀⢀⣼⠁⢿⣌⣛⡒⢒⣛⣴⣿⠿⢹⡂⠀⢠⡆⠹⣦⡀⠁⠀⠀⠀⠁⠠⠃⡄⠀⠀⢀⡾⠓⠿⡨⠀⣸⢠⡄⠙⢇⣦⠲
⠀⠈⠹⣦⣀⠈⠉⠉⠉⠉⠉⢁⣀⣼⠃⠀⢨⣭⡠⡀⠉⠒⠂⠀⠐⣉⠄⣠⣤⠀⠀⢸⣷⡿⡘⣡⣦⢁⣫⢸⠇⣈⡈⢛⡇
⠀⢠⠀⠂⠉⠛⠓⠒⠖⠒⠚⠛⠉⠐⠃⠀⢸⣿⡇⢀⣤⣄⢁⣤⠤⢤⣤⠏⢹⠀⠀⣾⢹⡇⣰⣮⡝⣘⡛⣤⣤⣿⡃⣌⣇
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⢳⣝⠛⠻⡛⠞⠃⠀⢠⣿⣤⣼⠃⠀⠘⢾⣇⡏⠙⣷⠋⢣⡏⠓⢹⣇⣹⡟
⠀⠀⠀⠈⠉⠒⠒⠤⠦⠄⠀⠂⠈⠀⠀⠀⠀⠀⠉⠛⠿⠿⠶⠶⠶⠿⠟⠋⠀⠀⠀⠀⠀⠙⠻⠶⢷⣶⣿⡷⠶⠞⠋⠉
⠀⠀⠀⢀⣤⠖⠒⠒⠀⠁⠒⢤⣀⠀⠀⠀⠀⢀⣤⠔⠂⠀⠀⠀⠀⠐⡢⢄⡀⠀⠀⠀⠀⢀⠀⠐⠶⠶⠒
⠀⠀⡠⠋⢀⣴⣎⠭⠇⠤⠐⣿⣏⢠⣄⠀⢀⡞⠅⢀⣴⠶⣚⣛⣛⠲⣦⡀⠹⡄⠀⠀⣶⠋⠀⠒⠚⠉⠑⠂
⠀⡀⠀⠰⢁⣶⠀⣤⣄⠀⢎⣻⢿⠈⠉⡇⠸⠀⢀⡞⣵⣿⢿⡿⢿⡻⣎⣷⠀⢧⠀⣼⢡⠂⠀⠀⡠⠤⠤⣄⠀⢢⠀⠀⡀
⠀⢷⡄⡛⠿⠿⠘⠕⠋⢀⡞⣹⠈⣤⠀⡇⠸⠀⢸⢰⣿⣇⢯⣙⣺⣧⡿⢸⠀⠨⠀⢻⣏⠀⠀⡎⠀⢴⠆⢘⠀⢀⡄⡾⡇
⠀⠘⣿⡘⢐⠦⡘⠮⠆⠾⢁⡠⠂⠁⡰⠀⢠⠀⠸⣆⢿⣝⠶⠿⠷⠟⣡⡟⠀⡀⠀⠈⠃⢠⠀⢧⠀⠀⠀⠁⢀⡜⠀⣹⠇
⠀⠀⠙⢷⣌⡑⠿⠀⣐⠰⠞⠉⣠⠔⠁⠀⠀⢣⡀⠙⢦⡙⠛⠷⠾⠛⠉⠀⡰⠃⠀⠀⠀⠄⠑⠀⠀⠀⠐⠖⢫⠖⡺⠋
⠀⠀⠀⠀⠈⠓⠫⠶⠤⠤⠔⠚⠁⠀⠀⠀⠀⠀⠉⠒⠠⠭⠗⠒⠒⠀⠒⠉⠀⠀⠀⠀⠀⠀⠘⠓⠦⠴⠿⠷⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠛⡏⠁⠀⢨⡍⠙⡆⢻⡆⢳⡄⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣴⢰⣿⣿⣿⢿⣶⢰⣦⢰⣦⢠⣄
⠀⠀⠀⠀⠀⣴⠋⢰⠇⠀⣧⠀⠀⠘⠦⠞⣃⡾⠁⢀⡇⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣸⣿⡸⣿⣿⣷⣙⣫⣾⢋⣾⣿⢸⣿⣷⣄
⠀⠀⠀⠀⣼⠁⠀⢸⡄⠀⠙⣦⡀⠀⠀⠘⠉⢀⣠⠞⣱⠏⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣇⢿⣿⣷⡙⢿⣿⣿⣿⣿⣿⠟⣡⠞⣼⣿⣿⡆
⠀⠀⠀⢸⡇⠀⠀⠈⢳⣄⠀⠀⠉⠛⠒⠚⠛⠉⣡⠞⠁⠀⢠⡟⢻⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣎⠻⣿⣿⣷⣮⣭⣭⣥⣶⡿⣫⣾⣿⣿⢱⣅
⠀⠀⠀⢸⡇⠳⣄⠀⠀⠈⠛⠂⠤⢤⣤⡤⠶⠛⢁⡞⢳⡄⢸⡇⢸⡇⠀⠀⠀⠀⠀⣼⣏⠻⣿⣿⣷⣮⣿⣟⣛⣛⣛⣋⣥⣾⢩⣌⢿⣿⢸⣿
⠀⠀⠀⣾⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠳⠶⠃⠈⠁⣘⣡⣈⡃⠀⠀⠀⠀⠀⣿⣿⣷⣮⣛⠿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣼⣿⣿⡷⠿⠿
⠀⠀⢠⡏⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠈⠹⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣵⣾⣿⣿⣦
⠀⠀⢸⠃⠀⠀⠀⠀⠀⣼⠀⡴⣶⠀⡴⣤⣀⠀⠀⠉⠀⣀⣤⠖⠀⠀⢹⡀⠀⠀⣾⣿⣿⣿⣿⣿⡇⣿⢏⡍⣿⢛⡛⠿⣿⣿⣷⣿⡿⢟⣻⣿⣿⡇
⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⢸⡇⢺⣰⡇⠀⠉⠛⠓⠚⠛⠉⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⢸⡇⡿⢸⣿⣷⣦⣭⣭⣵⣶⣿⣿⣿⣿⡿
⠀⠀⢸⡄⠀⠀⠀⠀⠀⣇⣸⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢻⣿⣿⣿⣿⣿⠸⡇⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⠞⢋⣩⡴⠶⢖⠶⠶⣭⡙⠻⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⣡⣴⠖⢛⣩⣭⣍⣙⠓⢦⣌⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⣰⣿⣏⠀⢾⣿⡀⠺⣿⣥⣴⠿⠋⣀⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⠏⠀⢸⣿⡁⠐⣿⣅⡐⠛⢛⣀⣼⡿⠀⡀⠉⢻⣿⣿⣿
⠀⠀⠀⣿⡏⠻⣦⣄⡙⠛⠷⠶⠶⠶⠶⠟⢛⣡⡾⢻⣿⠀⠀⠀⢸⣿⣿⣿⠀⣶⣄⠙⠿⣶⣤⣍⣉⣉⣉⣉⣥⡴⠞⢁⡄⠈⣿⣿⣿
⠀⠀⠀⢻⣧⠀⠈⠙⠛⠿⠶⠶⠶⠶⠶⠿⠛⠋⠀⣼⡏⠀⠀⠀⢸⣿⣿⣿⣆⠸⣿⣷⣦⣤⣀⣉⣉⣉⣉⣉⣁⣤⣶⣿⠃⣸⣿⣿⣿
⠀⠀⠀⠀⠙⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣁⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠷⠶⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣤⣤⣬⣉⣉⣉⣩⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢋⣤⠤⠤⠴⠤⢤⣄⡉⠙⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⣏⠁⢠⡿⠀⢴⣉⣉⠙⣦⡈⠻⣷⡄⠙⣦⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢸⣇⠀⠙⢿⣶⣬⣉⣉⣠⣾⠇⢰⣿⡇⠀⢹⡇⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⢽⣧⠈⠻⣿⣤⣄⠈⠙⠛⠛⠛⢋⣀⣽⡿⠁⢨⣿⣷⠀⠀⠽⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠄⠈⢿⣧⣆⣀⠉⠛⠿⠿⠾⠷⢾⠿⠿⠟⢀⢘⣿⣿⡟⠀⢠⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠸⡁⠂⢄⠙⠿⣿⣷⣶⣤⣠⣀⣠⠄⡠⣠⣴⣵⣿⡿⠋⠀⠀⣾⠃⡼
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠂⠀⠉⠙⠻⠻⠿⠿⠿⠿⠛⠛⠉⠁⠀⡀⡠⣶⢏⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠠⢄⢦⣷⣁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⣤⣵⣿⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣯⣤⣀⣀⣠⠔⣠⣳⣭⡯⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠒⠊⠉⠉⠉⠉⠉⠉⠉⠉⠶⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢡⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆
⠀⢀⣠⣤⣤⣤⣶⣶⣤⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⡀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡸⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⡀⠀⠀⠀⠙⢄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣰⠃⠀⡇⠀⢀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⡇⠀⠀⠀⠀⠈⢢⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢣⠀⠈⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢃⠀⠀⠀⠀⠀⠀⠙⠦⣀
⠈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠄⠀⠀⡴⠋⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠣⠬⠃⠀⠀⠀⠀⠀⠀⣀⠼⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠒⡤⠤⠤⡤⠤⠤⠤⠤⡤⠀⠒⠘⢏⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⢃⡀⠀⠙⡄⠀⢀⠎⠀⠀⠀⠀⠘⡆⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠚⠢⠉⠒⠄⠞⠀⠘⠄⢠⠶⢄⠀⠀⠃⠀⠀⠀⠀⠙⠢⠤⠤⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣀⡤⠖⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⡠⠞⠤⠄⠀⠠⠤⠼⣄⣠⠔⠉

⠀⠀⠀⠀⠀⠀⠺⣳⣄⠁⣀⣄⣀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣓⣒⡁⠀⠀⠀⠀⠀⠀⠀⠺⣳⣌⠁⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠄
⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⢇⠀⠉⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⢃
⠈⡃⣰⡆⠀⠀⠀⢀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⢷⠃⠀⡰⠊⣩⡉⠆⠈⡆⣰⡄⠀⠀⠀⢀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⣷⠃
⢠⠃⢹⠁⠀⢀⡄⠰⣄⠉⠘⠁⠀⠸⠰⠆⠀⠀⠺⠃⡀⢿⠀⠉⠐⠁⢰⠃⣻⠁⠀⢀⡄⠱⣀⠁⠘⠀⠀⠘⠰⠂⠀⠀⠻⠁⡀
⢤⡲⠋⠀⠀⡌⠻⢦⣄⣀⡀⠀⠒⡠⢠⣶⡄⠀⠀⠀⠑⠄⠀⠀⢴⢚⡵⡲⠋⠀⠀⡌⠳⢦⣄⡀⡀⠀⠚⡠⢠⣶⡄⠀⠀⠀⠑
⠉⠀⠀⠀⠀⢩⣅⠤⠀⠀⠀⣠⡬⠤⣾⡀⢳⠀⠀⠀⠀⠛⠢⠶⠻⠃⠉⠀⠀⠀⠀⢩⣅⠤⠀⠀⠀⣠⡬⠤⣾⠀⣳
⠀⠀⠀⠀⠀⠘⣿⣇⣰⣿⡦⠿⠀⢀⣾⣿⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣰⣿⡦⠟⠀⢀⣿⣿⠏
⢀⠀⠀⠀⠀⠀⠈⠳⠦⣶⣷⠶⠶⠟⠋⠁⠀⠀⢠⡆⠨⡀⠐⢛⠆⡀⢀⠀⠀⠀⠀⠀⠙⠳⠦⣶⣷⠶⠶⠟⠋⠀⠀⠀⢠⡆⠸
⠘⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣴⡈⠳⣄⠉⠀⠀⠈⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣴⡈⠳⣄
⢀⣴⡄⠀⠀⠀⡀⠴⠿⠛⠊⠉⠙⠂⠀⠀⠀⣶⣇⠦⠈⠉⡀⠀⠈⠥⢢⣴⡄⠀⠀⠀⡀⠴⠿⠛⠊⠉⠙⠂⠀⠀⠀⣶⣇⠦⠈
⢺⠈⣇⠀⠀⠐⡰⠂⣠⡤⢄⠀⠈⢦⢸⡆⠀⢿⣿⣠⣾⣦⢰⡞⠒⢶⡟⠈⡇⠀⠀⠀⡰⢂⣠⡤⢄⠀⠈⢆⢼⡄⠀⢿⢿⣠⣾
⣾⠾⠁⠀⢸⠆⠀⠈⠀⠠⣄⢱⠀⠘⠄⠁⠀⠈⠳⢦⣬⣯⣉⣀⣠⣾⣿⠞⠁⠀⢸⠂⠀⠈⠀⣠⡄⢱⠀⢸⠀⠁⠀⠈⠳⢦⣬
⠀⠀⠀⠀⠘⣦⡄⣄⠀⠀⠀⠊⢀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⣦⡄⡄⠀⠂⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⢴⢮⡓⠒⠒⣂⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠶⠶⠂⠀⠀⠀⠀⠀⠀⠉⢴⢮⡓⠒⠒⣂⠉⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠉⠀⠀⠀⠀⠀⢰⡏⠀⠚⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠉⠀⠀⠀⠀⠀⣰⠋
⠘⠆⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣯⠎⠀⢀⠔⢒⠒⡄⠘⠆⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣯⠎
⢀⠇⢻⠃⠀⠀⡀⢨⡀⠊⠹⠂⠀⠸⢠⠄⠀⠀⢾⠂⠀⣿⠀⠛⠡⠂⢀⠇⢿⠃⠀⢀⡀⢪⡀⠋⠹⠀⠀⠸⢠⠄⠀⠀⢿⠂
⣨⢤⠞⠀⠀⡘⢷⣄⡉⠀⠀⠀⠴⢀⢀⣤⡀⠀⠀⢀⠣⠈⠀⠀⢠⠴⣫⢤⠟⠀⠀⡘⢷⣄⡉⠀⠀⠀⠴⢀⢀⣤⡀⠀⠀⢀⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⠀⡠⠂⠀⡠⠀⠀⣁⡀⠀⢲⣦⡈⠹⣷⣄⠈⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⡏⠀⢸⣇⠀⠘⠧⠴⠞⠋⠀⣀⣼⣿⡇⠀⣿⠟⠀⢸⣿⠋⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢰⣿⣇⠀⠘⣿⣷⣶⣶⣶⣶⣶⣿⡿⠟⠉⡀⠜⢉⡄⠀⣸⠋⠀⠸⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⢟⠀⠈⠈⠉⠢⢀⠀⠉⠉⠛⠋⠉⠉⠁⠀⠀⠈⠀⠀⠈⣀⡴⠫⠀⢀⠇⢠⡟⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠈⢢⠀⠠⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⣠⠎⣠⡞⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠞⠋⠁⠀⠀⠀⢀⠔⣡⡾⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣥⠾⠛⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⡿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠶⠶⣤⣤⣤⡤⠤⠤⠤⠶⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣶⠿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡐⠰⣶⣦⠠⣤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡁⠀⠙⠛⠷⠶⠤⠤⠴⠟⠋⠀⢈⣤⢢⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢧⣌⣙⠛⠶⠶⠴⠤⠤⠤⠤⠴⠶⠚⣋⣡⠜⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⢒⣒⣒⣒⣛⣛⡯⠭⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡜⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠟⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠉⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢠⠌⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⣴⠃⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠃⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⡔⠀⠀⢠⡎⠀⠀⠀⣠⣂⠁⢀⡀⠴⠋⠀⠀⠀⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣠⠎⠀⠀⠀⡞⠀⠀⠀⠘⠏⣿⣿⡭⣿⣦⠀⢀⡠⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣴⠃⠀⠀⢠⠞⠀⠀⠀⠀⠀⢶⡈⠹⠤⢋⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⣸⠃⠀⠀⢀⡺⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠛⠉⠀⠀⠀⠀⡠⠠⡀⠀⠀⣀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠐⠁⠀⠀⠀⡵⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠄⡠⡠⠁⡠⠊⢁⠴⠋⠀⢙
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⡄⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⡇⠀⣠⠀⠀⡠⠂⠜⡰⡡⠊⣠⠞⠁⠀⡠⠒⣁⠤⠂⠐⡀
⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⡸⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⣰⠃⠀⠔⢀⢀⡼⠃⡠⠊⠀⠀⣠⠾⠀⡉⢀⣠⠴⠒⣄
⠀⠀⠀⠀⠜⣡⣤⡆⢀⡞⠁⠀⠀⠀⡼⠀⠀⢀⡠⠴⠒⠲⠦⣄⠀⢸⢰⣣⠟⠠⠂⡀⠁⣨⠔⠋⠀⢀⡠⠊⠁⣠⠴⢚⡩⠔⠚⠉⢁⠄
⠀⠀⠀⠀⢦⡃⢡⠿⣯⠶⣾⡀⡀⡜⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⠳⣼⣿⣿⣼⣃⢼⠿⠋⠁⠀⢀⠔⣫⡴⣒⡭⠖⠂⠁⣀⠤⠚⠉⠁
⠀⠀⠀⠀⠈⠫⠘⠙⡋⢀⡸⣡⠏⠀⠀⠀⠀⠳⠤⣤⡤⠤⠤⠴⠶⢿⣿⠛⣙⣷⣿⡀⠀⣀⣴⣾⠿⠛⠋⠁⣀⡤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⢀⣿⠊⠀⠈⢧⣹⣞⠋⠁⠀⢀⡠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⢀⠔⠉⢿⠀⠀⣠⢿⡅⢸⡧⠔⠊⡁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠂⢀⡠⠊⠀⠀⠀⢀⡴⢊⡠⠼⠟⠋⠁⠀⠀⢧⠀⢀⢣⡄⡆⠀⠄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠙⣿⣿⣇⣴⣯⡀⡄⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠐⣄⡈⣎⢠⡏⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⠛⣿⡛⠿⣿⣷⢠⣶⡿⢻⡣⠀⠀⠀⠀⠀⠀⣀⡠⠒⡀⠘⣳⣿⣿⣿⠋⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠺⣯⢹⣤⠿⢟⣿⠋⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠚⠟⡾⠟⣿⢿⡟⠻⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⡶⠾⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⡟⢼⡿⢭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠱⣼


⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡠⠔⠒⠋⠉⠉⠉⠉⠉⠙⠒⠢⢄⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢠⠋⠀⠀⠀⢀⠔⠒⠉⠙⠒⠤⡀⠀⠀⠉⢢⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢿⠀⠂⠀⠀⣇⠀⠀⢰⠀⠀⠀⢹⠀⠀⠀⠀⣇⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠄⠀⠈⠢⣀⠀⠀⠈⠑⠚⠁⠀⢀⡠⠎⠀⠀⠀⠀⡇⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠳⣄⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⣠⠞⠀⠀⠀⢀⡄⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠤⠒⠋⠀⠀⠀⣀⠴⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⢼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠤⠤⠤⠤⠖⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⣤⢀⣤⣀⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⣿⣷⣶⣿⠛⠉⠀⣰⣿⣿⣻⣿⣿⣿⣷⣿⣿⠉⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢺⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⣿⣿⣿⡿⢦⣤⠀⠀⠀⣿⣻⣿⣿⣿⡿⠿⣿⣿⣿⣿⡆⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣾⣿⣿⣿⣟⣻⣿⡇⠀⠀⠘⠟⣿⣿⣿⡀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⠉⠹⡇⠀⠀⠀⠀⠈⠙⠛⠛⠛⢉⢻⣯⣿⣷⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢸⣿⣏⠉⠉⠁⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⠒⠄⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠴⠒⠋⠁⢸⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⢀⡟⠉⡉⠉⢉⠉⠁⠀⠀⠙⢆⠀⣀⣀⣀⠀⡄⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⢸⣧⠀⢱⠆⠁⠀⣠⠄⠀⠀⠈⡎⢁⡤⣄⡑⣧⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⣀⢀⣦⣿⡟⠷⠿⠶⠴⠊⠁⠀⠀⠀⠀⡇⢻⣐⡦⢳⢸⣧⡀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⢿⣷⣦⣤⣤⣤⣾⣿⡿⠃⠀⠈⠉⢉⢥⣿⣧⠀⠀⠀⢀⣠⣤⠤⠀⠀⣼⣿⣤⣈⠴⢋⠎⠈⢿⣦⣄⣄⣀⣠⣼⡿
⠀⠀⠀⠀⠿⢿⠿⣿⣿⣿⣷⣖⣒⠒⢶⣶⣿⣾⣿⣿⣿⣶⣶⣿⣏⣀⣀⣀⣴⣦⣽⣿⣶⣾⣥⣤⣤⣤⣽⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣛⣟⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠈⠒⠖⠛⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣡⢖⢟⡭⢛⣩⠭⠭⠽⢒⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠉⠀⣰⢱⡏⡞⠀⡏⠀⠸⠛⠛⢦⠈⢳⣌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣼⡇⠀⠀⣿⢸⣇⠹⣄⠀⠀⠦⠤⠴⠋⡀⣠⡿⠀⡍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢿⣧⠀⠀⢹⣆⠹⣔⣌⠁⠂⠀⠀⠴⠿⠟⠋⠀⢀⡿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠘⣿⣦⠀⠀⢻⣷⠀⠙⠲⢦⣀⣀⣀⣀⣀⣀⣼⠚⢁⡺⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣦⠀⠈⠛⢿⣆⠀⠹⣿⣦⣄⡀⠀⠉⠉⠉⢉⠁⠀⡠⢞⡵⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠜⠂⢀⠀⠀⠉⠛⠦⣄⣉⠛⠻⠾⠶⠿⠶⠟⣚⡯⠶⢋⠴⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢛⢋⣋⡉⠁⠀⠛⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⢰⠛⠂⠂⡷⡄⣶⡷⡄⡇⠀⢠⡆⠿⡄⡼⠃⡞⠉⡆⡷⡀⡇⠀⠀⢸⠉⡆⡞⠉⡆⡇⠀⡇
⠀⠀⠀⠀⣄⠀⡎⠀⠀⠀⡇⠘⡇⡇⠘⡇⠀⠘⡇⡄⠈⢠⢰⡆⠀⡇⡇⠙⡇⠀⠀⡏⠀⠗⡆⠀⡇⡇⠀⡇⠀⣤
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⡇⠀⡇⡇⠀⡇⢠⠁⠃⡇⠀⢸⠸⡇⢸⠀⡇⠀⡇⠀⠀⣷⡞⠀⡇⢀⡇⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠳⠴⠀⠇⠇⠀⠒⠇⠀⠃⠈⠀⠀⠇⠀⠸⠀⠃⠼⠀⠇⠀⠇⠀⠀⠇⠙⠄⠃⠰⠃⠦⠄⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠛⠉⠉⠉⠉⠙⠛⠲⠦⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠶⠶⠶⠚⠛⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⣀⣠⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢸⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠉⠁⠀⠀⠀⢠⣀⣠⠤⠤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠉⠛⠓⠶⠦⢤⣤⡤⠤⠶⠞⠋⠁
⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠁
⠀⠀⠀⠈⠳⣦⣄⣀⣀⣠⣤⡴⠶⠛⠉⠀⠀⠀⠀⠈⠙⠲⠶⠤⣤⣤⣤⣤⡤⠤⠤⠶⠶⠖⠚⠛⠙⣯⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣰⠋⢠⡄⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠿⠃⢠⣀⣻⠀⠀⡟⠀⣀⡀⠀⠀⠀⠀⠈⣧⠐⡄⠀⣿
⠀⠀⠀⠀⠀⠀⣾⠉⠭⠭⠭⠭⢭⣭⣿⣗⣒⣒⣒⣲⣷⡶⢤⡀⠀⠉⠁⠀⠀⠉⠉⠉⠀⠀⢀⡴⠶⣆⣿⠴⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⢻⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣿⣇⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠉⠉⠉⠛⠛⠓⠲⠶⠶⠾⣦⣀⣴⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣴⣾⣧⠀⠀⠀⠀⠀⠀⢸⡜⡗⠒⠒⠲⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⣠⣞⡽⠁
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣒⣲⡶⠦⠤⠤⣤⣤⣄⣀⣀⣀⣀⣙⣼⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠒⠒⠒⠶⠭⠭⠽⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣤⡀⠀⠀⠀⠀⠀⣾⠁⠀⢶⠸⣇
⠀⠀⠀⠀⠀⠀⢠⡿⣁⠀⠀⠈⢻⣦⣀⠀⠀⠀⢹⡆⠀⢠⡄⣿⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠸⣇⠹⣦⡀⠀⠈⢁⡿⠷⣤⡀⢸⡇⠀⢸⡇⢹⡆⠀⠀⠀⣠⡞⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡻⠦⠀⠈⠀⠐⠟⣻⣾⡇⠀⠀⣿⢸⡇⠀⠀⠺⣯⡀⢀⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣜⠻⠂⠀⠐⠋⠘⣿⠀⠀⠙⠀⣿⠀⠀⠸⠌⢳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⣿⣀⡀⠀⠀⢸⡟⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣤⡀⠀⠀⠀⠉⠳⣿⡏⢁⡀⠀⠘⣧⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⠁⠀⠀⠀⠀⠀⢸⡟⠋⠉⠀⠀⣿⡀⠀⢀⣠⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⣿⡲⣄⠀⠀⠀⢸⣷⠞⠛⠀⠓⢹⡇⢀⣾⠁⠰⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣿⠋⠀⠀⠀⢸⣧⣠⡤⠀⠀⠸⣿⢾⣧⠲⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡳⡄⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠑⠃⠀⠀⠀⣿⢀⣤⠶⠶⢦⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢁⡴⠾⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠈⠳⠆⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠒⠒⠦⠤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢤⡤⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢈⠆
⠀⠀⣀⡀⠤⠔⠉⠀⠀⠀⠀⡀⠀⠀⣾⣷⠀⠀⢠⣀⠤⠼⠀⠀⠀⠀⣀⣀⠞
⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⡤⢞⠁⠙⡄
⢣⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⣳⠦⠤⠤⡤⠔⠋⠱⠒⠋⠉⠀⠀⠈⠢⡴⠃
⠈⠢⣄⣀⣀⣀⠤⠖⠉⠀⠀⡸⠁⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡄⢠⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⢸⠀⠀⠀⡀⠀⠀⡤⢤
⠀⠀⠀⠀⢀⣀⠀⣠⠤⡀⠸⡗⠐⢻⡏⢠⣊⡽⠀⢸⠔⠁
⠀⠀⢀⡔⠁⠉⣼⠇⠀⢹⠀⡇⠀⢸⡇⢺⡁⠀⣀⠘⠦⠴⠂⠀⠀⠀⠀⠀⣀⣤⣤⣤⣦⣤⣬⣥⣒⠤⡀
⠀⠀⣾⠀⠀⠀⣿⠀⠀⣸⢀⡇⠀⢸⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢌⣴⣟⣯⡿⣶⣯⠽⣛⣛⣿⣽⢿⣮⢖⠒⠒⣄
⠀⠀⣿⡀⢀⡀⠻⠤⠴⠁⠸⠁⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⢸⣿⢾⣟⣽⣯⣿⣿⣧⣿⣼⣿⣿⣞⡗⡸
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣷⣯⣷⣯⣿⣛⡳⠻⣿⣿⣿⡿⢫⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠒⠦⣄
⠀⠀⠀⠀⣠⣶⡞⡟⢻⡐⢯⣿⠙⡿⡲⣄⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈⢳⡀
⠀⠀⢀⣾⡇⢿⡄⠻⣤⣉⠓⠒⠚⢁⡷⢈⡆⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⣷
⠀⠀⡾⠘⣷⣌⠛⢶⣤⣉⣉⣛⣋⣩⠴⢋⡼⢄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠙⢮⣉⡛⠒⠒⠒⠚⣋⣩⠞⠀⠀⠀⠀⠀⢀⡿
⠀⠀⣇⠀⠈⠛⠷⣶⣤⣭⣭⣭⣭⡤⠖⠋⠀⠈⢣⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠹⣦⡀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⡀⠀⢀⣀⣠⣤⠶⠋⠀⢀⣀⣀⣀⡀⠀⠀⠉⠙⠛⠲⠶⠶⠶⠶⠶⠶⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⢀⡤⠒⢋⣉⠥⠤⠬⣉⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⢊⡕⢨⠦⠑⡄⠀⢻⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠿⣤⣭⣥⠴⠚⢁⣤⠿⢁⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠶⢤⣤⠤⠴⠖⣚⣉⣥⠶⠛⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡔⠒⠒⠋⠉⠉⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢦⣤⣤⣀⣠⣤⡴⠾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣲⠖⠋⠁⠀⠀⢀⡴⠾⣷⣄⠀⢀⣠⡖⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠃⠀⠀⠀⠀⠀⠘⢰⡷⢸⡏⣿⠉⠀⠙⣞⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⠀⠀⢀⣀⠚⠋⠀⢹⡀⠀⠀⡹⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠀⢸⣷⠀⠀⠘⠛⠀⢠⠴⠋⣡⣶⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠗⠶⠬⠭⠥⠤⠤⠴⠖⠛⠒⠚⠁⠀⠿⠛⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠘⣇⣀⡦⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠋⠛⠒⠦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⢸⡇⠀⠀⢘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠰⠚⠉⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⡤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⢦⣼⠁⠀⠀⠀⢀⠐⠘⡒⠀⠀⠀⠀⡀⡄⠀⠘⢷⠀⠀⠀⠀⣻⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠸⡆⠀⠀⠀⠠⠶⠀⠘⠁⠉⠀⠀⠁⣦⠀⠀⢸⡟⠲⠶⠞⠋⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠉⠄⠀⢾⣇⣀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠈⠙⠚⠂⠂⠀⣈⣀⡁⠀⠀⠀⠀⢾⠋⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣆⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣠⡴⠞⠛⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⣩⣿⠟⠁⠀⠀⠸⠃⠀⢀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠈⠷⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⢠⣾⡿⠃⠀⠀⠀⣀⡴⠖⣛⣩⣥⠤⠶⠶⠤⣤⣭⣙⡳⠶⣤⣄⡀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣴⢋⡾⠁⠀⠀⢀⣼⣫⡶⠛⠉⠀⠀⠀⠀⠰⠖⠀⠀⠈⠉⠛⠶⣬⡙⠳⣄⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⡼⠃⡾⠁⠀⠀⠀⣾⡿⠁⠀⠀⠀⢀⣠⣤⡤⠤⣤⣤⣄⣀⠀⠀⠀⠀⠙⢷⣌⠳⣄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⣼⠃⢸⠇⠀⣀⠀⣸⡿⠁⠀⠀⢀⣴⠋⣡⡴⠶⠶⠶⠶⣤⣍⡛⢶⣄⠘⠦⠀⠙⣦⠹⡆⠀⠀⣠⠀⠈⣷
⠀⠀⠀⠀⡟⠀⠀⠘⣦⢠⡏⠀⣿⠀⠞⠁⢰⣿⠁⠀⢀⡀⣸⠃⡾⠁⠀⠀⣀⠀⠀⠀⠈⠻⣦⠙⣆⠀⠀⠀⠘⣇⣿⠀⠀⠁⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠈⢸⡇⠀⣿⠀⠀⠀⢸⣿⡀⠀⠋⠁⢹⡄⢷⣄⣀⣠⣿⠀⠀⣠⠆⠀⠘⣧⢹⡄⠀⠀⠀⣿⢸⡆⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢸⡞⣧⠀⠀⠀⠀⠙⠶⠬⣭⠶⠋⠀⠀⠉⠀⠀⠀⣿⢸⡇⠀⠀⢀⡿⢸⡇⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⣧⠀⢹⡄⠀⠀⠈⢷⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⢀⣴⠃⣸⠃⠀⢀⡼⢣⡟⠀⠰⠃⠀⠀⢰⣿⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢹⡆⠀⢻⣄⠀⢺⡌⠻⢦⣌⡙⠲⠦⣤⣤⣤⣤⣤⣤⠴⠶⠛⣋⣠⡴⠋⠀⢠⡾⣡⠟⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠻⣄⠀⠙⠷⣌⡁⠀⠀⠈⠙⠓⠶⠶⠶⠦⠤⠤⠤⠤⠶⠛⠉⠁⠀⣠⡶⠋⣴⠋⠀⣤⠀⠀⠀⠀⢰⡏⡿
⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⣤⠖⠙⢷⣄⡀⠈⠙⠶⢤⣄⣀⡀⠀⠀⠀⠾⠀⠀⠀⠀⣀⣠⣤⠶⠛⣁⣴⠞⠁⠀⠀⠛⠀⠀⠀⢠⡟⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣿⠳⣄⠁⠀⠀⠀⠈⠙⠳⠶⣤⣄⣈⣉⣉⡛⠛⠛⠛⣛⣛⣛⣋⣩⣥⠴⠖⠛⠉⠀⣴⠀⠀⠀⠀⠀⠀⣰⠟⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⡾⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠈⠳⣤⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠈⠙⠶⣤⣀⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠶⠚⠋⠁⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠈⠉⠉⠛⠛⠛⠲⠶⠶⠖⠒⠛⠛⠛⠋⠉⠉⠁⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢛⢦⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠀⠱⡔⠙⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠢⠉⠀⠄⢣⠀⢣⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠢⢀⠈⢳⢸⢀⠂⣀⣀⠠⠤⠀⠀⠤⠰⠖⠢⠻⠙⠉⠋⠑⠈⠀⠀⠀⠘⡆
⠀⠀⠀⡠⠀⠲⡶⠤⠤⡴⠶⠶⠖⠶⠓⡤⠄⠐⠒⢚⡯⢮⠉⠁⠀⠀⠁⠒⣀⣀⠀⣀⣤⣤⣤⣤⡤⡄⠒⠒⠒⠂⡘⠳⡀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢣⡎⠑⠇⠀⠀⠀⠀⢀⣀⣠⣎⡀⠀⠀⢐⣩⡄⠀⠓⣒⣀⠀⠀⠀⣠⣄⠀⠀⠂⣁⠀⠀⠠⠀⠒⠒⠀⢹⢋⠙⠄⠀⠈⠁⠀⣀⠔⠁⠈
⠀⠀⠀⠈⠛⠾⠿⠭⠥⠭⣡⡭⠭⠀⠂⣀⣀⣀⣤⣤⠤⠶⠦⡏⣆⠈⠁⢲⠀⡈⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢖⠺⠤⣣⡀⠰⡀⠀⡐⣵⡗⢠⠁
⠀⠀⡠⠒⠦⠀⠒⢲⣶⠟⣿⣿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠃⠈⠳⢄⡀⢃⢡⠘⡀⠐⣩⡇⠀⠀⠀⠀⠀⢀⡑⠤⣀⠙⢤⡐⣤⣿⣿⡵⠑⢂⡠⠂
⠀⠀⢄⡇⠱⢵⠀⣸⠌⠘⢐⠊⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠂⠀⠀⠀⢉⣦⠀⠸⠁⠔⡱⠒⠀⠂⢩⡶⣯⣉⣉⣉⣉⣙⣓⣿⣷⣿⣿⣶⣿⣤⣀
⠀⠀⠰⣆⣔⡌⠀⢘⣖⠬⡊⢁⣿⣃⣠⣤⣠⣴⣤⡦⠤⠻⣯⡃⠶⠶⣄⡠⣈⣷⡂⣤⣍⡉⠑⢀⠀⠀⠙⠲⠴⠭⠯⠯⠽⠟⣻⡟⢎⠓⢯⠭⢛⣁⣙
⠀⣠⡄⠀⠀⠀⢀⡐⠉⠿⠿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⢳⡾⢋⠔⣱⣷⢳⢳⡈⢎⣀⡨⠇⠀⠀⠀⣀⠤⠔⠂⠉⠉⡽⠇⠘⣆⠀⢣
⡆⡮⡫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢤⠶⡚⠋⣿⠀⣡⢾⣯⡿⠀⡩⢷⠀⡄⡀⠀⠐⠀⠁⠀⢀⣖⣄⡤⠶⠺⡸⠀⡇⠉⠚
⠡⣟⢛⣢⣀⣀⣠⣠⣄⣤⣄⣀⣤⣤⣶⠾⠻⡙⠍⠉⠀⠁⠀⠀⠛⠋⠀⠈⣏⡇⢸⣃⠸⠣⡉⠀⠀⢀⣤⡴⠞⠛⠉⠁⠀⠀⠀⠘⣧⠃
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⡽⢁⡤⣌⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⡶⢻⣿⠏⠉⣁⣀⣥⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸⠀⠈⢳⡘⡆⠀⢀⣠⡤⠶⠚⢋⣩⡴⣞⣩⠿⠗⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣷⣄⠀⠻⠛⠛⣉⣄⣤⣶⣿⡿⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣶⣀⣰⡤⠽⠖⠋⠁
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⣛⠙⢻⢦⣤⣴⣶⣶⣶⠶⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣄⣈⠛⣛⣷⠀⣻⣿⣿⣾⡀⠙⢳⣾⠖⢶⣌⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣱⠋⣸⣿⡙⠻⠿⠿⠟⢃⡘⡟⣿⣿⣿⠇⠀⣾⣿⣇⠈⠟⢷⣦⡌⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣻⠋⢰⣯⠀⣿⣟⣿⠆⠂⠀⠀⡌⣡⣾⣿⣿⡿⠀⣠⣠⣿⣿⠀⠀⠸⣿⣷⡇⠈⣘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣲⡟⠀⢾⣿⡄⠻⣿⣿⣷⣶⣶⣾⣾⣿⠟⠿⠋⣀⣠⣾⣾⣿⠃⠀⠀⣔⣿⣿⣇⠀⠸⡎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢻⣿⡀⠐⣿⣷⣄⠈⠉⠉⠙⠛⠋⠀⠀⣀⣐⣤⣿⣿⡿⠋⠁⠀⠀⡺⣿⣿⣿⠇⠀⢀⢿⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠈⣿⣇⡀⠘⠿⠿⣿⣶⣦⣴⣤⣼⣷⣾⣿⠿⠛⠋⠉⠀⠀⠀⠀⢶⣿⣿⣿⠅⠀⠀⢙⡏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣆⠀⠈⠹⣿⣦⣀⡀⠀⠀⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣢⣴⣿⣾⡿⠏⠉⠀⠂⠀⣾⠃⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡱⣄⠀⠘⠛⠿⣷⣶⣦⣀⣀⠀⣀⣀⣀⣨⡤⣄⣶⣼⣿⣿⣿⠻⠋⠁⠀⠀⢠⢀⡸⡿⣢⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢀⠀⠪⡳⡄⠀⠀⠈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠀⢀⠀⡀⡄⢂⠵⣻⢼⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠐⡐⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⢈⡠⣒⣤⣞⣴⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣮⣈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠉⠈⠛⢉⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣅⣛⣙⡛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣦⣭⣶⣶⣦⣶⣶⣶⣦⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣂⣈⡁⠀⠀⣀⣄⡀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢛⣩⠤⠒⢐⠂⢈⠉⠙⠷⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠁⠀⠻⣅⢈⣆⣠⡇⢈⠀⠀⠆⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢒⣒⠲⢄⠀⠀⠀⠀⠀⠀⠀⣷⣧⣄⠑⠲⠶⠶⠨⠭⠥⠒⣡⣴⣦⡴⣶⣬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣎⢠⠌⣷⠀⢻⠲⡄⠀⠀⠀⠀⣿⢿⣍⡑⠀⢀⣠⣤⠀⠀⣉⣼⣿⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠿⢤⣈⣁⠴⠃⢀⡟⠀⣿⡀⠀⠀⠀⢿⠂⠈⢛⣶⣿⠿⢿⠷⠶⠛⠋⠁⣴⣶⣿⠏⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣠⣴⠃⠁⢰⣿⡇⠀⠀⠀⠈⠓⠾⣿⣿⣿⣶⣦⣤⣤⣤⣤⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⢩⣯⡿⠶⣤⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣯⣀⣀⣼⠿⠛⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⢠⡶⢲⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⢟⡥⢤⣤⡀⠈⠃⢀
⠀⠀⠀⠀⢀⡿⠀⡟⣸⠆⣴⡔⣷⢠⣶⢺⡆⢠⡞⣦⢀⣶⢺⣦⢺⡆⣠⠞⣧⢠⣦⢺⡆⠀⠀⠀⢠⣟⠙⣿⣧⣸⣴⣦⣿⣿⡆⠀⠈⣇
⠀⠀⠀⠀⢸⡇⠀⢀⡿⢠⡟⢸⠏⣼⠇⣾⢃⣿⢠⡟⣸⡇⣼⠃⡿⢠⡿⢤⡟⣼⠃⡾⢁⠀⠀⠀⢸⣿⡄⠘⠻⢿⣿⣿⡿⠟⠀⠀⣠⣿
⠀⠀⠀⠀⠈⠛⠒⠉⠛⠙⠃⠙⠊⠛⠀⠛⠋⠛⠉⣛⠙⢀⡛⠀⠛⠈⠛⠊⠀⠛⠈⠛⠁⠀⠀⠀⣨⣿⣿⣧⣤⣀⣀⣀⣀⣠⣴⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⢆⡟⡷⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢞⡟⣠⡏⣿⢠⣟⡞⣸⣣⠇⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡟⠈⠃⣿⢣⡿⢸⡏⠠⣿⢁⡔⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠋⠀⠈⠋⠁⠙⠋⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠠⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⢂⣀⢴⣶⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠁⣠⢞⡵⣢⠆⢉⡥⠶⣖⠒⠺⠩⣗⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠁⠀⣰⢡⣾⢰⡇⠠⠋⠀⠘⠛⠛⠻⢦⠀⠹⣦⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢡⣿⠀⠀⠀⣿⠸⣿⠈⢷⡀⠑⠀⢤⣤⣤⠴⠋⠀⠀⣽⠇⢸⡕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⣿⡆⠀⠀⢹⣆⠹⣇⢠⠙⠢⠤⢀⠀⠀⣴⣶⡿⠟⠁⠀⢸⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣷⣿⡀⠀⠈⢿⣷⡈⠓⢷⣀⣀⠀⠀⠀⠀⠀⠀⢀⠠⣤⡾⠃⣼⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡄⠀⠙⢿⣷⣤⡀⠈⢿⣧⣄⠀⠈⠙⠳⠶⢶⣤⣤⣴⠶⠚⠁⢀⣴⢎⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠟⠀⠀⠀⠉⠻⣷⣄⠀⠙⢿⣷⣶⣄⠀⡀⢠⣀⠀⣤⢀⣀⡤⢚⣡⠞⢨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠸⠈⠁⡄⠀⠀⠀⠉⠓⠦⢤⣈⡉⠙⠛⠛⠛⠛⠛⣛⣫⡭⠞⢋⣥⢸⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣋⣉⣉⡉⠀⠀⠈⠧⠀⠨⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⢭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠤⠄⠀⠀⠀⠀⠤⠤⠾⠛⠋⠉


⠀⠀⠀⠀⠀⠀⠀⢰⠏⠇⢸⠀⡷⡄⢸⣿⢦⠀⡇⠀⠀⡇⢸⢧⠀⢾⠀⡞⠉⠃⢸⢦⠀⡇⠀⠀⠀⡏⠙⡆⡾⠉⢳⢸⠀⠀⡇
⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠘⠀⡇⠘⢾⢹⠀⢻⡇⠀⠸⡇⢠⠈⠛⢰⢠⡆⠀⡄⢸⠀⢻⡇⠀⠀⢀⠇⠀⠇⡆⠀⣸⢸⠀⠀⡇⠀⢀
⠀⠀⠀⠀⠈⠋⠀⣿⠀⠀⢸⠀⡇⠀⢸⢸⠀⠀⡇⠀⠀⡇⢸⠀⠀⢸⢸⡇⠀⡇⢸⠀⠀⡇⠀⠀⢨⣀⠜⠨⡇⠀⡿⢸⠀⠀⡇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢯⠀⡀⢸⠀⡇⠀⢸⢸⠀⠀⡇⡜⠀⡇⢸⠀⠀⢸⠀⡇⠀⡇⢸⠀⠀⡇⠀⠀⢸⠛⣆⠀⡇⠀⡇⢨⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠁⠀⠈⠈⠀⠀⠁⠀⠀⠁⠈⠀⠀⠈⠀⠉⠈⠁⠈⠀⠀⠁⠀⠀⠈⠀⠈⠀⠉⠈⠁⠈⠈⠀⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠂⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠤⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⢉⣤⠶⠒⠛⢛⣛⠒⠒⠲⢦⣌⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⠋⠀⣶⠏⢀⣴⠟⠛⣉⣉⣙⡛⢳⣆⠈⢳⣄⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠣⣿⠀⢸⣿⠀⠸⣧⣄⣀⠙⠻⣿⣷⠀⢹⣇⠈⢿⣿⡆⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⣿⡀⠸⣿⡀⠀⠙⠛⠿⢿⡿⠿⠃⢁⣼⡟⠀⢀⣿⣧⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣿⣗⠀⠹⣿⣦⣤⣠⠀⠀⠀⣀⣀⣿⡿⠃⢠⢠⣿⡏⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠘⣿⣦⡀⠈⠙⠿⠿⣿⣿⣿⣿⠿⠛⢁⣴⣡⣿⣿⠃⡰⢨⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠐⠈⠻⣿⣦⣥⣂⠤⣀⠀⢀⣀⣠⣀⣼⣿⡿⠟⢀⣴⢓⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠙⢻⠿⠿⢿⢿⠿⠿⠿⠛⢛⣉⣤⠒⣩⣻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⣀⡍⢉⣸⣿⡿⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣤⣄⡤⠄⠀⣴⣂⣠⣀⣠⣺⣶⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠀⢀
⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠑
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⢸⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠃
⠀⢸⣷⡄⠀⠻⠓⠉⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠀⠀⠠⠂⢐⡀⢸⣿⣿⣿
⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⡀⠀⡠⠞⣠⣿⣿⣿⡏
⠀⠀⢻⡟⡇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠁⠐⠋⠀⠀⠐⣿⣿⣿⣿⠇
⠀⠀⢸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠞⠛⢴⣯⠀⠀⢀⣀⣸⣿⣿⣿⣀⣀⡠
⠀⠀⠀⣿⣿⣶⡀⠀⠀⠀⠀⠀⢀⢻⡿⠿⠄⢾⣿⡀⠐⢿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⢻⠻⡿⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⡄⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠛⠉⠛⠉⠁⠀⣸⣿⣿⡿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠤⠖⠚⠉⠉⠉⠀⠀⣀⣶⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠤⠤⠒⠒⠒⠋⠉⠉⠁⠀⡀⠀⣀⡀⠤⠤⠤⠀⣒⣋⣭⣭⣵⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠖⠊⠉⠉⠁⠀⠀⠀⡀⣀⣀⣀⢠⡄⠤⠤⠐⢒⣂⣊⣉⣩⣅⣶⠴⠶⠾⠿⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢗⢛⡛⠓⣢⣉⣉⣩⣥⣴⣦⠤⠤⠴⠞⠛⠚⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⡀⢀⣀⣠⣤⣤⣤⣤⣶⣲⣶⣖⠠
⠀⠀⠀⠀⠀⠀⠀⣀⣐⡀⣉⢡⣀⣠⣤⣤⣤⡈⣤⡭⠤⠤⡴⠶⠤⠴⠶⠀⠚⠋⠉⠉⠉⠀⠉⠉⠰⠳⢡⣄⢫⣷
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⢈⣠⡸⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠈⠾⣦⣄⣰⣀⣀⣀⣠⣄⡀⣠⣄⣀⣀⣀⣀⣀⣂⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⠿⠿⠿⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠸⠕⠖⠠⠄⠉⠥⠄⢀⣀⣔⣒⠂⠀⠤⠤⠄⠀⠀⠀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢇⣴⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠛⠛⠓⠒⠒⠶⠶⠦⠤⠚⠾⠽⠭⠤⠭⠿⢄⢀⠀⣲⣶⣄
⠀⠀⠀⠀⠀⠀⠘⠏⠄⣐⣂⣀⡀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠛⠿⠿⠿⠾⠿⠿⠧⠤⢤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣀⣲⣦⣤⣤⣤⣤⣴⣴⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢶⡲⣤⡤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢺⢽⣏⢉⣺⡿⢃⣿⠈⣷⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡘⢦⣍⣉⣥⠴⠟⠁⣼⡿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡙⠶⣤⣤⣤⣤⡶⠿⠋⢠⣼⡿⠀⢀⣠⢖⡤⣥⡄⢥⡒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⣠⢸⡇⠺⣄⣓⣨⡆⣿⠈⣯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠲⠖⠒⠋⠉⠀⠀⢸⠙⣦⡙⠳⠤⢭⣭⠶⠏⣼⡿⢀⣃
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⣀⠲⠀⠀⣀⠀⡀⠀⠀⠀⠀⢸⠀⠈⠙⠻⠶⢶⡶⠶⠟⠋⢁⣼⡙
⠀⠀⠀⠀⠀⢀⣾⠋⣼⢡⠖⢻⣽⡓⢮⠱⣌⠣⡀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠃
⠀⠀⠀⠀⠀⡜⢹⡀⢿⡈⠛⠶⠾⠃⣼⠇⢹⡇⢷⠀⠀⠀⠀⠈⠉⠛⠶⠦⠴⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠁⠘⣧⡈⠻⢶⣦⣴⠾⢋⣔⣿⠇⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⢧⡀⠈⠻⢶⣤⣤⣤⣶⠾⠟⢡⣮⡿⠀⠀⢀⣠⠤⠤⢤⣤⣴⡞⠷⠿⠡⠙⢛⣳
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⣤⣶⠟⠁⠀⠀⢺⣟⣉⣭⣭⣦⡶⠖⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⣠⣾⠉⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢶⠋⡁⠤⠤⢤⣀⠀⠉⠑⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡏⠁⠳⣄⠉⠙⠚⠉⣁⡼⠀⢄⡤⠕⢸⠉⢲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠙⣄⠙⠒⠑⠦⣭⠯⣍⣉⠥⠒⠮⢚⣀⠤⠞⠀⡎⠀⣻⢦
⠀⠀⠀⠀⠀⠀⠀⣾⠸⡜⣄⠀⣉⣉⡉⠉⠉⠉⠉⠉⠉⢉⣩⣥⣤⣴⠟⢉⣡⠔⠁⠀⢇
⠀⠀⠀⠀⠀⠀⠀⡏⡄⠘⠪⣍⣉⡉⠓⠒⠒⠉⠉⠑⠒⠉⣀⣠⠤⠖⠊⠉⠀⡔⠒⠒⣻
⠀⠀⠀⠀⠀⠀⠀⢹⠈⠉⠈⢢⡄⢉⣩⣛⠛⠛⠋⠉⣉⡉⠀⠀⠀⡺⠋⠙⠚⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠀⠀⠑⠂⠒⠉⠀⠈⠑⠊⠉⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠤⠤⠤⠤⠤⠖⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣉⠰⣶⡆⢹⣿⣿⡙⠻⣤⢭⣝⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢫⠏⣾⣏⠛⠛⠛⢡⢛⣿⣿⠇⠸⣿⡇⠉⢳⣤⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣽⠁⣾⡄⢿⣿⣧⣤⣤⣶⡿⠿⠋⣀⣯⣿⠃⠀⣸⣿⡇⠐⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢿⡄⠸⣷⣄⠉⠙⠛⢉⡉⣠⣠⣾⣿⠟⠁⠀⢸⣿⣿⠇⢀⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠘⢷⣤⠉⠙⠛⠻⠿⠿⠟⠛⠉⠁⠀⠀⢠⣄⣿⡿⠃⠀⢀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏⢀⠀⠙⠿⣶⣦⣀⡀⣀⣀⣀⣠⣰⣶⣾⡿⠟⠁⠀⢀⢀⡾⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠙⠢⡄⠀⠉⠙⠛⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⣀⢕⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢆⣵⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⠀⠀⢀⠀⠀⢀⡀⣀⣠⣤⡷⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄⠠⠔⠒⠒⠒⠒⠒⠒⠲⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡤⢄
⠀⢠⢀⣀⠀⠀⢀⣀⡀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⢈⠆⣰⡉⠙⠇⠀⠟⢯⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡖⠂⢄⡀
⠀⡉⠀⠠⡋⣀⠻⡂⠐⠃⠀⠀⠀⣰⠃⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠴⡋⠈⠖⠉⣕
⠀⢸⠉⠈⠉⢇⣠⠟⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⠀⠀⠰⡀⠀⠀⠀⠤⠀⣰⣁⡐⠷⠀⣠⣽⠉⠐⣠
⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠹⣄⠀⠀⠀⠀⠀⠢⠔⠦⡤⠀⠀⠀⠈⠛⠁⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢏⣀⢼⠅⠁⠘⠂⢻⡀
⠀⠀⠀⠉⠒⠒⠒⠒⠚⠋⠁⠀⠀⠀⠈⠙⠲⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠲⣄⠀⠀⠀⠀⠀⠀⠑⠄⠔⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠁⠀⠉⠉⠉⠉⠙⠛⠛⣻⠿⠛⠛⠢⢀⡀⠈⠑⠦⣄⣀⠀⠀⠀⠀⢀⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠚⠲⡄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠦⠤⠤⠤⠤⠤⠤⠤⠴⢤⣀⣀⡠⠾⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⡘⠀⠿⢵⣥⠄⠲⣦⣄⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡌⠁⠀⠙⠛⠷⠷⢦⣤⣤⣤⣤⠴⠿⠋⠀⠀⢑⣤⠐⡄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢢⣆⠈⠛⠶⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠾⠋⢀⡾⠀⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠶⠦⣤⣄⣀⣉⡉⣉⠉⣉⣉⢉⣉⣁⣀⣠⣤⠶⠞⣋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣉⣉⣉⣉⣭⡭⠭⠵⠔⠚⠋⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⣀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⣴⠁⢀⠃⠀⣀⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣠⡥⠤⠚⠈⠁⠀⢀⣠⠤⠒⠛⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠟⠛⠚⠧⢝⣦⡄⢀⣠⠤⠒⠋⠁⠀⠀⠀⠀⢀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠂⠉⠁⠀⠀⠀⠀⢀⣀⠤⠿⣍⠁⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⡀⡤⣔⠶⣆⠁⢀⠀⠊⠀⢀⠔⠉
⠀⠀⠀⠀⠀⢀⡴⠛⠻⠶⣦⡀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⡀⢄⣪⠗⡏⠙⢆⡠⠻⣇⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠀⢠⠀⢹⣷⣤⣤⣶⠋⠁⠀⠀⠀⢀⠤⢒⠭⠒⠁⠀⠀⣣⠔⢋⠀⠀⣈⠋
⠀⠀⠀⠀⣂⡺⡏⠀⠐⠋⠀⢸⠋⠀⠀⢠⠠⣀⣠⠔⣊⠕⠊⠁⠀⠀⢀⡴⠊⠑⠀⢈⠰⠊
⠀⠀⠀⠌⠁⠟⢸⣕⠠⢀⣰⡇⠀⢀⠈⠀⢈⣩⣖⠋⠀⠀⠀⠀⣠⠖⠉⠀⠀⢀⠼⢯⡀
⠀⠀⠠⠀⠄⠀⣼⣧⢔⡩⠒⣇⠀⠀⠁⡄⡠⢄⠈⠱⣄⣤⡴⠞⠁⠀⠀⢀⠔⠁
⠀⠀⠀⠓⣁⠾⣫⢶⠟⠦⢀⣼⢦⡀⠀⢧⣀⡰⠁⢰⡿⠋⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠉⠁⠘⢠⠏⢶⠀⠀⠈⢣⡈⣰⡶⠠⠖⠚⠻⡄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠓⠐⠊⠀⠀⡀⡿⡯⠴⠴⠌⠀⠀⣷⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠁⢸⠀⠚⠃⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⢤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⢀⠀⠠⠀⢀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⠀⡠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⠉⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠒⠑⢦⣀⣀⣠⠖⠉⠒⠒⠊⠀⠀⠀⣠⠔⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢃
⠀⠀⠀⠀⡰⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣀⠴⠤⠦⣀⣠⠴⠴⠦⡀
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠑⠄⣄⢀⣀⠄⠖⠐⠒⠂⠰⠊⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠁⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠆⠚⠉⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⢛⠀⣴⠀⠀⠀⡀⠀⠻⠀⢀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠀⠀⠀⠀⠀⠀⠚⠉⣅⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠑⠤⠄⠤⠴⠋⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠤⠠⠔⢲⠶⠒⠒⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠒⠒⠂⠀⠠⠤⠤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠤⠼⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄
⠀⠀⠀⠀⠀⠀⡜⠁⠛⠛⣁⣀⠤⠖⠒⢒⠐⠂⠀⣠⢴⡉⠉⠉⡉⠉⠉⠉⠉⠉⠀⠀⠐⠀⠀⠂⠒⠀⠒⠒⠒⠒⠒⠒⣄⢀⣀⣀⢧
⠀⠀⠀⠀⠀⠐⠀⣨⢀⡀⠀⠀⠀⢹⠀⡘⠀⠀⠀⢠⠀⠈⠋⠀⡩⠘⠛⠛⠯⠩⣉⠁⠉⠉⠉⠀⢈⠔⠒⠒⠒⠒⢲⠒⠁⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠃⣲⢀⠀⠉⠉⠙⠈⠸⠀⣇⡀⠀⠀⢸⠀⠀⢠⠈⢀⡀⠀⠀⠠⡠⠂⠱⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠕⢰
⠀⠀⠠⢤⡘⠤⢄⠉⠀⠀⠀⠰⠆⣇⠀⡇⠈⠄⠀⣼⠀⡎⠹⣀⣈⡁⣀⠤⠄⠣⠴⠒⢣⠤⢄⡁⠀⠀⠀⠀⠀⠀⣅⡇⣀⠒⠤⠀⠀⠀⡖
⠀⠰⠄⢴⣧⡀⣬⣁⣖⠒⠀⠀⣆⠋⢀⣒⠈⢀⢠⣼⠀⠜⠆⠈⠁⠈⢀⠀⠀⠀⠀⡄⠀⠀⠊⢌⠲⠒⠓⠒⠈⡅⠈⡇⠘⠄⠲⠀⠀⠀⢣
⠀⢀⠀⢸⠄⣀⠛⠉⠱⠖⠂⢤⣼⠀⢼⢠⣀⣀⣀⣸⠀⢆⡀⠀⢠⠀⠘⠀⠀⠂⠀⣀⡤⣠⠆⠀⠐⠃⠐⠂⠈⠀⠙⡇⠀⠀⠀⢀⢄⡀⢸
⠀⢨⢀⡯⠀⢨⡇⠊⠉⡇⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⣀⡀⠁⠀⡁⠘⠓⠙⠋⠉⠉⠉⠉⠉⠈⠉⠁⠐⠀⠶⠶⠚⠒⠃⠀⠀⠀⠀⠈⠀⢸
⠀⠠⣤⠏⠀⣲⠀⡄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠶⡼⠗⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈
⠀⢀⡿⠖⢀⣼⠲⠈⠉⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠐⠲⢄⠀⠃⠀⡃⣡⢰⠴⠻⠶⠻⢤⣷⠶⠛⠷⠟⣉⠸⠄⠀⠀⠤⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠑⠤⢀⣀⠀⠁⠂⠀⠀⠀⠀⠃⠀⠊⡠⠀⠀⣄⢢⠈⢂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡠⠀⡀⠀⠀⡀⠑⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⡀⠲⣀⠆⠈⠀⢜⠆⠈⡆⢇⡸⠄⠀⠀⠀⠠⠀⠀⠀⢠⢄⢀⡀⠀⢤⠀⡈⠐⠉⡠⡀⠑⡈⠆⢘⡀⠠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠰⢆⡈⠒⠀⠀⠚⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⢛⡀⠐⢄⣈⣁⣠⠃⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠄⠚⠁⠀⢀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⣤⡊
⠀⠀⠀⠀⠀⠀⠈⠠⡀⠄⠐⠟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠿⠆⠀⠀⠀⡠⢀⠀⠀⠃⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠐⢂⠘⠉⠉⠀⠀⠀⣔⠀⠋⠉⠁⠙⠲⠖⣄⡀
⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣦⠅⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠠⢁⡀⡁
⠀⠀⠈⡀⡄⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣐⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⡀⠀⡠⢀⣬

⠀⠀⠀⠀⠀⢀⡴⠒⠲⣤⠤⢤⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠠⠿⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⠶⠶⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠏⠙⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄
⠀⠀⢀⣀⣠⣤⠤⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠓⠦⢤⣤⣤⣤⠤⠤⠤⠤⣤⡀
⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢳⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⣒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢀⡼⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠈⠳⠦⣤⣄⣀⣠⣤⠤⠖⢊⡅⠀⠀⠀⠑⢦⣄⡀⠀⠀⠀⢀⡐⠈⠣⠠⠎⠑⢆⠀⠀⠀⣀⣠⠴⠋⠀⠀⠀⢀⠉⣷⠦⢤⣤⣀⣀⣀⣠⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠈⢧⡀⠀⠀⠀⠀⠀⠉⢉⡟⢻⡁⠀⠀⠄⠀⢀⠠⠊⣛⠻⡿⠷⢤⠀⠀⠀⠀⣠⠜⠁⢸⡄
⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣀⡙⠆⠀⠉⠓⠢⠤⣄⣀⡀⣼⢀⡀⠙⣆⠀⠀⣀⡀⡀⡞⠁⣠⣻⣰⣬⠧⠴⠒⠉⠁⠀⠀⠘⡇
⠀⠀⠀⠀⢀⡇⠀⢠⠞⠉⠉⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠃⠠⠄⠀⠠⠔⠛⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡄⠀⣼⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢧⠀⠹⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠄⠂⢄
⠀⠀⠀⠀⠀⠘⢧⡀⠙⢦⣀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡈⠓⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠢⢄⡀⠀⠀⠀⠀⠀⠁⠐⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠩⠓⢦⣌⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠉⠳⣄
⠀⠀⢀⡐⠀⢀⡞⠁⠀⠀⢣⠀⠛⠉⠺⣃⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠠⢀⠁⠐⢸⠀⠀⠀⠀⠀⡉⠀⠐⣔⠀⠀⠀⠙⡆⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⢀⣀⡤⠤⠒⠒⠒⠒⠲⣼
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠙⢃⣀⣇⠀⠀⠀⠎⡁⠀⣾⡏⠙⠒⠲⠶⠶⠶⠶⠶⠖⠒⠚⠉⢁⣠⠤⠒⠊⠉⠀⠀⠀⣀⣀⠤⢤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠑⢬⡂⠄⠀⠀⠀⠈⠙⠒⠚⠣⣄⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⢁⣀⣠⠤⠤⠒⠒⠉⠉⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⢀⣠⠭⠥⠖⠒⠒⠒⠒⠒⠒⢊⡩⠤⠒⠒⠉⠉⠀⠀⠀⠀⣀⣀⡤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⣞⢡⠀⠀⠀⠀⠀⠀⠀⢀⣴⡼⠭⠤⠤⠤⠤⠔⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠳⠤⠤⠤⠤⠔⣒⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠒⠒⠢⢤⡀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠠⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠈⢱⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠸⡄⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⠏⠘⢦⠀⠀⠘⢦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⢀⡟⠀⠀⢈⢇⡤⢤⡀⠈⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⠀⠀⠀⣀⡴⠋⠀⢧
⠀⠀⠀⠀⠀⢸⠁⠀⠀⡞⢸⠀⢠⠇⣠⠤⢤⣀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⣠⢤⡀⢠⡞⠁⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠋⢠⠏⢸⠁⠀⠀⠈⣧⠀⢀⣀⣀⠀⠀⠀⣠⠋⠀⠀⢹⡈⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⢠⡏⢰⡏⠀⠈⠉⢢⠀⣇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠒⠒⠒⠒⠒⠲⠖⠒⠒⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡷⢤⣀⣤⠞⠀⠀⡴⠋⠉⠙⢦⡀⠀⠀⣠⠴⠒⠲⣤⠀⠀⠀⠀⠀⢹⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡼⠀⠀⠀⠀⠀⠀⣸⢷⡀⠀⠀⣠⠇⠀⢰⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⣇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⠃⠀⠀⠀⠀⠀⢠⢏⡟⠈⠉⠉⠁⠀⠀⠀⠻⡶⣶⠚⠁⠀⠀⠀⠀⠀⠀⢹⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⣇⡀⠀⠀⠀⠀⢀⡟⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣆⠀⠀⠀⠀⠀⡴⠞⠛⠛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠯⣟⣲⠦⣤⡼⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢆⠀⠀⠀⠸⣇⠀⠀⢀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣦⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⣠⠴⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⡤⣄
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⣀⡴⠋⠀⠈⢙⡖⠋⠉⠁⠀⠀⠀⠀⠈⠉⢳⡋⠉⠀⠈⠳⡄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢈⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⢀⡾⠦⠤⠤⠴⠶⠒⠛⠛⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠉⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⠀⠉⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣄⣀⣀⣤⣤⠴⢾⠁⠀⠀⠘⠛⠀⠀⠀⢷⠀⡺⠁⠀⠀⠙⠋⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⣀⣀⣀⣀⣀⣀⣈⣒⣁⣀⣀⣀⣀⣀⣀⣀⡼⠛⠶⣤⣄⣀⣀⣀⣀⣀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠉⢹⡏⠀⢈⣻⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⡁⠀⣈⡟⠙⢦⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⢻⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⡴⠒⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠻⣄⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠈⠛⠤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡏⠉⠓⢦⣀⠠⣄⡒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠲⢤⣀⡘⣦⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠙⢧⠀⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢲⠀⠀⠀⠈⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡖⣸⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠙⢦⡑⠤⣀⠀⠀⠀⠀⠈⠙⠶⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠚⠋⠀⠀⠀⢀⣠⠴⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢮⡳⢤⡙⠓⠦⣍⣓⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⣋⣩⠴⠚⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠏⠁⠀⠀⠉⠉⠛⠒⠶⠦⠤⠤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠖⠚⠋⠉⠁⠀⠀⢀⡏⠻⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡶⢤⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠙⣌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⢙⡆⠀⠀⠀⠀⠀⠀⣸⢸⠇⠀⠈⢳⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⡇⠀⠀⠀⠀⠈⢧⣀⣀⡤⠞⠀⠀⠀⢀⡤⠤⠤⣿⣼⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⠀⠀⠀⠀⠀⠀⢻⡹⡄⠀⠀⠀⠀⣏⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠙⣆⠀⠀⠀⠀⢀⡤⠶⠾⢾⡆⠀⠀⠀⠀⠀⠀⢳⡜⣄⠀⠀⠀⠈⠳⠦⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⣠⠏⠀⠀⠀⠀⣾⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢹⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠈⠓⠲⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣄⠀⣜⣦⠀⢴⣤⡶⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⠿⠽⠆⢹⡿⣀⣱⠃⡀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⣦⠀⠛⠫⠓⠂⠸⠟⠹⠗⠋⠸⠃⠀⠀⠀⠀⠀⠴⣷⡖⢰⠆
⠀⠀⠀⠀⠀⠀⠀⢰⡟⣹⠟⠀⠀⠀⠀⠀⠠⢶⣦⡀⠀⠀⠀⠀⢿⢿⡶⠒⠉⢹⡷⠋⠀⠀⡶⣦
⠀⠀⠀⠀⣠⡎⠀⠘⣋⣁⣤⠄⠀⢔⡆⠀⠀⣠⠀⠻⠀⢀⣰⠆⠈⠦⣳⣤⣤⠞⠁⠀⠀⠀⠙⠃
⠀⠀⠀⠠⠀⢀⠀⠀⠧⠴⠀⠀⠀⣀⣤⡔⠈⠉⡠⡶⢠⡼⠁⠀⢰⠲⣄⢠⠆⢠⣤⠖⣲⣄⠺⠃⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⣶⡆⠀⠀⠐⢿⠿⠃⠘⠀⠉⠁⠀⠀⣄⡀⠀⠉⡭⣤⠀⣿⢲⣿⣿⣽⠆
⠀⠀⢀⣠⣤⣀⠀⠀⣠⠄⠒⠒⠢⡀⠠⠀⠀⠀⠀⠀⠀⠘⠧⠇⠄⢸⡴⠋⠀⠘⢮⡯⠿⠋⠀⢀⡀⠀⡄
⠀⠀⣿⣿⣾⣽⠄⣄⠁⠀⠀⠀⠀⠈⠀⢀⡀⠠⣤⠴⠃⣀⣀⡀⢀⠈⣤⠀⡶⣦⡀⢠⠀⢠⣖⠧⠕⢀⢤
⠀⠀⠹⣿⡯⠞⠀⠙⠷⣤⣄⣀⡄⠊⢀⠈⠁⣀⠠⢀⣸⢐⡤⢁⠎⠰⠂⠀⠈⠻⣿⠈⡄⠀⠉⠀⠀⠙⠊
⠀⠀⠀⢀⠀⠀⠰⠆⢰⡄⠈⠡⠀⢠⣽⣶⠐⠁⠀⣀⣄⡀⢀⠟⠀⠀⢀⡦⠄⢀⣤⣤⡄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⣤⣶⠦⠛⢻⡟⠃⠀⢶⣻⠿⠅⠄⠀⣀⠄⣀⡢⢄⠀⣿⣶⣻⠄
⠀⠀⠀⠀⠀⠐⠻⡻⠏⠉⠉⡃⠁⢧⡼⡗⠩⡄⠀⠈⠓⠂⣠⣤⠒⡄⣥⠿⣦⢃⢹⡮⠟⠀⠔⠀⡰
⠀⠀⠀⠀⠀⢠⡄⠀⢠⣄⠸⠕⠐⣀⡈⠀⢀⠀⠀⠀⡠⠚⠉⣿⠀⡀⠍⠉⠉⠁⠄
⠀⠀⠀⠀⠀⠈⣿⡆⠀⠈⢳⡀⠀⠈⠓⡈⠁⣤⡖⠁⠀⢀⣴⡏⢀⣀⢰⡷⠒⠂⠰⠄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠒⠀⠁⠀⠀⠉⠟⠐⠊⠙⠒⠛⠟⠋⠀⡑⠖⠀⠀⠁⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠊⠙⡶⠆⢀⡐⠑⠀⠀⠀⠸⣟⡆⢀⣡⡶⠃⢰⣶⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⡾⠓⣷⠸⢍⡆⠀⠀⠀⠀⠀⠀⠊⠁⠀⠰⠶⣭⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠟⠁⠀⠐⠁⢼⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⣀⣠⠴⠚⠛⠉⠙⠓⠶⢤⡤⠴⠞⢋⡵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡇⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠤⢤⢤⣿⣄⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⣤⣀⡀⢀⣠⠴⠋⠀⠀⠀⣀⡴⣏⣹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⡄⠈⠉⠉⠁⠀⠀⠀⣠⠾⣏⡿⠈⣁⣿
⠀⠀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣧⣧⡤⢶⣤⠶⠚⠛⠋⠙⠛⠓⠶⣤⣧⣿
⠀⣸⠋⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠛⠶⣤⡀
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⡄⠀⠈⠙⠶⣤⣀⣀⣀⡀
⠀⠈⠙⠶⠦⣤⣤⣤⡤⠶⠞⢻⡤⠤⢽⡋⠀⠀⣤⣀⣠⡄⠀⠀⣿⣿⠀⠀⢹⡀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣖⠒⠃⠀⠀⠸⣠⠏⠀⠀⠀⠨⣟⠒⢢⣼⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣟⠓⣶⠶⠤⢤⣤⣴⡞⢶⣤⣬⠽⠿⣧⡀⠙⢦⣄⡀⠀⠀⠀⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⢙⡏⠀⠀⠀⠀⠚⠀⠘⠟⣧⠀⡄⠈⢷⠀⠀⠈⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠋⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⣠⣤⣀⣀⣀⣀⣠⡴⠆⣹⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⠻⠤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡆⠀⠀⣴⠀⠀⢠⡾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⣿⠙⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⣰⠏⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⢻⠀⠀⠹⡌⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⠀⠀⠀⠈⣧⠀⠀⠘⢧⡀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡄⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⠷⣄⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⣷⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢷⡀⠈⢳⣄⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠻⣄⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠞⢷⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠉⠛⠲⠶⠤⣤⣤⣤⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣠⡶⠶⣄⠀⠙⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢀⡟⠀⠀⢹⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠛⠀⠀⠀⠁⠀⠀⢻⣀⢀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⣷⠀⠀⢸⠇⠈⣷⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⢤⣤⠤⠶⠚⠋⠁⠀⠀⠀⢹⠀⠀⢸⠀⠀⢸⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣼⠀⠀⠸⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠶⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠛⠒⠂⠚⢇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⠀⠂⠁⠠⠀⡀⠀⠀⠀⠀⠀⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠷⢀⡀⢀⠀⣀⠘⠃⠀⠀⠈⠀⠀⠀⠀⡠⠢⣀⣀⠐⠐⢀⠀⠁⢀⡄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠐⠀⠠⢈⡌⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡴⠧⠤⠏⠑⢧⠁⢔⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢰⠂⠂⠀⣸⣊⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀
⠀⠀⠀⠀⠀⢀⡔⠒⠲⡄⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⢠⡖⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀
⠀⠀⢀⠤⠴⠊⠉⠀⠀⠉⠐⠢⢄⠀⢄⡀⠀⠀⠀⠈⠀⠀⠀⠉⠓⠠⣀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠉⠁
⠀⠐⠁⠀⠀⣤⠀⠀⠀⠀⠲⠀⡀⠉⠀⠀⠈⢉⠀⠀⢀⠀⠀⠀⠀⠀⠈⠑⠂⠂⠀⠀⠀⡀⠀⠀⠀⢀⠀⠌
⠀⠀⢀⠆⡀⠀⠀⠈⠈⢁⣀⢴⠓⠤⣀⠀⠀⠀⡩⢘⠀⠀⡓⢤⠤⢞⠢⢄⡀⠐⠂⠂⠀⠀⠔⠀⠀⠁⠎⡀
⠀⠀⠊⢠⢼⠉⠉⠉⠁⠀⠳⢢⠇⠀⠀⠀⠀⠒⢀⠀⠓⠈⠄⣘⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠘⠂⠴⠤⠾⠴⠤⠦⠊⠀⠀⠀⠀⠀⠀⠉⠉⠀⠃⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠚⠛⠛⠒⠒⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⢠⡾⠛⣉⣭⣭⣍⡙⠳⣶⣄⠈⠳⣖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢱⣿⠀⢀⣿⣁⠀⢿⣴⣦⠀⢿⡆⠈⢻⣷⠀⠈⣷⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠸⣿⣄⡀⠙⠿⣷⣴⣠⣦⣴⣿⠇⢐⣿⣿⠀⡀⣿⡇⠀⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢻⣷⡀⠙⢻⣷⣶⣀⠈⠉⠙⠛⢋⣁⣄⣼⣿⠏⢀⣼⣿⣗⠀⠀⠜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣷⣷⣀⡈⠙⠛⠻⠿⠿⠿⢿⠿⠿⠟⢁⡔⣻⣿⣿⠇⠀⢀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡯⡉⠢⢀⠙⠻⣿⣿⣶⣦⣄⣠⡀⣠⠄⡀⢀⣴⣮⣾⣿⡿⠋⠀⠀⡺⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠀⠉⠂⠌⠉⠙⠛⠿⠿⠿⡿⡷⠿⠿⠟⠛⢉⠀⠀⠀⣠⢶⣟⡀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣡⣅⣇⣊⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⢁⣸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣴⢤⠤⠀⠀⠀⠀⠀⡀⡠⡸⢶⣶⣾⡷⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠶⠶⠾⣥⡿⠶⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠛⠛⠛⠓⠒⠦⢤⣀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⡠⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⠃⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠠⠖⠒⠲⣄⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⡆⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣆⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⠀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢧⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣰⣯
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡇⢀⣀⡀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⢀⣤⠞⠁⢸⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣰⠃⡏⠀⢙⡆⠀⠀⠀⠀⠉⠛⠒⠲⠶⠤⠤⠴⠶⠒⠚⠉⠁⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⣀⡇⠀⡼⢁⡞⠋⠉⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠛⣦⠐⣇⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠁⢸⡆⠀⠀⠀⠀⢹⠀⢀⣠⣤⣤⣄⡀⠀⠀⣼⠃⠀⠀⠀⢸⣄⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠻⣤⣼⠇⠀⠀⠀⢠⡟⠀⣾⠁⠀⠀⠀⠙⣆⠀⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⣿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡰⠲⢼⣿⢑⢹⣴⡴⢖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣭⣢⢹⣏⠼⢋⢈⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢖⠪⠽⠟⠯⠟⠨⠄⣚⠛⢿⣳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣴⢤⡈⠑⢂⡵⡄⠻⣿⠟⠏⠅⣴⢰⣨⡻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⢛⢷⣎⣠⡿⢒⡚⢛⡽⣻⡏⠀⣷⣄⢹⡒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡖⠖⠛⣛⢾⣝⠯⠫⣚⣷⣾⣿⣄⠛⠿⣼⣷⣦⠙⠙⠳⢷⣶⣬⣑⡲⣤⣄⣀
⠀⠀⠀⠀⠀⠠⠤⠀⣀⢤⣤⡤⠝⢶⣶⠾⡂⢀⡋⠡⢿⣶⣶⣶⣽⡷⠄⣀⠈⠙⠳⣦⣄⡀⠈⠙⠻⣿⣃⣶⣶⡱⡀
⠀⢀⣀⣚⣛⠃⢀⢎⣤⣤⡀⢀⣀⠞⠑⣡⣾⡱⢸⣷⠳⡝⣿⣟⣁⣴⣿⣿⡝⠢⣀⠀⠉⣺⢕⡦⣄⣌⡛⠟⠻⣧⡗⠒
⠀⠠⠤⠭⠤⠀⠸⣼⡇⠿⠇⣾⣿⣿⣿⣿⣧⢃⣾⠿⣷⣌⣻⣿⣯⣽⣿⣿⣿⣷⣦⠁⣠⣶⣦⡽⣷⡏⣴⣿⣿⡎⣯⣉⣉
⠀⠀⠀⠀⠀⠒⣒⣛⣛⣓⣛⣛⠛⠛⠛⠛⣛⣾⣛⣒⣂⣀⣈⣁⣒⣒⣒⣛⣛⣻⣿⣘⣿⣹⣿⣾⣿⣷⣌⣩⣿⠾⠷⠒
⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠉⠉⠉⠉⠉⠉⣉⣭⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠛⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣤⠄⠤⣀⣈⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⣀⠐⠄⣤⣴⣤⡿⠃⠀⠉⠉⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡀⠤⠤⠤⠄⠀⠐⠒⠒⠊⠉⠁⠀⠀⠀⢸⡷⣿⢿⣋⣁⣬⠭⠿⠓⢙⣿⡏⠁⠀⠀⠂⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣤⢐⠂⢀⠂⢠⠤⠒⠂⣉⡀⠀⠠⠞⠛⣅⢹⣎⣻⢤⣤⠶⠶⠐⠋⠀⠁⣀⣄⡤⠴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣛⣿⣿⣿⣨⣤⠤⠖⠂⠊⠉⠁⠀⠀⢀⣠⣤⣶⠿⠿⠛⢿⡟⣎⣤⣤⡶⠾⠒⠛⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠿⢿⣟⠛⠉⠉⠁⢀⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣅⢤⡀⢰⣶⣿⡧⡉⢉⣁⣤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠐⢰⣿⣟⣠⣔⣿⣾⣿⣿⣧⣷⣿⣶⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⡿⠴⠚⠉⣉⣰⣷⡿⠛⠉⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣅⣴⠾⠟⠋⠉⠉⠉⠉⠉⠁⣠⣰⣶⣮⠿⠟⣀⠠⣠⢊⣵⠴⢲⣲⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠿⣟⣯⢿⣿⣿⣿⣯⡀⠀⢀⣀⡠⣔⣤⣴⢾⣿⣭⣷⡶⠶⢦⣄⠙⡇⠻⣿⠋⣠⣷⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⠼⠟⠉⠁⠀⠘⣿⣿⣾⣿⠦⣶⣩⢁⣀⣚⠂⣘⠿⢿⣿⣿⣷⣍⣁⢂⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⢀⡩⡛⠵⣒⣿⣿⣾⣿⡿⢿⠘⣧⡌⠑⠪⡙⢿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢨⠙⠻⣿⣿⣿⣿⣿⣼⢈⣼⣈⣿⣿⣧⣄⡻⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢶⣶⣿⣿⣿⣿⣵⣿⣽⣿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡀⠀⠀⢸⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠛⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣦⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⢿⣿⣽⣿⣷⣿⣷⡄⠀⠀⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠙⣦⣀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠙⢣⡄⢄⣿⠍⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⢾⠃⠀⠀⣀⣴⢾⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢀⡤⠤⠴⠶⠚⠛⠉⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠚⠀⠐⣦⠀⠀⠀⠀⢸⣷⣤⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠉⠉⠀⠀⠀⠀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣠⣾⣟⣛⣋⣅⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣀⡀⡀⣀⢀⠀⣀⡀⣀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠾⠟⠟⠻⠿⠟⠿⠟⠛⠿⠿⠷⠀⠀⠀⠀⠀⠀⠶⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣄⡼⣥⣧⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣤⡤⠖⠋⠉⠁⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠈⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣸⠁⠂⠀⠀⠀⠀⢀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠆⠶⠚⠙⠦⣄⣀⡙⠂⠀⠈⠀⠀⣣⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣭⠀⠈⠉⡭⠿⣽⡏⠈⢧⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⠠⡚⢎⡇⠀⠀⠙⠒⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠟⠚⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢠⠊⠉⢳⡖⠲⡄
⠀⠀⠀⠀⠘⣄⠀⠉⠁⡰⠁
⠀⠀⠀⠀⠀⠈⠓⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡤⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀
⠀⡠⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢆⠀⠀⠀⠈⠉⠛⠛⠋⠉⠉⠉⠓⢦
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢻⡀⠀⠀⠉⠀⠀⠀⠀⠀⢒⠀⠀⠀⠀⠈⠁⠀⠀⡸⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠉⠒⠤⠤⠤⠤⠖⠚⢹⠀⠀⠀⠙⠢⢤⣀⣀⣀⠠⠂⠑⠀⠂⠐⣄⣀⣀⡠⠴⠊⠀⠀⠀⣀⢹⡓⠢⠤⠤⠤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⣠⠤⠒⠒⢦⡈⠳⢄⣀⠀⠀⠀⢀⡏⠘⢄⠀⠀⠀⠐⠈⡸⠉⢟⢉⢢⠀⣀⡤⠖⠁⠀⡇
⠀⠀⠀⠀⡜⠁⢀⠔⠒⡶⠀⠀⠀⠈⠉⠓⠒⠚⠴⠦⠼⠃⠐⠀⠐⠸⠧⠴⠛⠛⠋⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⡏⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢣⠀⢧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠈⠣⣀⠑⢦⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢈⡱⠦⣌⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠑⠦⡀
⠀⠀⠀⠀⠀⡴⠋⠀⢈⠀⠽⠇⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠈⢢
⠀⠀⠙⠀⢸⠀⠀⠀⠀⡃⠀⢠⡈⠁⠈⢲⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⣀⡀⠤⠤⠒⠂⢤⡄
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠙⢤⣸⣄⠀⢀⢈⠀⣸⡏⠑⠒⠒⠒⠒⠒⠒⠒⠒⢉⣁⠤⠒⠊⠉⠀⣀⣀⡠⠤⢴⡾
⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠈⠉⠉⠑⠄⠸⠃⢀⣀⠀⣀⢀⣀⠠⠔⣊⣁⠠⠤⠒⠒⠈⠉⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⢔⡠⠔⠂⠉⠁⠉⠉⠀⢉⢡⠴⠊⠉⠁⢀⣀⣀⠠⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡸⢄⣀⣀⣀⠤⣴⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠀⠀⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠦⡀⠀⠀⠀⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠱⠀⠀⠀⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣇⢠⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡀⢧⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⣿⣧⣶⡦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣺⡛⢷⢲⢲⡌⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣌⣒⣾⣝⣁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠲⡆
⠀⠀⠀⡀⠀⠦⠈⠇⠀⠀⠀⠸⡀⠀⠀⠠⠋⠴⠒⢀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⡶⠊⠁
⠀⠀⠀⠀⠀⢀⠀⠂⠀⠰⠀⠀⠁⡢⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣟⠿⢻⣏⣉⣉⣙⡛⠿⣿⣿⣿⠋⠹
⠀⠀⠀⠀⠀⠀⠀⢃⠀⣰⠀⠀⣰⣡⠾⠟⣳⣿⣿⣿⣿⣿⢟⢩⣭⣍⡈⠀⠘⣋⢹⣽⣿⣦⡈⢻⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠘⠀⠀⠀⠃⢸⠀⠁⠀⡜⠀⠀⠀⣰⣿⣿⣿⣿⣟⣫⣍⠉⠉⣿⠧⠀⠀⢸⡛⠿⢿⣿⡇⢸⠃⠀⠀⠂⡞⢠⠄⠀⠀⠈⠀⠀⣀⣁⣐⣉⡉⠁
⠀⠀⠀⠀⠐⠂⢈⠀⢳⠀⠀⡇⠀⠀⢀⣿⣿⣿⣿⣿⣷⣿⣿⣶⣴⣧⡃⢀⣠⢔⣴⣐⡿⣿⢁⡞⠀⢀⠊⠀⠶⠁⣀⢀⠉⠛⠆⠰⠁⠀⢈⠉⢁⣀
⠀⠀⠀⠀⠠⢀⠀⠁⠀⠱⠀⠸⡀⠀⣸⣿⣿⣿⣿⣿⠿⠛⠛⠛⢿⣿⣦⣿⠇⣊⢿⣿⡷⠂⣸⣀⠞⠁⢠⠀⠠⠖⢋⠁⠀⢀⡴⠀⠀⣈⠁⠜⠋
⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⡇⠀⠱⠀⣿⣿⣿⡿⠋⣀⣴⣾⣷⣦⠀⠹⣿⢋⡌⢠⠈⠈⠀⣰⡟⠉⠀⡌⠁⣀⠡⠞⣁⣤⡒⠉⠀⠀⠘⠁⣀⣀
⠀⠀⠀⠀⠀⢀⡀⢀⠴⠒⣣⣤⡄⢸⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠘⣀⠈⠁⠔⠋⠁⠀⠀⠉⠀⠀⠈⠀⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠣⣾⣿⣾⣿⣿⣿⣿⣷⠿⠿⣿⣿⣿⠇⣸⣿⣿⣿⡿⠀⠀⢸⣿⡇⠀⡘⠁⠀⠂⢀⡀⠀⢄⡀⠀⣀⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠁⠁⡄⠈⢱⢿⡟⢰⣿⣿⣿⡟⢱⠂⠀⢸⣿⠆⠠⠀⡀⠠⢤⡍⢅⣁⠀⠈⠢⣀⠉⠉⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠁⠁⡠⠆⡀⠀⠒⠀⢀⣿⣿⣿⠋⠀⠸⡄⠀⠸⡏⡀⠀⠀⠀⠀⠈⠛⠆⠙⠂⠤⠀⠈⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⢠⣼⣦⣴⣴⣾⠀⠀⠀⣼⣿⣟⣵⣶⣶⠶⢷⠀⠀⢃⠁⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣷⣿⣼⣦⣽⣿⣿⣿⡿⠠⠀⣸⣿⣿⣿⣯⣤⣤⠴⠞⢇⠀⠀⠑⠀⠤⢈⣤⣴⣤⣄⣴⣶⡀
⠀⠀⠀⠀⠀⠠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠁⠀⠉⠀⠁⠀⠀⠀⠀⠌⢣⣄⣀⡰⠄⣿⣿⣿⠿⣿⡟⠿⠃⠎⠼⡶⡆⡤
⠀⠀⠀⠀⠀⠘⢿⠿⠻⠿⠛⠋⠙⠹⠿⠿⣿⣿⣦⣤⠤⠶⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠁⠈⠁⠀⠀⠈⠀⠁

⠀⠀⠀⡀⠤⠄⣀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠐⠂⠑
⠀⠀⠈⠀⠤⠤⠤⠤⠤⣤⣀⣠⣄⣀⣈⣀⣀⡀⠀⢀⡀⠂⡀⠐⠀⠀⢀⣀⣀⡤⠄⠐⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⣏⣡⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⠀⠀⠉⠉⠉⠉⢉⡉⠠⠍⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠐⠂⣁⣠⣿⠻⢎⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠬⠍⠛⠛⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣈⣁⣄⣤⣴⡶⠛⠛⠛⠻⠛⢾⣦⠈⣭⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠄⠀⠐⠒⣂⣀⣁⡠⠔⠦⢴⣶⣶⣿⣿⣟⣉⠅⠀⠀⠀⠀⠀⢠⡾⠙⠼⠿⠀⠑⠁
⠀⠀⠀⠀⠀⣁⣀⣀⣁⣠⢤⠤⠤⠤⠤⠶⡶⠾⢞⣿⠩⣭⡉⢇⣀⡠⢛⣨⢥⡍⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠳⠭⠿⣆⠁⡬⠁⠀⢲⣍⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⢀⣷⡘⠊⠻⣶⠶⠿⠿⣶⣄⣨⡉⢐⡒⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠁⡷⠀⢀⣼⡆⠀⠀⠀⠀⠀⠉⠉⠉⠁⠃⠰⠶⠤⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⢩⡴⠶⠒⠛⢙⣛⠒⠒⠲⢦⣌⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⠋⠀⣶⠏⠀⣴⠟⠛⣉⣉⣙⡛⢳⣆⠈⢳⣄⡈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠣⣿⠀⢸⣿⠀⠸⣧⣄⣀⠙⠻⢿⣷⠀⢹⡇⠈⢿⣿⡆⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⡀⠸⣿⡀⠀⠙⠛⠿⢿⡿⠿⠃⢁⣼⡗⠀⢀⣿⣧⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣿⣖⠀⠹⣿⣤⣠⣀⠀⠀⠀⣀⣀⣿⡿⠃⢠⢠⣿⡏⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠘⣿⣦⡀⠈⠹⠿⠿⣿⣿⣿⡿⠿⠛⢁⡴⣡⣿⣿⠁⡰⢨⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠐⠈⠻⣿⣦⣥⣂⢠⣀⠀⢠⣀⣠⣀⣴⣿⡿⠟⢀⡴⠓⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠙⢻⠿⠿⢿⠿⠿⠿⠟⠛⢛⡉⢤⠒⠩⣳⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⢠⠀⠴⣾⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣤⣤⡤⠄⠀⣴⣂⣠⣄⣠⣠⣤⣾⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠿⠿⢿⡿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣬⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣬⣶⣿⣿⣻⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⢿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⡿⣽⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⡋⠅⢀⡈⠤⠌⢉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⡀⠁⠔⠁⠠⠀⢀⡀⠀⠀⡂⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⡀⠀⡀⠀⡀⢀⠀⠀⠂⠀⡀⠀⠠⠀⠀⠈⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣿⠋⡀⠑⡀⠑⢀⠈⠂⠨⠄⠑⠊⠀⠔⢁⠂⠀⢀⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣤⣶⡾⠿⠛⠛⠉⢉⠁⡌⠀⠘⠢⣈⠀⠀⠅⠀⠀⠀⠀⠄⠐⠈⢀⠀⠐⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠈⡉⠉⠛⠛⠿⢷⣶⣤⡀
⠀⠀⠀⠀⣴⡟⠋⠀⠀⠀⠠⠒⠉⠀⠀⠃⠀⠀⠀⠀⠈⠁⠀⠒⠂⠀⠒⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠉⠐⢄⠀⠀⠀⠙⢻⣦
⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠠⢀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⠈⠻⣷⣄⡐⠀⠄⢀⡁⠀⠀⠀⠠⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠄⠀⠀⠀⢈⡀⠠⠀⢂⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣄⣈⡉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⣉⣁⣤⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠾⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠄⠀⠁⠄⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠁⠄⠀⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠄
⠠⡀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠐⠄⠀⠀⡀⠀⠀⠁⠄⠠⡀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠐⠄
⠀⠑⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢘⠐⠀⠠⡀⠀⠑⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢘⠀⠀⠠
⠀⠀⠈⢂⠀⠀⠀⡁⠀⢠⠃⠀⠀⡀⠀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⡁⠀⢀⠃⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠙⠀⠀⠡⠀⠀⠀⢀⢂⠠⠀⠀⢈⠀⠀⠀⠀⠠⡀⠀⠁⠀⠙⠀⠀⠡⠀⠀⠁⢀⢢⠠⠀⠀⢈⠀⠀⠀⠀⠠⡀
⠀⠘⠀⠀⠀⢀⠀⠀⠀⢀⠌⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⢀⠎⠀⠀⠈⠀⠀⠀⠀⠠⡄
⠀⠂⠀⡄⠀⠀⡑⠀⢀⡎⠀⠀⠐⠀⡀⠀⠀⠂⠀⠤⠀⡀⠀⠀⠈⡄⠀⠀⠑⠀⢀⡎⠀⠈⠑⠀⠀⠀⠀⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢈⠐⠁⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠈
⠈⠂⠀⠀⠀⠀⢄⠀⠀⠤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠄⠀⠀⠀⠄⠀⠀⠐⢄⠀⠀⠠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠄
⠀⡀⠀⠀⠀⠀⠆⠀⠀⠠⠄⠀⠀⠀⠀⠀⠁⠀⠐⠄⠀⠈⠂⡀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠘
⠐⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠁⠄⠀⠀⠀⠐⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠄
⠠⡀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠐⠄⠀⠀⡈⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠀⠀⠠
⠀⠑⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢐⠀⠀⠠⡀⠀⠑⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢘⠀⠀⠠
⠀⠀⠈⢂⠀⠀⠀⡁⠀⢠⠃⠀⠀⡀⠀⠀⠀⠨⠈⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⡑⠀⢀⠃⠀⠀⡀⠀⠀⠈⠠⠈
⠀⠑⠀⠀⠡⠀⠀⠀⢀⢪⢠⠀⠀⢈⠀⠀⠀⠀⠠⡀⠀⠁⠀⠙⠀⠀⠡⠀⠀⠀⢀⢢⠠⠀⠀⢈⠀⠀⠀⠀⠠⡀
⠀⠘⠀⠀⠀⢀⠀⠀⠀⢀⠌⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⠠⡄
⠀⠂⠀⡀⠀⠀⡑⠀⢀⡎⠀⠀⠐⠀⡄⠀⠀⠂⠀⠤⠀⠀⠀⠀⠀⡆⠀⠀⡑⠀⢀⡎⠀⠀⠐⠀⠀⠀⠀⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠐
⠈⠀⠄⠀⠀⠰⢄⠀⠀⠤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⠀⠈⠂⠄⠀⠀⠐⢄⠀⠀⠠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠄
⠀⡀⠀⠀⠀⠀⠆⠀⠀⠠⠄⠀⠈⠀⠐⠀⠀⠀⠘⠄⠀⠈⡂⡀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠘⠄
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠿⠿⢿⡿⠿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢉⣠⡀⠀⠀⠀⠘⣧⠀⠀⣠⣬⣉⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⣿⣴⠟⠹⡷⢀⣠⣤⣤⣼⣷⣴⣿⣄⣉⠛⠒⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⣿⡀⠉⠁⠀⠀⡇⠺⣿⣄⡀⠀⠀⠀⠀⠉⠛⠻⢶⣼⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⢻⣷⡀⠀⠀⠀⣧⠀⠈⠙⠛⠻⠟⠛⠁⠀⠀⠀⠀⢻⣿⣿⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠙⠿⣦⣄⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⢻⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣿⡏⠀⠀⣀⡀⠀⠀⠈⠙⠻⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⡿⠋⠀⠀⢀⣼⣿⢿⣿⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⢠⣿⡇⢀⡾⠛⣿⡄⢠⣶⠶⣦⣤⡤⠏⠉⠉⠙⠛⠛⠛⠋⠉⠉⠀⢀⣀⣤⣴⡿⠟⠁⠘⣿⠀⠀⠉⠻⢷⣤⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣠⣼⣿⡇⣸⠃⠀⢸⡇⣿⠁⠀⠀⣠⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠋⠉⠁⠀⢠⣤⣄⣿⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⢀⣾⡟⠀⠀⠀⣰⡾⠋⠉⣿⣷⠏⠀⠀⢸⡇⣿⠀⠀⣰⡿⠋⣠⣤⣤⣀⠀⠀⠀⠀⠀⢀⣠⠴⢶⣶⡄⠀⣿⠁⠙⣿⠃⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⣾⡟⠀⠀⢀⣾⠏⠀⠀⠀⢻⣿⡀⠀⠀⠸⣷⣿⠀⠀⣿⠁⢸⣿⠃⠉⠻⢷⣦⣀⣠⡴⠋⠁⠀⠀⢹⡇⠀⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠙⠁⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠸⣷⣴⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⣿⣇⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⡀⠀⠸⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠸⣿⣆⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣷⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠈⠙⠓⠒⠦⠄⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣶⣶⣶⣶⣷⣾⣿⣿⠿⠿⠿⠟⠛⠛⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⣤⢠⠤⣤⠄⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠔⡈⠉⢭⠅⠀⠀⠉⠉⠙⠒⠒⠂⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠁⠀⢀⠀⠠⠀⣈⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⢀⠀⠤⠀⠀⠀⠉⠙⠓⠒⠒⠚⠒⠒⠒⠒⠈⠉⠀⠀⣀⡠⠔⠁⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⢀⠀⠈⠓⠲⠤⢤⣤⣀⣒⣒⠤⠤⠤⠀⠀⠖⠒⠒⠂⠀⠈⠁⠀⠀⠀⣀⡤⠂⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⠑⠒⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⠐⠚⠉⠀⠀⠀⠀⠀⠀⣀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠲⣀⠀⠀⠉⠓⠒⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⢷⡀⠠⠃⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⠶⠶⣶⣤⡼⠁⠀⠀⠈⢷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⡆⢀⣄⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⢀⡴⠚⠋⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⠃⠘⢻⠁⠀⡞⠉⠉⠀⠁⠙⠓⠤⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⢠⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠸⡆⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠦⠀⠀⢀⣤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠑⠂⠚⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⣻⣍⣉⣿⠖⠒⠒⠒⠊⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠻⠛⠋⠈⠉⠀⠀⣶⣄⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠁⠀⡄⢀⣀⠀⢂⢀⠀⣠⡇⣿⠍⠉⠁⠀⠀⠀⡀⠠⠒⠍⠁⠐⠂⠀⠀⠀⡀⠤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⣠⠴⠊⢙⡾⠻⣝⡄⠀⠠⢸⣻⡟⠀⠀⠀⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠁⢈⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⣻⡄⣀⣤⠾⠾⠃⠀⠀⠠⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⡄⠤⠀⠀⢰⣆⣾⡍⢉⠛⢛⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⠛⠻⠛⡲⣶⣦⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢸⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠁⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⢸⡿⢋⣉⠻⠉⠛⠛⠛⠛⠻⠿⢿⣿⣿⡇⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠝⠧⠸⠿⠇⠿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢼⡇⢿⣿⡗⠀⢠⠀⢀⣤⡲⠖⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⢐⣦⠀⢸⣿⡇⠀⠀⠀⠀⠘⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⣛⣋⣉⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢹⣿⡇⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡦⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣷⠀⢀⣠⡶⠶⣶⠖⠋⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠒⠀⠀⠉⢁⣾⢋⣻⠶⠾⠋⡄⢸⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⣜⠀⠀⠀⣸⠟⠛⡋⠀⢠⠀⡀⠴⣿⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⡠⠞⠁⠀⣄⣶⣶⣤⣅⠀⠔⢸⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢃⡀⢀⡼⠁⢹⡋⠹⢿⣄⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠑⠒⠋⠈⠁

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⠀⠸⠀⠋⡇⠘⢸⠀⠚⠀⠃⠋⠸⠐⠗⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠲⢤⡀⢠⡞⠁⠀⡴⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠚⢳⣦⣄⣹⣼⣇⣴⡾⠥⢤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⣉⣩⣿⣿⣷⣿⣿⣿⣿⣿⣥⣴⣞⣩⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠋⠀⣠⠖⠁⣠⠼⠋⡩⠟⠿⢿⣯⡙⢷⣼⣥⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣻⢵⡠⢔⡡⠀⡠⢊⣡⠴⠋⢁⠄⠉⣠⠆⠀⠠⠻⣿⣮⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⡯⠁⠀⠔⠉⠐⢉⣀⠤⠒⠉⡀⠀⠀⢀⡴⠂⠀⠀⠀⢀⠞⣿⡇⢻⡤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢛⣛⣓⢦⣀⠀⠀⣠⠔⣱⠟⠓⠲⢤⣄⠀⠀⠀⠀⠐⠀⢀⡔⠁⠀⢸⣷⠀⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⢲⡟⢉⠉⠁⠘⢷⠞⠁⠀⢻⣄⣀⠆⢀⠙⢷⡄⠀⡀⢈⣴⠏⠀⠀⠀⠸⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈⢿⣏⠀⠀⠀⣼⢃⡠⣪⣴⡌⠁⠰⡏⠀⠈⣷⢀⡴⠛⠋⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣛⠦⡝⠿⣿⣿⡵⣯⣴⣅⣀⠀⠀⠞⡙⢦⡾⢿⠏⠀⠀⠀⠀⠀⠀⢠⢞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠈⢙⢷⣖⣠⠄⠁⢘⣉⣉⣉⠛⢷⣥⡞⢠⡯⢶⣅⠀⠀⡀⠀⡠⠊⡴⠿⠞⠃
⠀⠀⠀⠀⠀⠀⠈⣿⠀⣾⢿⣆⠋⣁⡤⢠⣿⠋⠉⠹⢷⡀⢻⣆⡸⣄⠂⠘⣧⠊⠀⠊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢿⡀⢻⠀⠉⠈⢿⣀⣼⣿⡴⠀⢀⡼⢃⣼⢏⣴⣉⠓⠂⢹⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠓⢤⣤⡾⠋⠀⠙⠿⣶⣶⣶⡾⠋⢸⠀⢹⣆⠴⣿⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢼⡥⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣸⠀⠀⠈⣦⠊⠁⠢⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠚⠀⠀⠯⡀⢐⠀⡔⠁⠀⠀⠀⠀⠀⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑
⠀⠀⠀⠀⠀⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠀⠀⢀⠀⠀⠄⢦⡀
⠀⠀⠀⢀⡌⣁⣢⣠⠤⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠙⠠⢦
⠀⠀⢰⠛⠓⢯⢝⣫⢤⠜⢹⣀⣠⣤⣌⠤⠒⠒⠒⠁⠒⠒⠢⢬⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⣀⣀⣀⣀⣧⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠬⠤⠤⠤⠼⠶⠤⢄
⢀⡞⠉⠉⠉⠉⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠘⠦⣄⣀⣀⣠⠤⠖⠋⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠈⠙⠒⠶⠤⠤⢤⠴⠖⠋
⠀⠀⠀⡈⢀⣴⡖⢦⡀⠀⠀⣨⠵⠬⣽⠋⠟⠁⠀⠀⢀⠉⠉⢻⢉⠞⠀⠠⠄⢠⣀⠤⠂⠠⣜
⠀⠀⠀⠈⢃⠉⢨⠘⠇⠀⡎⠀⡀⢠⠃⠄⡀⠀⠀⠐⠀⠀⠐⠄⡟⢠⠒⡖⡲⠖⠚⢋⣠⠶⠔⠃
⠀⠀⠀⠀⠈⢦⢿⠏⠀⠀⣇⠀⠣⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⣄⡉⢉⠉⢉⣁⡠⠤⠐⢃
⠀⠀⠀⠀⢠⣿⠾⡀⠀⠀⠈⠑⠒⠚⢧⣀⡤⠄⣀⣀⣀⠤⣄⣨⠇⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀⠜
⠀⠀⠀⠀⠢⠍⠀⠈⠘⣆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⣀⠖⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢄⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡠⣀⡀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠒⠈⠑⠒⠒⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠂⠁⠀⠀⠀⠀⢀⣸⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠠⠤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠊⠁⠀⠈⠉⠉⣀⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⢀⣼⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢠⣄⣀⠀⠤⠤⠐⠒⠉⠉⠁⣀⣴⡾⠟⠋⡇⠀⠀⠀⠀⠀⠘⡛⢻⣿⣿⡿⣿⣿⢿⣿⡿⠛⠿⢋⠝
⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⠁⢀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠈⠐⠩⠿⣁⣉⣁⣀⣉⣁⠤⠔⠃⠀⢀⣀
⠀⠀⠀⠀⠸⣶⠶⠾⠛⠋⠉⢀⣠⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣴
⠀⠀⠀⠀⠀⠧⠤⠀⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⣴⡿⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⠈⠻⠃⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣿⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢻⡀⢈⡿
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠳⠶⠷⠿⣅⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠒⠀⠀⠀⠈⠉⠓⠢⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠁⠀⠀⠉⠉⠓⠦⡀
⠀⠀⠀⠀⢀⣠⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠉⢢⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠊⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⠀⠀⣶⠀⠀⠀⡣⠤⢀⡀⡀⠀⠀⠠⠤⠤⠤⠐⠒⢚⠆
⠀⠀⠈⣇⠀⠸⡿⠿⢧⣀⣀⠀⠀⠀⢀⣤⠔⠁⠀⠛⠒⠖⠃⠀⠀⠀⢣⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⡿
⠀⠀⠀⠘⠲⠒⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡞⠙⢷⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⢀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢸⣀⣴⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣿⣅⣀
⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢀⠔⠻⣏⠉⢻⣷
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⠄⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⣸⣷⣤⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠁⠈⢻⡛⠁⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣇⣠⣴⣿⡿⠆
⠀⠀⠀⠀⢰⡄⠀⠀⠈⠀⠁⠋⣀⣠⢤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠉⠉⠉⠁⣠⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣶⣶⣶⣶⣿⠟⡇
⠀⠀⠀⠀⠈⠲⠄⣀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⣶⣦⠀⠀⠀⠀⠁⠀⠀⠀⢠⡀⠈⠉⠉⠁⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢠⣤⣄⠀⠈⣿⡟⢀⣶⡷⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠈⠁⣾⠟⠁⠀⠀⠀⠉⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⡀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠙⠛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⡟⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⠉⠉⠉⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠻⢿⣿⣿⣿⣿⡿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡀⠀⠁⠀⠀⠀⠀⠀⣠⣴⠾⠃⠺⠆⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠇⠘⣇⠎⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠘⢠⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⢢⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⡆⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢹⣆⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢆⡀⠀⠀⠀⣠⠔⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡹⠁⢀⣴⡞⠉⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⢀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰⠋⠁⣀⣠⣤⣶⣶⣾⣭⣥⣤⣤⣤⣶⣶⣶⣂⣀⣀⠒
⠀⠀⠀⠀⢻⡯⠀⠀⠀⠀⠀⠀⠐⢠⣤⣼⠿⠿⠿⠛⠛⠉⠉⠉⣀⣀⣤⣤⣤⣶⣶⣤⣾⣿⣿⣿⣿⣧⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⠾⠋⠁⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠖⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣫⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⡉⠉⠉⠛⠳⢦⣀⠀⠀⠀⠀⠀⠈⢷⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠐⠛⠉⣻⠄⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⢿⠛⢦⣀
⠀⠀⠀⠀⢀⣤⠖⡿⠁⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠛⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠙⢷⡀
⠀⠀⢀⡴⠋⠀⢸⡇⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⣆
⠀⢀⡾⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠸⣆
⠀⣾⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⠶⠶⠶⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢹
⢰⡇⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈
⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⣼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠉⠁
⣿⣿⣿⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣶⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠘⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠙⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣻⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⠘⠿⠼⠿⠿⠀⠀⣹⡆⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⣿⠉⠛⠿⠤⣤⣤⣤⠤⠶⠞⠋⠀⢀⣾⣦
⠀⠀⠀⠀⠀⠀⢀⡔⠋⢰⣿⡇⠈⢻⣇⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡿⠋⠀⠈⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢺⣿⣤⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿⡿⢸⡄
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣾⠟⢁⣼⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠈⠙⠿⣿⣦⣤⣤⣴⣤⡴⡶⠾⠿⠟⠛⠋⠉⠉⢀⣴⢟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣶⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢸⠋⢺⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠈⡇⢰⡷⠆⠀⢠⣷⡀⠀⣤⣶⠦⠤⠞⠉⢧⠸⡄⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡇⠀⠀⡇⣿⠀⢸⠀⡼⠛⢧⢀⡟⠁⠀⠐⠀⠀⣸⣴⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⣲⡇⣿⣀⣘⣾⣇⣀⣸⣟⣁⠀⢀⣤⣾⣼⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠒⠛⠿⠿⠷⠗⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠎⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⠊⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⣃⠤⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠤⠚⠉⢀⠤⠂⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⢀⠤⠊⠁⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⢀⡠⠚⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣀⠔⠋⠀⠀⠀⣠⣴⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⡠⠞⠁⠀⠀⢀⡠⠞⢡⢏⠎⢆⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡠⠊⠀⠀⠀⢀⡴⠋⠀⢀⡏⡜⢀⠈⢆⠀⣀⠴⠒⢉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡠⠊⠀⠀⠀⢀⣴⠿⡒⠠⠤⣞⡀⡇⠀⠃⢸⡞⡡⠺⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣀⠀⠀⣠⠊⠀⠀⠀⠀⡰⠋⡞⠀⠱⡀⢤⠤⣉⠻⣜⠀⢸⠰⠑⣡⠞⢉⣉⡉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡸⡡⣢⠲⣳⣜⡁⠀⠀⠀⡠⠊⠀⡼⠀⠀⠀⢹⠦⣉⣒⡁⠈⢣⣌⡠⠞⠑⠊⠁⠐⣪⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠻⢾⣡⠒⡍⣆⢠⠞⠀⠀⣰⠁⠀⣀⠤⠛⢉⠤⠈⣉⡩⠜⠟⢫⠉⢉⠁⠚⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠉⠔⣣⠞⡿⢂⢐⢦⣇⣜⡛⠢⡤⣄⣁⣠⠟⣁⠄⢸⠀⡀⢳⡈⠣⣉⠢⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠸⣠⢱⣤⣿⡔⠐⡜⡶⠀⠀⢠⢃⠎⡱⠁⣼⢰⠙⡀⠉⠑⠂⠠⠤⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⣈⣩⣜⠴⠁⠀⠀⡜⠀⢉⠠⠊⠘⡌⢆⠃⡘⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠚⠀⠉⠀⠀⠀⠀⠘⡄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠠⠂⠀⠀⢰⠰⣞⣛⣫⡴⠞⠃⣠⡾⡀⠀⠀⣶⠀⠀⡔⠀⡤⠐⠀⢀⢠⡆⠀⠀⠐⠠⠵⠦⠄⠀⡠⠴⠀⠀⠀⡆⢶⣛⣛
⠀⠀⠀⠀⡜⢦⣄⣀⣄⣠⠴⠚⠉⠀⢀⡇⠀⠙⠀⡄⠣⠀⠀⠀⣀⠇⣸⠇⠀⠀⠀⣠⠤⠤⠄⠠⣀⠀⠀⠀⠠⠻⣤⣀⣠
⣾⢠⣀⠀⠐⡀⠂⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⢈⣀⠀⢀⣏⢱⡯⠋⠀⠀⡠⠊⣡⣴⠐⠢⡄⣾⣇⣤⡀⠀⢀⠐
⠸⠆⠙⠀⠀⠙⠓⠢⠤⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣈⣼⠂⣴⡄⠐⣹⠻⠈⢡⠀⠀⠙⠒⠤
⠀⠶⢀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡗⡹⠮⡶⢂⣀⠀⠀⠘⣦⢍⢙⠀⣨⣀⡾⠘⡀⠆⡀⠀⠀⠀⠀⡠
⠐⣠⠂⠀⢀⠰⣇⠘⣄⠉⠙⠀⠀⠄⠀⠀⠀⣼⣧⠌⢕⠠⢔⣤⠙⢇⣄⠀⠀⠻⣆⠊⣤⠉⠁⣤⠖⢂⡐⠀⠀⠀⢸⡀⠣
⠚⠁⠀⠀⢘⡆⡙⠳⠄⡀⠀⠤⠈⠐⠂⠀⢰⣹⡇⣥⣻⢧⡮⠼⢁⡋⠿⡄⠀⠀⠈⠛⠦⠶⠤⠤⠖⠋⠀⠀⠀⣛⢈⠛⠦
⠀⠀⠀⠀⢸⣿⠉⣠⡀⢂⣀⣚⣡⠟⡇⠀⠈⢿⣼⠉⡿⠷⡲⣶⣿⢁⣸⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢁⣄
⣀⠑⢄⠀⠘⢯⣛⢻⡳⠟⠀⣨⣿⣠⠗⠀⠀⠀⠙⠻⠷⣾⣧⣠⣿⣼⠏⠀⠀⠰⠉⢀⡴⣖⣒⡶⢤⡈⠢⡀⠀⠻⣝⣛⣟
⡜⡇⢸⠀⠀⠀⠉⠛⠛⠷⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣾⢿⣿⢿⢷⣹⠀⡇⠀⠀⠈⠙⠛
⢋⡇⢸⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡰⠀⣈⡩⠍⣀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣽⣮⣿⡿⣹⠁⡃
⠚⢀⠀⠀⠀⠀⢰⡻⢟⣹⢜⣿⠏⢣⠀⠀⠀⡼⡀⠀⠀⣀⣀⡀⠀⡄⠀⠀⠀⢇⠘⢧⠻⢯⣭⣭⡴⠋⠠⠀⠀⠀⢀⣞⠯
⠰⠋⠀⠀⢸⠸⣮⣩⡭⠷⠛⠁⣠⠞⡄⠀⠀⣻⠁⠀⡎⠀⡶⢈⠀⢠⢰⡇⠀⠀⠁⠂⠕⠲⠄⠠⠤⠔⠁⠀⠀⡇⢿⣍⣭
⣀⠀⠀⠀⠞⠷⣤⣤⣤⠤⠖⠋⠁⠀⢀⠇⠀⠉⠀⡄⠣⠀⠀⠀⣠⠃⣸⠇⠀⠀⢀⡠⠄⠀⠐⠂⢄⡀⠀⠀⠠⠻⢦⣤⣤
⢾⣣⣄⠀⠐⣄⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠈⣄⠀⣨⣍⢸⠝⠃⠀⠀⡰⢋⢤⡶⠐⠀⠄⣾⣏⢤⡀⠀⢠⡐
⠘⡇⠈⠄⠀⠈⠛⠒⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠉⠀⠀⠀⠀⠀⠀⣬⣼⢃⡶⡆⢘⣽⠻⠀⢱⠀⠀⠙⠓⠒
⠀⠟⠠⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠾⡏⠴⠪⠖⠀⠤⠀⠀⠈⡦⠮⠙⠠⠤⠄⡞⠘⠐⠃⠄⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⠒⠒⠒⠤⠤⠤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣀⠀⠈⠉⠉⠙⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡇⠀⠳⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠡⡀⠀⠈⠑⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⢀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠩⠈⠉⠒⠺⠅⣐⢄⣀⡀⠀⠉⣉⢛⣛⣛⠋⠉⠀⠀⠀⡰⠃⠀⠀⠀⠀⠤⠔⢁⣠⠴⠋⠁⠉⢢
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠓⠤⠤⢀⣀⣀⣀⣀⣀⣈⣀⣀⡠⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⢀⣇⡀
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⢾⡯⠓⡖⢤
⠀⠀⠀⢀⡤⠴⢦⡀⠀⠀⠈⠓⠂⠒⠊⠉⠀⠀⠉⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠤⡀⠀⠀⠀⠀⠀⡰⠋⢁⣀⠔⠋⠀⢀⠟⠈⠳⡀
⠀⠀⡰⠋⠀⠀⠀⠈⠁⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠉⠢⡀⠀⢀⡴⠀⠒⠁⠀⠀⡀⠔⠁⠀⠀⠀⠹⡄
⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⣈⠭⠉⢀⠔⠒⢶⡶⠊⠀⣠⠤⠊⠀⠀⠀⠹⡄
⢸⠁⠂⠀⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠉⠁⣠⠤⠒⠁⢀⠔⠋⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢹
⡏⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⣀⢤⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⣒⡒⠒⠒⠊⠉⠀⠀⠀⠀⣰⠋⠀⠀⢠⠖⠁⠀⠀⠀⡏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠌⠀⠀⠑⠄⠀⠄⠠⠔⠈⠉⠈⠁⠀⠉⠑⠲⣄⠀⠀⠀⠀⢠⠃⠀⠀⢠⠋⠀⠐⠄⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠤⠒⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⡤⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⢒⣒⣒⣒⣒⣒⣊⣂⣀⣀⣚⣒⣂⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⡀⠀⢀⣠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⣀
⠀⠃⠓⢾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣯⣌⠋
⠁⠁⡀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾
⣘⣁⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠃⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⣽⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣆⠀⣠⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣀⡏⠁⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠻⡟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠛⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠁⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡄⠀⣅⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣄⣀⣀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣮⡁⠶⢭⠋⠀⣯⢋⣿⣷⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟
⢉⠉⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⣯⡻⣿⣆⠀⠀⢀⣾⣿⣿⣄⠀⠀⠠⠈⠀⣤⠈⢁⣲⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣿⣷⢀⣸⡿⠛⢿⡛⢿⣿⣷⣦⡶⠚⠓⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣛
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣄⣴⣶⡏⠠⣿⣿⣝⢿⣿⣿⠃⠀⠀⣼⣿⡟⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⢀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⣿⡏⢀⠈⣀⢨⣽⣿⠙⣿⣿⡿⠀⠀⣰⣿⢿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡀⢠⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⢻⣷⡿⣶⣿⣾⣻⠟⠙⢻⣿⣿⣥⣴⣿⣿⣿⣛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⡉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠣⣿⣿⡇⢿⣿⣿⠿⡄⠀⠀⢻⣿⢻⣿⣿⣌⣿⠺⢏⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠟⣿⡂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⣇⣀⡽⢻⠿⡀⠁⣤⣀⣿⠁⠙⠏⣿⣿⡄⠐⠲⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⡃⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡏⣷⠘⠀⠙⣢⠌⠛⠁⠀⠀⡀⣻⣿⣃⡴⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒⠀⠀⠀⠤⢇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁⢀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣟⣻⡗⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠑⣄⢹⠁⠀⠀⢀⡀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⢿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⢤⣼⣷⠀⢠⣫⣿⣿⠋⢩⣻⣟⣻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠨⠘⠀⠚⢻⣿⣿⣤⣼⣿⣿⣿⣿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠷⣾⣷⠀⠀⣠⣾⣿⣿⠆⢀⡟⢣⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⢸⣏⠹⠙⣿⣧⠀⠘⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠿⠄⠀⠙⢻⣶⡄⠀⠀⠀⠀⠀⡋⡉⠙⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠿⡿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠢⠄⠽⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣶⣶⠰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣸⡆⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡟⢻⠃⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿
⣶⣿⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
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