Rocket Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣖⣶⣶⣿⣿⣿⡿⢿⣿⣿⡷⢶⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⣿⡿⠋⢟⣽⣧⣶⣿⠿⡿⠇⢁⣾⣆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠛⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠢⣦⣤⣿⣿⡧⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠃⠀⠀⣀⠠⠊⠁⠻⣧⣿⢟⠙⡃⣤⣄⣾⣿⣿⣟⠅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⣐⡴⠥⠡⣤⣀⡀⠙⢯⡶⢶⣿⣿⣿⣿⣿⡟⠩⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⣴⠫⣹⣦⣤⣴⣶⣄⣩⠷⣄⠹⢿⣿⣿⣿⣿⣿⠫⢸⣿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⢀⡾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢷⣁⢙⠿⣾⣿⡉⣲⣿⣯⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣽⢿⠁⠀⢠⡾⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠹⣿⣦⣀⠀⢹⡟⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⢻⡏⣿⢹⡉⣽⢹⣟⡦⣼⠿⢛⣄⢘⠞⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢠⣿⣿⠿⣣⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣿⣏⢨⣦⣿⣿⣿⣷⣿⣿⡟⣹⡏⠀⠁⡜⡿⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢍⣿⣿⠓⢠⡅⠁⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣵⣿⣿⣿⣿⣿⡿⣿⢿⣿⣽⠟⠀⠠⢎⡞⠀⠀⠀⠈⢷⣝⠻⣿⣿⠿⡿⠟⠙⣦⣿⡿⣪⣝⠈⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢻⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢻⣏⣠⣴⣷⢾⢶⢢⣄⠀⢀⠀⡙⣷⣷⣾⣶⣷⢼⡺⣟⡯⡮⠁⠁⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣵⣿⢿⡷⠿⠿⠿⢟⣹⣿⣯⣷⣿⢿⠿⡏⣧⣿⣿⣽⣿⡟⠀⢬⣻⣾⣿⣿⣿⣿⣿⣿⣎⢡⢀⡀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⡿⢁⡤⠖⠒⠚⠛⢛⣿⣿⡿⢁⣿⣼⣿⣿⡿⡿⣿⣿⣯⣔⡙⢮⣿⣿⡿⣿⡿⠿⠟⠁⠀⡉⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠚⠁⠀⠀⠀⢀⣴⢿⣟⣧⡾⠟⣛⣽⣯⣢⣴⣶⣿⣷⣿⣿⣿⣷⣍⠛⠛⠂⠁⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⢀⡴⣫⣷⣿⣿⣷⠶⠿⠿⣿⡿⣿⣿⣿⣿⡿⠏⠛⠛⠉⠀⣀⣤⣴⡶⢶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⡿⠟⠛⠛⠻⣏⢻⣿⣿⡿⡻⠇⠀⠀⠀⣀⣤⣶⢿⣿⣿⣿⢟⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⡾⠛⢉⣣⡀⠀⠀⠀⠀⢿⣷⡙⠳⣄⡀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⣋⣴⠷⣦⠁⠑⢄⡀⡀⠳⠄⠙⠻⣦⣬⢿⣿⣿⣏⣿⣿⣿⣿⣿⣿⡷⠬⠭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⡋⢑⣾⣿⣦⣀⣦⣿⣿⣄⠀⠀⠀⣰⠁⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⡍⢓⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠦⠞⣰⣿⣿⣿⣾⣿⣿⣿⣿⠿⠷⢄⢀⡌⣼⣿⣿⡿⣿⠙⣻⣿⣿⣿⣏⣠⢤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡗⠀⠀⣀⡤⣺⣿⣿⣿⣿⣿⣿⡿⠛⠁⣄⢀⣤⠟⣽⣿⡿⠋⢰⡏⢠⣿⣿⣿⣉⢕⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢋⠞⠀⠖⠛⢃⠜⣫⣿⣿⣿⡿⡿⠛⣀⣤⣼⠃⠀⠀⣾⠿⠋⠀⣠⣟⣴⣿⠿⠝⣫⣷⠞⠁
⠀⠀⠀⠀⠀⠀⢠⡎⠀⢀⠤⠀⠁⠀⠀⠉⠊⠁⠀⣠⣴⣿⠟⡇⠀⠀⠀⠀⠀⣀⣴⣿⣿⣟⣯⡶⠟⠋
⠀⠀⠀⠀⠀⢠⣿⠀⠐⣠⠂⠀⠀⠀⠀⠀⢀⢄⡾⠋⠐⠁⠈⠀⠀⠀⠀⠀⠸⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠉⢀⣾⠇⠔⢀⢀⣀⡴⠊⠠⢏⣀⡤⠂
⠀⠀⠀⢀⠃⠀⠀⢐⣡⣦⠞⠙⠉⠀⠀⠀⠀⠛⠋
⠀⠀⢀⣤⣴⠀⠰⠋⠁⢀⣀⡴⠊⠐⠋
⠀⠀⠀⠹⠃⣀⣤⣶⢾⠟⠁
⢀⠀⡰⠷⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠒⠒⠒⠒⡶⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠉⠀⠀⢀⡤⠤⣤⡀⠀⠹⡄⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⢤⣠⠖⠋⠁⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠙⣆⠀⠹⣄⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡾⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⠤⠞⠁⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⠀⠀⠀⠀⣀⡤⠖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣇⠀⣧⡤⠖⣋⡥⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣁⠴⠚⣹⣚⡥⢶⡋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢀⡴⠁⠀⣀⣠⢼⣦⡀⠳⣄⣀⣠⡤⠤⠶⢲⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⠉⠉⣉⡥⠚⠉⠀⠉⠉⠙⡇⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠤⠤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠰⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⣩⣴⣦⠠⠖⠞⠈⠀⢠⣤⣾⠋⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⣴⣿⣿⣿⣿⣄⠤⢀⣄⣶⠿⠦⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣼⣿⡿⢟⣿⣿⣿⣿⣦⠊⡏⠀⠀⠀⠀⣰⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣰⣿⡿⡏⠟⠈⠉⠉⠙⠛⢽⠷⣄⠀⢀⠀⢐⡾⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢰⣿⡿⣱⠋⠀⠀⠀⠀⠀⠀⠈⢻⠙⢿⣦⣄⢛⡀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⢰⡆⡄⢰⠏⣠⡼⣿⣂⣹⡀⠀⠀⠀⠀⠀⠀⠀⣺⠁⠀⣼⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠈⠀⠀⠀⠀⠀⠎⣸⣿⣯⣤⣿⣿⢇⡀⠀⠀⠀⠀⠀⣸⠆⢀⣾⣛⣿⣿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠖⠂⣀⣼⠿⠳⠱⠿⣿⣿⣷⣿⠂⠶⠆⠾⠛⢀⡤⣮⣼⡿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⢀⣀⣀⡀⠀⡠⠖⠋⠁⡀⠄⠈⠋⠃⣸⣿⠉⠃⠀⠀⠀⠈⠸⢗⡷⡿⠛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠋⠉⢁⠴⠊⣀⠴⠃⡁⢀⣤⠀⣠⠞⠛⠬⡁⠀⢄⣠⣤⣾⣿⣳⡴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠘⠈⠀⠒⠋⠀⠈⢀⠜⠁⣀⣀⣠⣬⣿⣾⠿⢿⠝⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⢀⣠⣴⣾⡻⡇⠠⠴⣋⣾⣾⣿⣿⠿⠛⠉⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢑⣣⣾⣟⡻⣿⣿⣿⣄⠙⢦⣙⢿⡟⠉⠀⠀⠀⠀⠀⣻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠞⢫⣵⣾⣿⢯⠻⢿⣿⣿⣦⣽⠁⠈⢸⡀⠀⠀⠀⢀⣲⡃
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⠐⣠⣾⣿⣿⣿⣄⡀⢀⣙⣿⢿⠇⠀⢐⠸⣦⠀⠀⠀⣴⡟⠠⠁
⠀⠀⠀⠀⠀⠠⡿⠃⡠⠔⣺⣿⣿⣿⣿⡿⠋⢉⡿⠟⢫⠎⠀⠀⠈⣸⠃⠀⠀⡲⠏⠐⠁
⠀⠀⠀⠀⠀⡰⠁⢀⠠⠊⠉⠛⠿⠋⢉⣠⣾⠿⠀⠀⠀⠐⠀⠀⠐⢁⠠⠞⠉
⠀⠀⠀⠀⢼⠇⢐⡅⠀⠀⠀⠀⠀⣴⠏⠙⠁
⠀⠀⠀⡀⠀⠀⠞⢀⡤⠤⠒⠋⠐⣥⠖⠁
⠀⠀⣀⡤⠀⠴⠋⠉⣀⠄⠴⠂
⠀⠀⠹⢃⣠⡴⠾⠋
⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣀⠘⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡎⠀⢱⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠃⠀⠀⠈⠉⠁⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠇⠀⠀⠀⠀⢀⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⠔⠄⠀⢀⠔⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⣒⢶⠌⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠌⠁⠀⠀⠁⠀⠘
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡢⠀⠐⠐⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠢⠐⠀⠉⠀⠂⢄⠀⠠⠀⠀⠀⢀⠄⠀⠈⠁⠃⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣊⣀⣀⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠟⠁⠀⠈⠚⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠈⢢⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡠⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⠌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠥⠒⠥⠀⠀⠀⠁⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠁⢀⠁⠄⡀⠔⢹
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠐⠁⠀⠀⠒⠦⠛⡊⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡈⡈⡀⠊⢀⠄⠀⢰⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⢀⠀⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠀⠀⠀⠊


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠰⣦⣾⣿⣤⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠴⠛⠋⠛⠇⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠒⠒⠚⠛⠛⠛⠛⠛⠒⠲⠶⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣶⠶⠶⠶⠶⠶⠶⣶⣤⣤⣄⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⢋⡥⣤⡉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡿⠀⠈⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⣇⢷⣤⡴⢃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠙⠶⠤⠶⠛⠁⠀⠀⠀⡴⠖⠒⠒⠻⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣧⣂⣀⣂⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⢰⠫⣟⣛⡳⠶⠶⣶⣤⣤⣤⣭⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠈⠣⣕⡻⢿⣿⣗⣚⣛⣳⢒⡿⠀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠈⠉⠉⡛⠒⠛⢻⡋⠀⠰⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡷⠀⠀⠀⢀⣴⣟⠋⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢠⣿⣿⣿⣷⠆⠀⢸⡶⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢸⡿⣿⡿⠁⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢷⣄⡀⠘⠋⠀⠀⢀⣴⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⡤⠖⠋⠁⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠙⠛⠳⠶⠶⠶⠶⠶⠛⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⡄⠀⠀⣸⡿⠀⠀⠀⠀⢠⣾⠟⠛⠻⣦⡀⠀⠀⠀⠀⢿⡇⠀⠀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠘⢿⡄⠀⣿⠇⠀⠀⠀⣴⡿⢇⣀⣀⣀⡹⣷⡄⠀⠀⠀⢸⣇⢀⣾⡟⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣤⣼⣿⣼⣿⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢸⣿⣼⣿⣀⣀⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢸⣿⡇⠀⠀⣸⡿⢁⣤⠴⠶⠒⠲⠶⣤⡘⣿⡄⠀⠘⣿⡿⠀⠉⠉⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⣿⠃⠀⢠⣿⣵⠟⠁⠀⠀⠀⠀⠀⠈⢻⣼⣷⡀⠀⣿⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⣿⠀⠀⣼⡟⢿⣤⣤⡴⠶⠶⠶⣤⣄⣤⠟⢿⡇⠀⣿⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⠀⠀⢸⡏⠀⠀⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣿⠂⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⡿⠁⠀⣾⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣿⡇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣀⣀⣀⣿⡇⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⣿⣧⣄⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣌⣉⣉⣩⣿⣷⡿⢿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠟⣿⣿⣧⣈⣉⣉⣉⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢉⣡⣾⠟⠁⠀⢸⡇⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⢰⣿⠀⠈⠻⣿⣬⡉⠉⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣇⣴⡿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠇⢿⡇⠀⠀⠀⢸⡏⠀⠀⢠⣯⣿⢿⣦⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢰⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠊⠹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠒⠒⠒⠐⠊⠉⢉⢹⣿⣉⠓⠂⢼⣿⠀⢸⣿⠤⠤⢴⣿⣀⣀⣀⣀⣀⣀⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠒⠉⠉⠉⠉⠀⠀⠀⠀⢿⡏⠉⠒⢺⣿⠀⢸⣿⠀⠶⣾⡿⠴⠶⠦⠄⠠⠤⢤⣬⡉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠿⠿⠿⠿⣿⣿⡿⠿⢿⡷⣶⣼⣿⠀⣾⣧⣤⣴⣿⣷⣶⣶⣦⣤⣴⣶⣶⣶⣦⣿⠇⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣄⣀⣀⣤⣿⢻⣧⣀⠘⠳⠿⠶⠿⠿⣿⣽⣥⠟⠀⠀⣼⡿⣿⡀⠀⠀⠀⣸⡿⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡙⢻⡛⣿⠁⠀⠙⣿⡟⢻⡿⢿⠶⣾⠿⢶⠿⣶⢿⣿⠟⠀⣿⡿⡿⢿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠃⠀⢸⣿⣤⣾⣤⣼⣤⣤⣤⣼⣤⣽⣬⣿⡄⠰⣿⣶⣷⣾⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⡶⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣠⠄⠀⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠃⠀⢸⠀⠿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠃⠀⡀⠀⠀⠆⠈⣷⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡆⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠿⣶⠀⠁⠀⠀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⡀⠘⠀⢀⣴⡿
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⠀⢸⡟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡀⢀⣾⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⠃⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⢷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢸⣎⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠸⠿⠯⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢰⣿⣿⣯⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⠀⠸⢿⣿⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢈⡴⠒⢒⣶⣌⠻⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠄⡞⠀⣰⣿⣿⣿⡇⢻⣷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠻⣄⢿⣿⣏⡹⢃⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠐⠈⠁⢛⣩⣴⣿⣿⣿⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢜⣹⣆⠀⠀⢀⡞⠱⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⡇⣝⢦⠀⠀⢀⡾⠡⢝⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⣿⣿⣤⠴⣋⡀⠀⢁⠀⠀⢠⠁⠸⢿⣿⣿⡟⣼⣿⢏⡑⢦⣾⠁⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢸⣿⣿⣷⡆⣤⠅⣀⡤⣆⠀⠁⠀⢸⣷⣹⣿⡶⣽⡃⢥⡬⠀⠉⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⢟⡷⠊⠁⠀⢸⡇⠀⠀⢸⣿⣷⣿⠀⠀⠉⠳⣄⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣷⠏⠀⠀⠀⠀⣼⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠈⢻⡀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⡀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⣯⠏⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⢧⡀⠸⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⣙⣿⡆⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢸⣿⢷⠏⠀⠀⠀⠀⠀⠀⠀⣾⣋⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠓⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⣴⣒⣲⡄
⠹⠿⠿⡣⡀
⠀⠀⠀⠈⠪⡢⡀
⠀⠀⠀⠀⠀⠈⠪⡢⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠍⢈⠉⠙⣂⠀⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣃⢁⡠⠊⠀⡐⠀⠈⠒⠠⣀⠀⠁⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⣀⡠⠊⠀⠀⡀⠀⣀⠀⠁⠠⡀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⡠⢀⣴⠖⠠⠑⡀⠀⠈⠐⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⡆⡀⠀⣧⢸⣿⡆⢀⠀⠇⠀⠀⠀⠀⠑⢄⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢻⡔⠄⠘⠢⣭⣉⡤⠊⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢻⣆⠢⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⢢⠀⠀⢢⣤⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⣧⡑⢄⠀⠀⠀⠀⠣⣻⣂⠀⠀⠀⠀⠀⢀⠗⠀⠀⠙⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⢌⠻⣦⡑⢄⠀⠀⠀⠀⠀⡄⣾⠁⠀⢠⠊⠀⠈⠀⠀⠈⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠑⢌⠻⣦⡁⠀⠀⠀⠀⠙⠺⢠⠞⣡⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣯⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡻⣶⣌⠂⣀⠤⠊⠀⢧⡻⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢝⡻⣦⣔⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣝⢷⣦⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⣸⣛⠄⡀⠈⠙⢿⣿⣿⣿⢀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣠⣾⣿⣿⣦⡄⠐⠄⠀⠙⣿⣿⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣄⠛⣿⣿⣟⣿⣿⠎⠛⠶⣌⣙⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣣⡈⠹⣿⡿⠃⠀⠀⠀⠨⣿⢿⡣⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀⠈⠑⣎⠁⠀⠀⠀⠀⠀⠀⢈⡑⣄⠐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣦⣀⠹⣆⢀⡀⠀⠀⠀⠀⠀⠹⡹⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⢙⠛⠛⠛⠳⣌⣿⡷⣄⢠⣄⠀⠀⠀⠹⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡈⠛⢅⡈⠻⢷⣝⠲⢄⡀⠈⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠲⠄⠈⠀⠀⠳⣄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣿⣿⣿⣿⣿⣭⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠟⠿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⠛⠛⠛⢿⡟⠛⠛⠋⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠰⢶⣶⣿⣷⣶⡶⠂⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠉⢹⠉⠉⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⣦⡄⠸⠀⣠⠆⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣴⣶⡏⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣿⡆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠈⣿⣧
⣠⣶⣶⣾⣿⣿⣷⣾⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣶⣿⣿⣿⣶⣶⣦
⣿⣿⣦⣴⣶⣝⣫⣽⣿⣿⣿⣿⣿⣷⢶⣶⣶⣤⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣤⣴⣶⣶⣶⣿⣿⣿⡿⣛⣛⠛⣋⣭⣛⣫⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣮⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⣋⣦
⠙⠛⠛⡠⡀
⠀⠀⠀⠈⠠⡂
⠀⠀⠀⠀⠀⠀⢪⠖⠒⠖⠶⢦⠤⠀⢀
⠀⠀⠀⠀⠀⠀⢹⠄⠊⡠⠂⢀⠁⠂⠄⡀⠈⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠸⣅⠉⢀⠄⠁⠀⠀⠀⠀⠁⠠⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⢠⢠⣶⠂⠄⢂⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡠⠀⢸⡸⣿⡆⠀⡈⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢷⡁⠀⠙⠒⠖⠊⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠢⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠻⣄⠂⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⡆⠀⠹⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⢷⡕⢀⠀⠀⠈⠑⠀⢠⡄⠀⠀⡔⠀⠀⠀⠘⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠈⠢⠙⢦⡀⠀⠀⠀⠀⠳⠇⡠⢊⡀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⢷⣌⣀⣤⠔⠈⠰⣙⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣛⢶⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⡿⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠙⡿⡛⠛⠻⢿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣼⣷⣇⡑⠠⡀⠙⢿⣿⡆⠄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡹⢿⣿⣿⣿⣶⠗⠶⣌⣛⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠀⠙⣄⠋⣿⡿⠋⠀⠀⠀⣿⡿⡧⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⡀⠈⢳⡁⠀⠀⠀⠀⠀⠀⣙⣦⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣌⠳⣤⡄⠀⠀⠀⠀⠘⢞⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣁⠉⠳⢿⡟⠦⣻⡦⣀⠀⠈⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣈⠙⠂⠙⢦⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣄⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠹⣦⣠⣴⠶⠟⠛⠛⠛⠻⠶⢶⣤⣀⣴⠟⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣽⠟⢋⡁⠀⠀⠀⣠⠤⣤⠀⠀⠀⠈⠙⠻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢠⡾⠃⠀⠿⡽⠀⠀⠀⠻⣤⠼⠃⠀⠀⢴⣛⡆⠈⠻⣦⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣠⣤⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⣥⣤⣀⣀⠹⣧
⠀⠀⠀⠀⠀⣀⣤⡴⠾⢛⣛⣉⣩⣭⠤⣴⣶⣶⡖⠒⠒⠒⠒⠛⠒⠒⢒⣶⡶⠬⢭⣭⣛⡻⢷⣤⣀
⠀⠀⠀⣴⠞⣫⠵⠖⠛⠉⠉⠀⠀⠀⠸⠿⢿⣿⣃⣀⣀⣤⣄⣀⣀⢾⣽⣿⣽⠇⠀⠀⠈⠉⠓⠮⣝⣷⣤⡀
⠀⠀⢸⣇⡞⠁⠀⢀⣀⣀⣀⠀⠀⠀⣠⣶⣿⢿⡿⠿⠿⠿⠿⠿⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣷⡄
⠀⠀⠸⣿⡀⠀⠀⢯⣿⣭⣿⣿⠀⠀⣿⣺⣄⣾⠃⠀⠀⠀⠀⠀⠀⢹⣏⢛⣿⣧⠀⠀⣞⣩⣙⡍⣳⠀⠈⢻⡷⠸⠇
⠀⠘⢦⠙⠷⣤⡀⠀⠀⠉⠉⠀⠀⠀⠈⠛⣿⠃⠀⠀⠃⠀⠀⠀⡄⠀⢿⣯⡿⠃⠀⠀⠈⠙⠛⠉⠁⢀⣠⡿⠁
⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⣀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⣧⠀⠀⠀⠀⢀⣀⣠⣴⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣹⡟⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⢿⡟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⣇
⠀⡀⠀⠀⠀⠀⠀⠀⢀⡿⢁⣀⡤⠴⠖⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠲⠶⢤⣄⣀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠋⠁⠆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉⠁
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⠿⠿⠛⠛⠉⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠉⠀⠀⣠⣾⠟⠛⠻⣷⣄⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠘⣿⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⠀⣀⣼⡟⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠀⠀⢠⣶⠿⠿⠿⣶⡄⠉⠛⠛⠛⠉⠀⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⠀⢀⣴⡿⠀⠀⠀⠀⢠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⠟⠀⠀⠀⠀⢀⣴⡶⠿⢶⣦⡀⠙⠻⠿⠛⠋⠀⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠛⠉⠉⠉⣹⣿⣿⡿⠁⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⠋⠁⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⢠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⣾⣿⡿⠀⠀⣀⣤⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⠋
⠀⠀⣸⣿⣿⣷⣾⣿⣿⣿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿
⠀⠀⢿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠟⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⡀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠋⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⢀⣠⣴⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣥⣴⣾⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠒⠒⠒⠒⠒⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⣭⣅⢀⣠⣤⠐⠒⠉⢀⣀⣴⠟⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⣶⣿⣿⣿⡄⢀⠀⠀⢀⣠⣯⡉⠋⠀⠘⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⣴⣾⣿⣿⠿⣷⣿⣿⣌⢀⡿⠟⠋⠉⠀⠀⢀⠻⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⣿⣿⠿⣯⠱⠾⠿⢿⣿⠿⣦⡐⠀⠀⠀⠀⢀⣿⠀⡚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣰⣿⣿⢛⠎⠁⠀⠀⠀⠀⠈⠙⣯⡻⣦⣀⠒⠀⣬⠏⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⣿⣿⠣⣮⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆⠈⠻⣿⢆⣤⣤⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢰⠟⠀⠹⠓⠺⢂⠇⣴⣷⡛⢷⣥⣷⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠠⣨⣟⣹⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠊⠁⠈⠀⠀⠀⠀⠀⠏⣸⣿⢯⢶⣾⣿⣟⢣⡀⠀⠀⠀⠀⣀⠠⠏⠂⡼⣯⣽⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠁⠀⠀⠀⠀⠀⠐⠒⢁⣌⡼⠿⠛⣓⣿⢿⣿⣿⣷⡿⠉⠒⠃⠛⢟⢁⣴⢻⣶⣿⣟⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠆⠁⣀⣀⣠⣄⠠⠀⡴⠚⠉⢠⡀⠶⠐⠉⠋⢠⣿⡷⠍⠁⠀⠀⠀⠀⠑⠏⡿⣿⠟⢻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠉⠁⣀⠖⢈⣴⠾⠃⡈⢀⣠⡤⢀⡴⠋⠳⢌⠀⠀⢄⣠⣤⣼⣿⣿⣶⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠁⠄⠉⠠⠖⠋⠁⠈⠁⡰⠋⠀⣀⣀⣠⣽⣷⣾⠿⢿⡻⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣀⣦⣾⣿⡅⠄⣠⣞⣹⣶⣿⣿⣿⠿⠟⠉⠁⢰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠜⣠⣶⠟⣿⣿⣿⣷⡍⠰⣤⡙⠿⣿⠛⠉⠁⢀⠀⠀⠀⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣰⠿⣛⣭⣿⣿⡿⢿⣿⣿⣶⣌⣛⡖⠉⡄⡆⠀⠀⠀⠀⠀⣨⡯⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣈⡅⣠⣿⣿⣿⣟⠉⠀⠉⢿⣿⣿⣽⠁⠀⢠⣡⠀⠀⠀⠀⣸⣿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⢀⡠⣼⣿⣿⣿⣿⣿⠷⠦⣾⣷⠿⣡⠃⠀⡠⠆⣽⠏⠀⢀⡠⡟⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠠⠚⠉⠜⣩⣿⣿⣿⠟⢃⣤⣶⠉⠁⢸⠁⠠⠊⠐⡰⠋⢀⣴⠖⠊
⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢄⠀⠀⠀⠀⠉⠁⢀⡴⢿⠟⠋⠀⠀⠀⠀⠠⠊⠀⠠⠐⡋⠄
⠀⠀⠀⠀⠀⠀⠀⠻⠂⣴⢏⡄⠀⠀⣀⠀⡰⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠰⠀⠂⢈⣃⣠⠔⠐⠊⠁⠀⠵⠟⠁
⠀⠀⠀⠀⢀⣦⠆⠀⠋⠀⣀⡤⠂⠐⠋
⠀⠀⠀⠀⠀⡙⣠⣴⠾⠿⠉
⠀⠀⠠⠀⠘⠉⠁

⣶⣶⣶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣷⣴⣤⣾⣥⣾⣵⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⠟⠻⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠛⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⠛⠉⠀⠑⣤⡆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠁⠀⠀⠀⣠⡾⠃⠉⠓⠲⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⣀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⣤⣶⢶⣾⣿⡿⠁⠀⠀⠀⠀⢀⣴⢯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⣾⡏⠀⠀⠈⣿⡇⠀⠀⠀⠀⣠⣿⢏⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⢻⣧⣀⣀⣴⡿⠁⠀⠀⣠⣾⣿⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣿⡀⠀⠀⢠⣾⡿⠛⠛⠉⠀⠀⢀⣴⣿⣟⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢿⡿⣀⠷⣄⠀⠟⠉⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠒⢲⣤⣿⣙⣾⠛⢆⡽⡀⢈⠗⠦⣀⠀⠀⢀⣴⣿⢿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⣤⠼⠋⢉⣵⣿⣿⡟⡇⠈⠳⣜⠛⠦⣠⠊⠉⡱⣻⣿⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡶⠁⠀⢠⣿⢋⠵⣾⣷⡾⢿⣦⠈⠙⠲⠧⢽⣭⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⣼⣷⠋⢸⡿⠋⠀⣼⣧⡟⣒⣿⣿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢞⡇⠀⢠⠊⣿⠃⢠⡟⠁⣠⣾⡷⡿⣿⢫⣿⣿⡭⠗
⠀⠀⠀⠀⠀⠀⢰⣋⣸⠀⠀⠆⠀⠀⢠⡟⣠⡾⠋⠁⢀⡴⣫⣾⠟⢹⠓⢦⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⡏⠀⢸⠀⠀⢠⢟⡿⠋⠀⣴⡾⣿⠞⠛⠁⢀⣾⠙⠺⠃⠀⠀⠀⠀⠁⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡆⠀⠀⠘⠋⠀⠀⠀⢀⡴⠁⠀⠀⣠⣞⢹⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡸⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⣀⢴⡾⠁⠘⣾⡇
⠀⠀⠀⠀⠀⠀⠀⡿⢠⠃⠀⠀⣀⠤⠚⠉⣀⡤⠖⣿⣡⠞⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣇⠏⢀⡴⠊⣡⣤⡶⠛⠁⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⣸⢏⣴⡥⠚⠉
⠀⠀⠀⠀⠀⢰⡿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣻⣿⣿⣯⡸⢉⣦⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣠⣷⣿⣿⣿⣿⣾⡿⠋⠁⠀⢡⠞⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⢷⣿⠟⠙⣛⣿⣿⠟⠁⢀⣠⣤⣄⠈⠑⣾
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣟⣿⣿⣿⣫⣶⠟⠁⣠⣾⡿⠛⠁⠀⢠⣿⣿⣿⣙⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣻⢿⣿⣿⢿⣿⣿⠿⢤⣤⣾⠿⠋⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⠐⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣺⠛⣠⣔⣶⣿⣿⣿⡼⠋⣡⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠠⢊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠿⣿⣿⣿⡿⠛⠉⠉⣷⠟⣡⠞⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢂⣤⠀⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣶⢄⡜⠻⣄⠀⠀⣼⡷⠊⢀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣠⣼⣷⣉⣼⣡⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠿⣻⠏⠀⠀⠈⠓⢀⡉⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠉⣹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⡾⠁⠀⠀⠚⠙⢤⡀⠈⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⡟⢀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠳⣄⠀⠀⠀⠀⠀⠀⡠⠈⡡⠗⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡔⠁⠀⠀⡀⠀⠀⠀⢀⡟⢀⠦⠀⢀⡰⣆⠀⠰⢂⠔⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠈⠁⠀⠀⢀⣾⠁⠁⣠⠞⠁⠀⠈⠳⠀⠂⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢀⠀⠀⠀⠀⢠⡞⠀⣠⠞⠀⢀⣴⡶⠃⠀⠀⣖⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⠀⠀⠀⢠⣏⢠⡞⠉⠀⠀⠀⢀⣤⡶⠒⠀⠀⣷⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣿⣱⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠈⠉⠁⠁⣈⢿⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠰⡉⠓⠒⢦⡤⣀⣀
⠀⠀⠀⠀⠀⠀⠹⡄⣠⠋⠀⠀⢈⠟⠓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⡰⠋⢀⡠⠤⠤⣝⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠞⠁⢠⢏⡔⠉⠙⢦⢱⠈⠳⣄⡔⠋⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠘⡌⢇⡀⣀⡼⣸⠁⠀⠈⠳⡤⠦⢤⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡲⠭⠥⠚⠁⡞⠓⠦⣤⡇⠀⠀⠈⠳⢄⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠈⢢⡀⠀⠙⠦⡀⠀⡀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢹⠒⠊⠉⠳⢄⡀⠈⠢⡈⠒⢄⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠳⣄⠀⠀⠀⢍⠓⠦⣜⣦⡀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡈⠳⢄⡀⠀⠑⠢⣀⠉⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠭⢷⣤⣀⠀⠑⠢⢄⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢽⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣻⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠧⣾⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡾⡙⣲⣿⣿⣿⡿⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⠀⠀⠂⢠⣞⡕⣱⣿⣿⣿⡿⢥⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣿⢏⣼⣿⣿⣿⡟⡰⡴⠁⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢫⣾⣿⣿⣿⢏⣜⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⣣⣿⢏⣿⣿⢫⣮⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣵⣿⡟⣼⡿⣣⣿⣏⠀⠀⠐⠶⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⢛⣿⡻⣿⣿⡟⣸⣿⣵⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⣰⣻⣦⣿⣾⣿⣴⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢯⣿⣿⣏⣼⣿⣿⡾⠙⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠟⠀⠛⣣⡝⢿⣟⡷⠁⢀⣼⡟⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣡⣴⠃⠈⠋⣠⡔⡸⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠈⢠⣴⡶⢋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠀⠥⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠈⠁⠀⠀⠀⠀⠀⠈⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣠⣶⣿⠿⠿⢿⣶⣄⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣼⡿⠋⠀⠀⠀⠀⠙⢿⣧⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢻⣷⣄⠀⠀⠀⠀⣠⣾⡟⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠙⠿⣷⣶⣶⣾⠿⠋⠀⠀⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⢸⣿⠀⠀⠀⠀⣠⣶⡿⠿⠿⢿⣶⣄⠀⠀⠀⠀⣿⡇⠀⠀⠈⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠁⠀⠀⠀⠀⢸⣿⡀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠈⢿⣧⠀⠀⢀⣿⡇⠀⠀⠀⠀⠈⢻⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢻⣷⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠻⣿⣄⠀⠀⠀⠀⣠⣾⠟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣾⡟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠙⠻⢿⣶⣶⡿⠟⠋⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⣀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢻⣷⠀⢠⣿⠿⠿⠿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⠿⠿⠿⣿⡄⠀⣾⡟⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⢸⣿⣤⣿⠏⠀⠀⠀⠈⢻⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠁⢀⣤⠀⠹⣿⣄⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⣿⣿⠃⢠⣶⡄⠀⠀⢸⣿⣅⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⡇⠀⢸⣿⠀⠀⠙⣿⣿⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠁⠀⢸⣿⡇⠀⠀⠈⢻⣿⡛⠛⠛⠛⠛⠛⠛⢛⣿⡟⠁⠀⢸⣿⠀⠀⠀⠈⠋⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⢿⣦⡀⢀⣼⡿⠃⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣀⣀⣤⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠉⠙⠛⠛⢻⡟⠛⠛⠛⠉⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠶⣶⣶⣾⣷⣶⣶⡶⠆⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠈⠛⢻⡟⠛⠋⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⣇⠀⢸⠇⠀⣸⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⣄⠀⡄⣰⢿⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣷⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢻⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠘⠁⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⠀⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠐⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⢾⣿⡀
⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣄⡀
⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣶⣤⣶⣦⣍⣋⣭⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣤⣶⣶⣶⣶⣿⣿⣿⣿⠟⢛⣛⠛⢋⣩⣉⡛⣫⣭⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣛⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⣵⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⢿⣿⢿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⠿⣿⣿⠿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠾⠶⢶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠉⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣦⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠘⣿⣿⣿⣿⣿⣿⡇⠸⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⢠⣇⢿⣿⣿⣿⣿⣿⢱⣆⠀⠀⠉⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⣾⣿⢸⣿⣿⣿⣿⡟⣼⣿⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⣿⣿⣿⢣⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠉⠉⠉⠉⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣾⣇⣤⣤⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣰⣿⣿⣿⣿⣄⣀⣀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣤⣤⣄⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⣠⠖⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢰⠃⠀⢀⡠⠊⠉⠳⢤⡀
⠀⠀⠀⠀⠀⣾⠀⠈⠁⠀⠀⢀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⣿⠀⠀⣠⠞⠉⠉⠉⠉⠐⠲⢌⠓⢄
⠀⠀⠀⠀⠀⣿⠀⠰⠃⠀⠀⠀⠀⠀⣀⡤⠞⠁⠈⠳⡀
⠀⠀⠀⠀⠀⢹⠀⠃⠀⠀⢀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢸⠀⢧⡴⠚⠁⠀⠀⠀⠀⠐⠀⠀⠀⢀⠤⠻⡄
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠠⣙⣄
⠀⠀⠀⠀⠀⠀⠘⣆⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢏⣀⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠙⢏⠓⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣹⠄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⡨⢇⠒⠢⢤⡈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡒⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡈⢿⠒⠞⠁⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡏⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⡤⠂⣁⡽⢈⣧⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⡄⢀⠜⠁⠀⠀⠀⠀⠀⠈⠓⣊⡥⣺⡵⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡟⣆⠀⠀⠀⠀⠀⢀⣠⣔⡪⠗⢈⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡾⢢⣀⣀⣤⣶⠽⠚⣩⡤⠞⠉⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⣡⣴⡿⠛⠉⠓⠖⠋⠁⠀⠀⠀⠀⡀⠑⠆⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡾⠟⠋⠁⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠸⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⠀⠈⢢⡀⠀⢀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⠆⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠻⡟⡛⢻⡻⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡵⣾⠁⣋⢿⣿⣿⣿⣿⣿⣾⣿⣶⠦⢼⡦⣼⣿⣛⢋⣿⣿⡛⣿⣿⣿⣿⢴⢒⠏
⣿⣿⣿⠑⡀⠛⢸⣏⠻⠿⢿⣿⣿⣿⣯⣷⣺⢀⣹⣿⣿⣿⣿⣯⣽⣾⣿⣋⠀⣸⡾⡀
⠣⣷⠶⢚⠁⠀⠀⠤⠐⢤⠤⡭⡝⢛⠏⠙⣿⢸⣿⣽⣿⣿⣿⡏⠉⣽⣯⡛⠃⢹⡇⡷
⣷⣠⡞⠋⡴⠀⠀⠀⠁⠀⠀⠳⠈⠀⠀⠀⠁⠾⢿⣿⣿⣿⡿⣖⣺⡾⣿⣻⢿⣿⡇⢱⡴⠀⠤
⢿⣇⡄⢀⠀⠲⣇⣀⣄⠠⣀⣶⣂⢀⡀⠀⠨⠛⢻⣿⣙⣿⣿⣿⣷⣿⡿⢼⣷⣽⣷⣸⡇⠁
⣶⣿⣿⣿⣟⣧⣄⣽⣍⠀⢈⠙⠉⠀⠀⠀⠠⠀⠀⠘⢻⣿⣿⣿⣿⣿⡿⢲⣿⣏⢿⣿⣦⣄
⣾⣴⣿⣿⣫⣤⣬⣾⣧⣿⠏⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠙⠛⣻⣿⣷⣽⠏⢹⠀⢸⠀⠹⠀⡀
⣽⢷⣿⣿⣿⣟⣿⣫⣿⢿⣽⠂⠀⡀⠀⢠⡆⠀⠀⠀⠀⣀⣀⣽⣿⣿⣿⠿⢿⠿⠿⡄⢠⡞
⢿⣿⣿⢯⣿⢧⣽⣿⡹⣾⣿⣿⣶⣛⡀⢸⡗⠶⠶⠾⠿⠿⠿⣯⣥⣴⣿⠤⠴⠦⣀⡿⠉
⡿⢏⣹⣾⣟⣿⡟⠙⠃⠛⡷⠯⣿⡀⡛⣿⡿⢿⣶⣬⣿⠇⣀⣿⠿⣿⡯⠀⠰⠀⠀⢇
⡴⠏⢁⣽⠿⠛⢲⡁⠀⠤⠄⠠⠀⢀⣠⣿⠛⠧⢛⣯⠛⢤⣆⣿⠀⣿⡟⠀⠀⠀⠁⢸⠀⠀⢀⣀
⠓⣶⠟⠁⠈⢙⣶⡏⣀⠂⠐⠂⠘⢛⣿⣿⣄⠛⠀⠃⣀⣠⠟⣿⣿⡿⠄⠀⠀⠀⠀⢸⠀⠀⠂⠀⠁
⡼⣟⣠⣤⣰⣶⣟⣱⣤⣀⠀⠒⢶⣾⣽⡧⣿⡶⠁⠂⠉⠢⠀⣿⣿⡗⠃⠀⠀⠀⠀⠈⡀
⣿⣿⠤⠒⣛⠹⠿⣧⡷⢿⣲⢦⡻⣿⣿⡇⠁⠀⠂⠀⠈⠉⠈⣻⢿⡇⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⡀
⣟⣢⣷⣿⣿⣝⠞⢻⡶⢌⣭⡊⣉⢻⣿⠧⠛⠘⠩⠄⠉⣉⢩⡿⠛⠻⢿⠧⠄⠀⠀⠀⣿⡀⢈⡠⠛⡇
⢉⣼⣿⣿⣧⣠⣞⠷⢤⣤⣬⣷⣽⣿⡻⢷⣀⠈⠀⠀⠀⠀⢸⠀⠀⢹⠙⠉⠀⠀⠀⠀⢻⠀⠁
⣿⣿⣭⣿⣭⣿⣿⢷⣿⣿⣿⣿⡛⠛⣧⡀⠀⠀⠀⠶⢦⣶⣾⣧⣤⣼⣦⣤⣤⣠⣿⣷⣿⣴⣦⣄⠀⠀⡀
⣿⣵⣾⣿⣿⣾⣿⠟⡿⣏⠙⣉⣹⣿⣿⠁⠀⣠⣀⣰⣾⣾⣿⣿⣯⣾⣿⣿⣿⡿⣿⣿⢻⡇⣹⣿⠳⣼⡇⣀⢀⣀⣀⣤⣀
⣿⣯⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⢿⡿⣤⣸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣏⣾⣧⣷⣿⣾⡝⣷⡿⢾⣧⠽⣧⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣿⣾⡏⣦⣈⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣻⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡻⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠘⣋⣀⣔⣺⣿⠿⣿⣿⣾
⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣯⣙⣻⣿⣫⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣏⠹⣿⡿⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣮⣿⡟⠟⠷⢪⣿⣷⣷⣿⣿⣿⣿⣿⣯⠛⢻⣷⣿⣿⣯⣼
⠛⠋⠶⠻⠿⢿⡷⣿⣿⣏⠻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡉⠩⣿⣿⣿⣷⣄⡈⢻⠟⢬⡝⠛⢿⣿⣿⣿⣿⣦⣮⢻⣿⣿⣿
⠄⠀⠀⠀⢀⡘⠦⠈⠉⠛⠳⣿⣿⣿⡿⠥⢼⠿⣿⡿⠉⠽⢃⣈⣹⡟⠋⠛⢻⡃⠀⠀⠀⠀⠸⡇⠙⠻⠂⠉⣿⢸⣟⣯⣬
⠆⠈⠓⠂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⢸⣷⣤⣶⣿⣿⣿⣷⣷⣶⣼⣷⠂⠀⠀⠀⠀⣧⠀⠀⠀⠈⠉⠁⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣿⣿⠻⠇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠓⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣟⣶⡷⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠛⠉⢹⣟⣋⣫⣾⣶⣿⡟⠿⠃⣠⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡿⠁⠁⠀⢀⠀⢿⡿⣿⣿⣿⠛⠉⢻⣿⣿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢠⠢⡈⠀⠀⠻⣿⣑⣰⣼⣿⣾⣿⣿⢳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⢀⡔⢻⣁⣀⣨⣝⠒⣦⡙⢷⣽⣿⣿⣿⣿⠗⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⣰⢛⣶⣿⣿⣿⣿⣿⣿⣷⠙⣦⡛⠿⣯⣿⡟⣤⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣽⢿⠁⠀⣴⠗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⣤⡀⢉⡗⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⡟⣿⣽⣹⡅⣯⢹⣳⣼⠟⣫⢄⡘⠹⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⠿⢋⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⢿⣦⣾⣾⣿⣿⣿⣿⣿⣵⡟⠀⠀⢎⠃⠀⠀⣈⢿⣿⣿⣿⣿⣿⣿⡿⣪⣿⠟⡁⠶⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⣿⣾⣿⣿⣿⣿⣟⣻⣿⣿⠏⠀⣀⣳⣃⠀⠀⠀⠈⠷⣍⣟⣛⣻⡋⣀⣽⡿⡻⠷⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣵⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⣾⢿⣿⣟⣵⣽⡆⢀⢦⣄⣿⣿⣿⣿⣿⣿⢕⡉⠋⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣉⠭⠥⠴⠶⢿⣿⣿⠋⣏⣽⣾⣾⣿⣿⣿⢏⡔⢦⣿⣿⣿⣿⣿⣿⠟⠙⠚⣾⠷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠗⠋⠀⠀⠀⣠⣾⣿⣯⡴⠿⣛⣽⣏⣤⣶⣿⣿⣿⣿⣿⣏⠛⠷⠏⠁⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢀⢜⣿⣿⣿⣿⠶⢿⣿⣿⣿⣿⣿⣿⠿⠙⠛⠋⠀⣀⣤⣴⠶⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⠛⠋⠉⠛⢯⣻⢿⣿⠟⠋⠀⠀⣀⣤⣶⣿⣿⣿⡿⠍⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡵⢛⣁⠨⠧⡀⠀⠀⣀⠻⣧⡉⠳⣄⣶⣿⣿⣿⣿⣿⣿⣿⣟⠤⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡶⢏⣹⣇⠀⣘⣶⣤⠈⠀⠈⠙⡟⣹⣿⣿⣷⣿⣿⣿⣿⣿⠯⠍⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡡⢂⣼⣿⣿⣷⣾⣿⣿⣷⣄⠀⢐⢁⣿⣿⣿⣿⠼⣿⣿⣿⡟⢁⣰⡿
⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⣁⢴⣿⣿⣿⣿⣿⣿⠿⠋⡄⢈⣠⢏⣾⣿⠟⢹⠇⣸⣿⣿⣟⡫⣽⠟
⠀⠀⠀⠀⠀⠀⢊⠝⠠⠞⠛⡱⣫⣿⣿⣿⣿⠟⢁⣤⣴⠃⠈⢠⡿⠟⠁⣠⢟⣴⡿⠟⣛⣽⠞⠁
⠀⠀⠀⠀⠀⢠⡎⠀⠠⠔⠀⠀⠀⠉⠋⠀⢀⣴⣿⠟⠇⠀⠀⠀⠀⣀⣴⣿⢿⣻⡵⠞⠋⠁
⠀⠀⠀⠀⠠⣿⠀⢈⡖⠀⠀⠀⠀⢀⠠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉
⠀⠀⠀⢀⠀⠂⢀⠟⠀⣡⡤⠴⠚⠁⠘⣤⠶⠋
⠀⠀⠀⢀⡄⠀⡴⠊⠋⠁⡀⢀⡤
⠀⠀⠘⡿⠁⣀⣠⣴⠶⠋
⢀⠀⣰⠴⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠑⡀⣉⠀⠀⠀⠀⠀⠀⠀⠀⣈⢀⠊⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⡀⠀⠉⠁⠀⠀⠀⠈⠁⢀⡎⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣄⣀⠀⡼⠁⠈⢇⠀⢀⣠⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⣶⣶⠤⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⠃⠀⠊⠎⢁⡈⡀⠰⠀⠐⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡤⠄⠠⠀⠀⢤⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⣴⡇⠀⠀⠀⠀⢸⣤⠠⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠒⠒⠒⠂⢺⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡟⠀⡇⠀⠀⠀⠀⢸⠀⢻⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡽⠀⠚⡏⠀⠈⠉⠀⢹⠛⠁⢯⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠴⡫⠃⠄⢀⡇⠀⠀⠀⠀⢸⡀⠀⠘⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠊⡠⠐⠀⠈⡏⠈⠉⠀⠁⢸⠁⠈⠂⢄⠑⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠊⡠⠊⠀⠀⠀⢀⣇⠀⡀⢀⠀⣸⡀⠀⠀⠀⠑⢄⠑⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⢠⢏⡔⣁⢀⣀⡀⣀⣀⣀⣀⡰⠃⠀⢰⡆⠀⠘⢆⣀⣀⣀⣀⣀⣀⣀⣈⢢⡹⡄
⠀⠀⠀⠀⠀⠀⠸⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⢸⡇⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠴⠀⢀⠀⢀⠀⡀⠀⠀⢸⡇⠀⠀⢈⠀⡀⠀⡀⠀⠦⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠲⠒⠂⠏⠹⣒⣒⣿⣟⣖⣒⡋⠸⠒⠒⠖⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠻⠿⠟⠛⠿⠿⠃⡀⠀⠀⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠒⠚⠓⠒⠺⠂⠀⠀⠀⠀⠀⠀⠀⡗⠒⠚⠓⠒⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⢆⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡀⠊⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠂⡞⠀⠀⠀⠀⠀⠀⠆⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⣿⡗
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡇⠀⡀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢈⡷⠾⠷⣒⠒⠿⠷⡿⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠂⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠳⠂⠉⠁⠉⠐⡲⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠼⢄⠀⠀⠀⠀⠹⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢡⣮⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⢸⣇⠀⠻⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠆⢀⣨⠿⠀⠀⠙⡿⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⠊⠀⠈⣱⣤⡀⠀⠀⢛⣦⠈⢦⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢠⡏⠀⠀⠘⣻⡍⠀⠀⠀⠀⠹⣷⠀⠁⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣴⣄⡊⠀⢠⠄⠾⡟⣀⠀⠀⠀⡄⠘⠿⢀⣤⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢨⣿⣿⣟⣷⣶⣦⣬⣥⣭⣤⣤⠤⣤⣶⣾⣬⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⢸⣿⣿⡷⣿⠿⣻⣿⠍⠏⢥⣯⣉⠂⠈⠐⣧⣬⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹⣿⣿⠛⣿⡟⠀⠀⠀⠀⠀⠀⠙⢷⡀⠈⣹⣦⣽⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⣿⡿⣦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠐⢈⢋⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣿⣧⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡁⠠⣜⣻⣿⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠹⣿⣿⡐⣳⡀⠀⠀⠀⠀⠀⠀⠀⡨⠽⡠⢝⡞⢿⠙⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢻⣿⣗⠈⡳⣦⣄⡀⠀⠀⡠⠾⠍⠀⠈⠀⢨⣾⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣔⢘⢻⠿⠞⣿⣿⣯⣤⣀⡄⠀⠐⠂⠀⠀⢀⣿⣿⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⢸⣽⣖⣢⣿⣿⣿⣿⡛⠛⣃⡀⠀⣤⣽⣿⣯⣝
⠀⠀⠀⠀⠀⠀⠀⡠⢐⣡⠆⢳⠈⣿⣿⣙⡹⣛⣍⠙⣿⠶⠀⠉⣁⣤⣿⡿⠀⢶⣌⠂⢄
⠀⠀⠀⠀⠀⠀⢊⣜⠳⠁⠀⠈⠂⢸⣿⠏⠁⠋⠁⠀⣿⠉⠉⠉⢐⣿⣿⠃⠀⠐⢻⣿⣦⠐⠄
⠀⠀⠀⠀⡰⠀⣷⠀⠀⠀⠀⢠⠀⣤⠏⢀⠖⠃⠀⡀⢻⠀⠀⣠⣾⣿⡏⠀⠀⠀⠈⠑⢱⣇⠈⢆
⠀⠀⠀⢠⠁⡰⡎⠀⠈⠀⠘⠃⢀⡏⢀⣼⠀⠀⣾⠃⢸⠀⢰⣾⣿⡿⠀⠀⠑⠀⠀⠀⠀⠻⠗⠈⡀
⠀⠀⠀⠈⠠⢢⠀⠀⠀⠀⠀⡀⢸⠀⣰⠇⢠⠄⠀⠀⢸⡃⣿⣿⣿⠃⠀⡀⠀⠀⠀⠀⠀⠠⡀⠀⠃
⠀⠀⠀⢨⢈⡅⠀⠀⠀⠀⣠⠃⡠⠀⠟⢀⡞⢀⡠⢀⠼⠃⠛⠟⡛⡏⠐⢌⡳⢄⣠⡀⠀⠀⣩⠇⠄
⠀⠀⠀⠈⡀⠞⠀⠀⢀⡼⠃⠂⠀⠐⡁⠈⠠⣿⡿⠶⠀⠛⠛⢛⣁⣧⠀⠀⠘⢮⠹⣧⠀⢀⡗⢀
⠀⠀⠀⠀⠡⢘⡀⢨⣾⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡛⠻⣿⣿⣿⣯⣷⠀⠀⠈⠀⢹⠀⢨⠃⡌
⠀⠀⠀⠀⠀⠀⢡⠀⠏⠀⠀⠀⠠⠀⠀⢰⠿⠿⣿⣿⠟⠛⠛⠛⢿⣿⡉⣇⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⡄⣾⣿⢾⣿⣿⠃⠀⠀⣘⣿⣿⠥⠙⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠢⠐⠀⠀⠀⠀⠀⠆⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣭⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣫⣶⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⡾⠉⠀⠀⠉⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣿⡁⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣿⣿⣿⣿⣧⣐⠀⠀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣾⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣷⣄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠋⢀⡬⠙⢿⣿⣷⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⢀⣴⣿⠁⠀⠀⣙⠻⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢋⠀⣰⣿⣿⠇⠀⢀⣼⡟⢀⡎⠻⠇⠀⠈⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣵⢏⣼⣿⣿⡟⢠⣦⣾⠟⣠⣿⢳⡆⠀⠀⠀⠀⠹⣿⣿⠟
⠀⠀⠀⠀⠀⢠⣿⣿⣫⣾⣿⣿⣻⣿⠟⣰⣿⡿⢋⣴⣿⠏⣼⡇⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢟⣵⣿⣫⣾⡿⢋⣤⣾⣿⢏⣼⣿⠁
⠀⠀⠀⠀⢠⣿⣿⡿⢛⣵⣿⣿⣿⠟⣋⣴⣿⣿⠟⣡⣾⣿⠃
⠀⠀⠀⠀⣼⡿⣫⣴⣿⡿⢟⣩⣴⣾⣿⠿⢋⣥⣾⣿⠟⠁
⠀⠀⠀⠀⢏⣾⣿⣿⣯⣾⠿⠟⣋⣡⣴⣾⣿⡿⠛⠁
⠀⠀⠀⣴⣿⣿⡿⠟⣉⣤⣶⣿⠿⠿⠛⠋⠁
⠀⠀⣼⣿⡿⣫⡴⠛⠋⠁
⠀⣼⡿⠫⠊⠁
⢰⠟
⠏
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠐⠒⣂⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠤⣶⡆⠀⠀⠀⠀⠠⠖⢆⠀⠠⣤⠤⠀⠀⠒⠒⠀⠀⠄⠀⠐⠂⢀⠈⠉⠉⣄⡘⠉⠁⣠⣤⣶⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⢻⡃⢀⣀⣀⠀⠄⠀⢼⡄⠀⠘⠲⠦⠀⠀⠁⠀⢀⣀⢀⡠⠄⠀⠑⠀⠀⠀⠀⠀⠀⠋⠀⣀⣠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⡷⢷⣮⡁⢠⡉⠀⠀⠀⠀⢀⡈⢀⠀⠀⠀⠀⠀⣂⡉⠁⠀⠀⠀⠀⠀⠀⢀⣁⣤⣤⠴⠖⠞⣛⡛⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢣⣾⡟⣁⠸⡷⠀⣼⠧⠀⠀⠁⠈⠃⠉⠀⠀⠙⠹⠂⠐⢀⣉⣤⣤⡶⠚⠙⠋⠉⢁⠀⠀⠀⠈⠙⠀⠠⠔⢀⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⢳⣿⣾⡀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡿⣛⣉⠩⢧⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢹⣎⡠⣤⠀⣀⡀⠤⠴⠂⠛⠿⢿⡽⢋⠲⠯⠷⠒
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣘⣫⠖⠛⣏⢠⠴⠶⠊⠉⠑⠀⠀⠘⠂⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠂⠈⠑⠉⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠘⣿⣧⡈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣽⣿⠷⣀⣿⣿⣟⣄⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⣼⣿⣟⣨⠉⣽⣿⣿⣦⠻⣿⣏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠛⣱⣿⡿⠿⣁⣼⣿⣿⣿⣿⣑⢌⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠻⣿⣿⣟⢿⣋⣩⡿⣿⣿⣿⣿⣿⣦⡽⠟⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣠⠍⠉⠛⠛⠚⠛⠛⠛⠛⠯⡉⠉⢛⡀⠀⠰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⠔⣁⣠⠄⢚⣛⣌⣛⣩⢿⣗⢾⣝⡊⡟⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣫⠁⣠⣿⣿⣿⣿⣿⣿⣧⣈⢿⡾⣅⠛⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢘⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣮⣹⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢾⡳⢭⡆⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡾⢭⣇⡄⣦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠸⣶⣎⠛⠿⣿⣿⣿⣿⣋⣬⣿⣿⣿⡷⠉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⣐⣋⡀⠀⠀⠐⠂⠀⠈⠻⣿⣿⣿⣿⠃⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡂⠏⢹⢋⠀⠀⠀⠀⠸⠿⣷⣾⡿⠿⠁⠀⢰⡋
⠀⠀⠀⠀⠀⠀⠀⣀⡴⡾⣻⡜⣧⡀⠰⠾⣇⡴⣲⣶⢂⣶⣦⣭⡿⠟⠁⢠⣿⢍⡷⣦⣀
⠀⠀⠀⠀⠀⢠⣾⢽⣌⣾⣿⣷⣻⡄⠀⣾⣿⣞⣽⣿⣦⣤⣵⣿⣖⠀⢀⣿⣿⣷⡄⡀⢝⣷⡄
⠀⠀⠀⠀⣰⣿⣻⣿⣿⣿⣿⡟⣿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⣾⣿⣿⣿⣿⣾⣕⢡⢿⡄
⠀⠀⠀⢠⣿⡿⣦⣿⣿⣿⣯⣼⣿⣾⣿⡕⣾⡿⠃⣿⣿⣿⣟⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⡅⢈⣻⡀
⠀⠀⠀⢸⡷⣻⣾⣿⣿⣿⣿⣿⣿⣿⡝⣿⡟⣿⣾⣿⣿⣿⡄⠀⢠⣿⣿⢿⣿⣿⣿⣿⣿⣤⣀⢸⡇
⠀⠀⠀⢸⣯⣽⣿⣿⣿⣿⠟⣾⢿⣯⢶⣿⢡⣿⣿⣷⣿⣧⣀⣀⣼⣾⣽⣷⣿⣻⡿⢿⣿⣿⡯⣭⡇
⠀⠀⠀⠘⡷⢾⣿⣿⡿⢃⠞⠁⢸⣛⣿⣿⡿⣱⣯⢯⣽⣭⣭⣥⡼⠙⣿⣿⣿⡿⣦⠘⣿⣿⡛⣾⠃
⠀⠀⠀⠀⢻⣋⣿⡏⢁⠏⠀⠀⢸⣭⣿⣿⠝⠀⠀⠀⠙⠛⠃⠀⠀⠱⡈⣿⣯⡇⠘⣧⢿⣿⣬⡟
⠀⠀⠀⠀⠈⢯⣹⣷⡜⠀⠀⠀⢸⣺⣿⣿⣐⠀⠀⢀⣙⣛⣓⣂⣀⣀⢶⠸⣿⡇⠀⢻⣾⡷⡾
⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠨⡽⣿⠃⢘⡋⠈⠉⢹⣿⣿⣿⡅⠀⡼⠀⢿⡇⠀⢸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⣷⡿⠀⠈⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠉⠙⣿⡉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⢀⣼⠷⣦⣼⡇⠀⠀⠀⠀⠀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣴⠟⠁⠀⢀⣠⣤⣤⣄⣀⣴⠟⠁⠀⠀⣹⡇⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⠉⠉⠉⣹⡿⠁⠀⠀⣰⠟⣡⣤⣤⡍⢻⣇⠀⠀⠀⢀⣿
⠀⠠⣶⡆⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣿⠀⣤⣭⠉⠀⠀⣿⠀⠀⠀⣼⠇
⠀⠀⠈⠀⠀⠀⠀⢠⡿⠁⢀⣀⡀⠀⢰⡟⠀⠀⠀⠀⠀⢹⣦⣀⠀⠀⣀⣼⠏⠀⠀⣼⠏⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠛⠉⠛⢻⣿⣦⡀⠀⠀⢀⣴⠟⠉⠙⠛⠛⠋⠁⠀⢀⡾⠋⠀⠀⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠻⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢠⡶⠿⢶⡄
⠀⠀⠀⣴⢶⡄⠀⠀⠀⠀⠀⣀⣀⣀⠙⢷⣄⠈⠻⣧⡀⠀⠀⠀⣀⣤⡾⢿⡅⠀⠀⠀⠸⣧⣀⣼⠇
⠀⠀⠈⠻⠾⠃⠀⠀⢀⣴⠟⢋⣿⠋⠀⠀⠙⢷⣄⣈⣿⣦⠶⠟⠋⠁⠀⢸⡇⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢸⣇⣀⣤⣾⡇⠈⠉⠉⠈⣿⡀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠈⠉⠉⢁⣾⠃⠀⠀⠀⠀⣿⠃⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣤⣴⠟⠁⠀⠀⠀⠀⣰⣿⣠⡴⠞⠋⠀⠀⠀⠀⠀⢰⣟⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠗

⣿⡿⠿⠿⠷⠶⣶⣶⣦⣤⣤⣄⣀⡀
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢷⣶⣤⣄⣀
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢶⣦⣄⡀
⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄⡀
⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣄
⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄
⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠈⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⠛⠛⠛⠛⠛⠛⠛⠿⢿⣧
⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⢻⣿⣷⣄⡀⠀⠀⣀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⢻⣯⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠻⣷⣌⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣀⣀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⠛⢷⣦⡙⢿⣦⡀⠀⠀⠀⢀⣴⣾⣿⣟⡛⠛⠛⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠙⢿⣦⣉⠻⣷⣤⣾⠟⠉⠙⠻⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠈⠻⣷⣌⢻⣧⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠈⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠻⢷⣤⣾⠏⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠛⢿⣦⣄⡀⠀⢠⣿⡋⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⡀⠈⢿⣿⣏⠉⠉⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⢻⣷⣤⡀⠀⠀⠈⣿⣿⣿⣷⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣷⡀⠀⢸⣿⣿⣿⣷⣤⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⡀⠀⠀⢿⡇⢻⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣼⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠙⠛⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠈⢿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠀⠉⠻⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⠀⠀⠀⠀⠀⠀⠸⠿⣷⣰⠆⠀⠀⣰⣶⣿⠂
⠁⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣶⣿⣿⣿⣷⡶⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠻⢿⣿⣼⣿⣿⣿⣫⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⡀⠙⢿⣿⡿⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠶⠶⠤⣤⡀⠹⣦⣸⣿⣷⠏⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⣿⣦⣦⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣦⣿⣿⣿⠃⢀⠀⣠⡟⠁⠀⠀⠀⠀⠀⣀⠀⠀⡇⢀⣠⣾⣿⡿⢻⣿⣆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⣿⣿⣟⢠⣿⡼⠋⠀⠀⠀⠀⠀⠀⠻⢿⣷⣄⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⡿⢿⣿⡿⠏⠙⠛⠛⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠘⣿⣿⣿⣿⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⠀⠉⠀⣠⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢸⣿⣿⡇⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣰⣿⣿⣿⣧⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣼⣟⡏⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣴⡿⠿⡿⠟⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡿⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢹⣇⣁⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠀⠀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⢸⣿⠈⣿⡿⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⣴⣶⣠⣾⣿⣶⣇⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠘⣿⡄⣿⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⠿⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣽⣿⣿⡇⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣾⣿⣿⣿⣿⣷⠄
⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣿⣿⣿⣇⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣿⣿⣿⣿⠃⢀
⡇⠀⠀⠀⠀⠀⠀⠘⠿⣆⡀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠁⢀⣿⣿⣿⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⣿⣿⠿⠛⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⢸⣿⠃⠀⢀⡄
⡇⠀⠀⠶⣦⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⢹⣧⠀⣿⠀⣠⣿⠁⠀⣄
⡇⠀⠀⣠⡄⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣿⣷⣿⣼⣿⠇⠀⡀⣌
⡇⠀⠀⣰⢣⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠁
⡇⠀⠀⠛⠛⠀⠀⠀⠈⢻⣿⣿⣿⣿⡧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠘⣿⣿⣿⡇⢠⣾⠃
⣦⣶⣶⣶⣴⣶⣶⣶⣶⣶⣾⣿⣶⣦⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡄⢈⠀⠀⠀⠀⣿⣿⠀⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣷⠨⠀⠀⣤⣌⣿⣿⠠⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢸⡇⠀⡀⠀⠀⣿⣿⡇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣸⡇⠀⣴⠖⢶⣿⣿⡧⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣯⠀⠀⠀⠐⣿⣿⣯⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⣿⣿⣴⠀⠀⢰⣿⣿⣿⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⠀⠀⢨⣯⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣿⣿⠋⠀⠀⢸⣿⣿⣿⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡟⢸⠀⠀⢰⡏⣿⣿⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡾⠋⠀⣾⠀⠀⢸⡇⣿⡏⠳⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⢀⣿⠀⠀⢸⡇⣿⡇⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢀⡀⠀⠀⣼⠷⢤⣤⣬⠧⢿⣷⡀⠀⠀⢀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠉⠁⠀⢴⡏⠀⣾⠇⡟⠀⣿⣿⣷⡄⠀⠉⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠀⢀⣀⣀⣸⣇⣰⣿⠇⣿⣠⣿⣿⣿⣏⣀⠀⠠⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⣿⣷⣟⣻⡆⣿⣟⣾⣿⠋⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠐⣿⡇⠉⠉⢱⠉⠉⠁⣿⠀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⢀⣿⡷⠀⠀⠀⠀⠀⠰⣏⠀⣸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠉⠹⠂⠀⠀⠀⠀⠀⠀⠪⠉⠉⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠯⠭⠭⠭⠭⠭⠭⠭⠭⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣉⣁⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⢚⣛⣛⣉⣭⣭⣭⣤⡤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠬⣭⣭⣭⣝⣛⣓⠶⠦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⠴⢞⣫⣥⠴⠶⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⢰⣖⣲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣈⠉⠉⠛⠲⠦⣭⣙⠳⢦⣀
⠀⠀⠀⢠⡴⣫⡵⠚⠉⠁⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣩⣭⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠘⠳⠞⠋⠀⠀⠀⠀⠀⠀⠉⠛⢦⣝⠳⣄
⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⠐⠯⠴⠟⠁⢀⣠⣶⣾⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣶⣦⣄⠀⠀⠀⠀⠀⢀⣀⡀⠀⠙⢧⣽
⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠛⢿⣷⡄⠀⠀⠐⠿⠾⠟⠀⠀⠘⣿
⠀⠀⠀⠈⢷⣀⠀⠀⢰⣋⣹⠇⠀⠀⠘⣏⠀⠀⠀⢀⣤⠶⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⢀⠉⠉⠙⠳⢦⡄⠐⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠠⠤⠀⠀⣙⡳⣄⣀⣿⣄⠀⢠⠀⠀⢀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⠠⢿⣤⡴⠋⢰⣶⡦⠀⣀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⣬⣿⣃⣀⣉⡿⠀⠁⢹⠀⠐⢾⡆⠀⢸⡇⠀⠐⠒⠒⠀⠀⠀⠀⢸⣇⣀⣤⡤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⢸⠀⠀⢸⠇⠀⢸⠇⠀⠀⠀⠀⠀⡇⠀⢠⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠈⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠿⠀⠀⢸⡇⠀⠂⠀⠀⢸⠀⠀⠀⡇⠀⠀⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢸⡇⠀⠀⠁⠀⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠀⠀⢠⡀⠀⠀⢸⠀⠀⠸⡇⠀⠀⡄⠀⢻⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⢸⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿
⠘⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠋
⣀⣀⣹⣤⡀
⢻⡟⣿⢿⣷⢆⡂⢀⡀⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡶⣷⣿⣾⣷⣼⣤⣾⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⠀⢀⣀
⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⣠⣴⣭⣸⣶⣶⠿⠿⠦⢤⡀
⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣭⡀⣼⣿⠤⢾⡿⠁⠹⣇⢰⠀⠀⢳⡀
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⠀⢿⣼⣀⠀⠀⢷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣼⣂⣀⣘⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⡛⠓⠒⠂⠐⠆⠘⣟⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⡒⣿⣿⣟⠀⠉⢀⣤⣾⣿⣿⣿⣿⣶⣤
⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡏⠀⠀⣼⠃⢹⣻⣻⣿⣛⣿⣿⣿⢿⣿⣿⣿⡾⠶⠶⠶⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠶⠶⠶⠶⠶⢿⡟⠋⠉⠘⣿⣿⣿⣿⣿⣿⣿⣿
⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⢻⠀⠀⠀⠀⠀⠀⢧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢿⣿⣿⣿⣿⠿⠭⠍⠛⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⡇⠀⠘⡆⠀⠀⠀⠀⠀⠈⢇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⣸⠃⠈⠉⠉⢸⡏⠀⠀⠀⠀⠀⢻⣿⠀⣧⠀⠀⢣⠀⠀⠀⠀⠀⠀⠘⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⢠⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣏⢻⣿⣯⣫⡅⠀⢸⠃⠀⣀⣀⣠⣤⣤⣾⣷⣦⣿⢲⣧⠈⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡆⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢿⣿⡇
⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢓⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡇⢸⣿
⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣿⣷⣁⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠉⠁⠸⣿
⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⢃⣛⣫⠙⠛⠛⠛⠛⠻⢟⡛⠋⠁
⠀⠀⠉⠉⠙⠀⠙⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⢀⣀⣠⣿⢿⠿⠿⠻⠂⠀⠀⠀⠀⠀⠙⠢⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡖⠛⠉⠉⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠻⣄⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣴⠶⠶⢦⡄⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠓⠲⠶⢶⡏⠀⠀⢀⣤⡶⠶⠖⣤⡿⠦⡤⠾⠃⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⣼⠃⠀⠀⣎⠋⠀⠀⠀⠈⡞⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⣄⣀⢰⡏⠀⠀⠀⠡⣧⡀⠀⢀⡠⡹⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣴⠃⠀⣠⠞⣡⠏⠉⠋⢀⣠⣤⡀⠀⠈⠓⠒⠚⠋⠀⠀⠀⣠⠞⠁
⠀⠀⠀⢀⡼⠁⢀⡼⠃⠠⣯⡶⣴⠚⠉⠀⠀⣽⠀⠀⠀⠀⠀⢀⢀⡴⠞⠁
⠀⠀⢀⡞⢁⡴⠋⠀⠀⣴⠛⠷⣌⠳⣄⠀⣰⠃⢀⣤⠴⠖⠛⠉⡏
⠀⠀⠘⠶⠋⠀⠀⠀⣴⠛⢦⡀⠈⠳⣌⠻⣇⠀⢈⣧⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⣄⠙⢦⣀⡼⠿⠵⠚⣩⠞⠁⠀⠀⢀⣸⠄
⠀⠀⠀⠀⠀⠀⣰⠏⠀⣠⠼⠳⠊⠉⠀⠀⣠⠞⠁⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠐⢧⡴⠛⠁⠀⠀⠀⢀⣤⠞⠁⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣹⣏⣛⣽⣯⣥⣉⣟⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣭⣭⣽⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠟⠛⠛⠿⢿⣿⣿⣿⣮⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣴⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⠒⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠙⠿⠻⠿⣫⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⣀⣠⣴⣶⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠁

⠀⢰⡄
⠀⠀⠇
⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀
⠀⠀⠀⠈⣆⠀⡀
⠀⠀⠀⠀⢻⡄⢻⡇⠀⡀⢀⢀⣲⣦⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠘⣿⣆⢻⣰⣿⢿⠟⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⢠⠆⠤⢴⠯⣌⠒⠒⠒⢦
⠀⠀⠀⢰⢢⢻⡿⢿⡻⣿⣇⢀⣿⣿⣿⣿⣿⣿⣧⣄⠀⣰⠃⠀⢠⠇⠀⠸⡀⠀⠀⠘⡄
⠀⠀⠀⢠⣾⠸⣷⣬⣟⣻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⡾⠀⠀⠀⣇⠀⠀⠀⠹⡀
⠀⠀⠀⠈⢿⡇⢻⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⣿⡄⠤⠀⠠⣷⡀⠀⠀⠀⠀⠀⣠⣶⣶⣆⣀⡀
⠀⠀⠀⠀⠀⣧⠸⣿⡙⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠀⠰⠂⠈⣷⣄⠀⠀⠀⠁⣰⣿⣿⣿⣀⠐
⠀⠀⠀⠀⠀⢿⡇⢿⣷⠻⣿⣿⣿⣯⠙⠋⠀⠀⡎⠁⠙⠏⣿⠻⠟⠉⠙⠀⣷⢸⠀⠀⠀⠀⣻⣿⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠈⣿⠘⣿⣳⣿⣿⣿⣦⣤⣤⣤⣼⣧⣦⣴⣶⣷⣶⣶⣶⣤⣤⣷⣼⣧⣀⣀⣀⣈⣹⡿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠄⢷⠀⠀⠀⠀⠀⢣⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣷⣸⣿⡇⠀⠀⠀⠀⢀⠏⠈⠉⠁⣸⠃⠀⠀⠤⢸⣿⡇⡇⠀⠘⡀⠀⠀⠀⠀⠈⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠀⠀⠀⠀⠎⠀⠁⠀⢠⠏⠀⠀⠀⠀⠀⢿⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠘⡀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⡘⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⢰⠁⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⣶⠀⣼⠀⠀⢸⡇⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣄⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⡷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡅⠀⠀⠀⣸⢃⠀⡀⠀⠀⢀⣤⣼⡗⣞⣿⣧⣄⠰⡗⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣄⠀⢰⣇⣼⣾⣷⣾⣿⣿⣿⣽⣿⣭⣿⣿⠶⠲⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣯⣝⣻⣿⡿⠿⠿⠿⠛⠿⣿⣇⣰⣦⡄⠀⠀⠀⠀⠐⠂⠘⢻⡟⠋⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠿⢿⠾⣿⠿⠟⠛⠋⠀⠀⠀⣀⡀⠀⠚⠛⠛⠻⢿⣟⠛⠁⡀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠟⠛⠂⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠒⠂⣀⠐⣠⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠤⠐⠊⠁⠀⠀⠀⡀⠀⣈⡉⡍⠿⠿⢯⣴⣶⣠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠾⠇⣩⣤⣶⣾⣷⣾⣿⣊⠛⢛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠋⠁⠀⠀⣀⣠⣾⣾⣿⣿⣷⡿⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠄⠀⠀⠀⠘⠶⣮⣁⢀⣄⣠⣴⣤⣶⣷⣿⣿⣿⣿⣿⠋⠀⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⡄⠀⢀⣠⣤⠄⣊⠻⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣺⣿⣿⡫⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠐⠻⠿⠿⠿⣛⣛⣧⣬⣍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣸⣿⣿⡇
⠀⠀⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇