ML Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⡄⠹⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠘⣿⣆⠹⣿⣿⡟⢠⣶⡆⢸⡇⣴⡆⢸⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢀⠈⢿⣆⠙⠟⢠⣿⢿⡇⢸⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣧⠈⢻⣧⣰⣿⠃⢸⡇⢸⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⠀⡀⢻⡿⢁⡀⢸⡇⢸⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢸⣿⠀⣿⡄⢀⣾⡇⢸⡇⢸⡇⠙⠁⠘⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠸⠿⠀⣿⣿⣿⣿⡇⠸⠇⢸⡇⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠣⢤⢄⠀⠀⠀⠀⠉⠂⢠⣤⠀⠀⠀⣠⠠⠶⡂⣈⣱⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠸⡟⠀⠀⠀⠀⠄⣠⢘⠃⠀⠁⠀⠀⠀⠀⠀⠉⢉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡘⢃⠀⢀⣀⠴⠂⠄⠠⠀⠀⠀⠶⠲⠂⠆⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠨⠄⠀⢐⠀⠀⠀⠀⠀⢀⠀⠉⢌⠶⡌⠡⠖⠰⠊⡵⠀⠀⠀⢄⡠⠄⠁⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⠅⠈⠃⢀⡀⠀⠀⠐⠄⠀⠓⡄⠃⠀⠈⠐⢈⢃⡾⠆⠐⢂⣠⣴⡀⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠀⠀⠀⠀⠀⠀⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⠈⠀⠀⠀⠀⠀⢀⡆⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⢹⠆⢀⡀⠀⠀⣴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡯⢀⣠⣠⡀⠀⣴⠼⡤⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠁⠁⠀⠀⠙⣤⠊⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⡇⠀⠀⠀⠠⣠⠴⣶⡀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄⠀⠀⠀⢨⠏⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡄⠀⠀⢀⠄⣤⠄⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠂⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⣄⠀⠀⠐⠀⢀⣦⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡦⠶⠟⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠵⢀⠉⣹⡿⢶⢀⡈⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⢂⡀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣤⠀⠁⣠⡀⡞⠀⠀⢡⠍⢘⠁⢳⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠋⠀⣀⡀⢀⠀⠐⠛⢢⡗⠂⠀⠀⣀⠀⠀⡛⢳⡤⠂⢀⣾⠛⣹⣷⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠋⠃⠀⠀⠀⠀⠉⠀⠑⠀⠀⠀⢍⠉⠀⠨⣽⡿⠯⢽⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠄⠀⠌⠀⠀⠀⠊⠒⣀⠐⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣦⠀⠀⠄⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠳⢦⣄⡉⠀⠀⠀⠀⠀⠀⠀⣨⣻⣛⣥⣶⠿⠀⠀⠰⠾⠛⣁⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠳⢦⣌⡙⠣⠀⠀⠀⠀⠀⢠⣝⡻⣟⣯⣶⡿⠃⠀⢠⡾⠟⣉⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠙⠶⣤⣈⠛⠷⣆⠀⠀⠀⢠⣬⣛⡿⣟⣫⣵⡾⠇⠀⢀⡶⠟⢋⣡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠓⠶⣤⣉⠛⠶⣦⡀⠀⠀⣶⣭⣛⠿⢿⣫⣵⣶⠟⠀⢠⣶⠾⢋⣡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠳⢦⣄⠙⠻⢶⣤⣉⠀⢴⣮⣝⡻⠿⠻⣛⣭⣶⠿⠂⢠⣴⠾⠛⣉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠙⠲⢦⡄⠈⠳⢶⣬⣙⠻⢷⣮⣝⡻⠃⠘⣛⣩⣴⡾⠃⢈⣤⡶⠟⣉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠙⠶⣤⡀⠀⠐⣦⣌⡛⠿⣶⣭⣛⠋⠀⠀⢟⣫⣵⡾⠟⢈⣥⡶⠟⢋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠓⠦⣄⠀⠀⠀⠀⣍⡛⠷⣶⣭⠋⠀⠀⠀⢿⣋⣥⣶⠿⢈⣡⣴⠞⢋⣁⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠳⢦⡄⠀⠀⠀⠀⠉⠻⢷⣦⡍⠀⠀⠀⠀⠸⣛⣭⣶⠿⢋⣩⣴⠾⠛⣉⣤⠶⠚⢉⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠲⢤⠀⠀⠀⠀⠀⠀⠻⢶⡬⠀⠀⠀⠀⠀⠸⠟⣩⣴⡾⠛⢉⣤⠶⠛⠉⣠⠴⠚⠉⢀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⣀⠀⡀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣽⣿⣞⣿⣾⣿⣿⢻⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠁⠀⠈⠉⠈⠈⠁⠉⠈⠁⠀⠁

⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣤⣤⡀⢀⣀⣀⢀⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣾⣿⣿⣿⣿⣧⠘⠛⠚⠚⠓⠃⠀⣴⣿⢦⢀⡀⠀⠀⠀⠰⢄⠂⠆⠘⠀⠀⡀⣀⣴⠟⠁⠀⠀⢄⡠⠀⠀⠀⠘⠷⣀⠾⠀⠀⠀⠀⡀
⠀⠀⠀⠻⠿⠿⢿⡏⠁⠀⠀⢀⡤⢤⡀⠀⠈⡋⠃⠀⠀⠀⠼⢊⡖⠉⠈⢻⣓⣆⠺⠟⠉⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠿⠟⠻⠇⠀⣠⡄
⠀⠀⠀⢀⣤⣤⣈⡁⠀⠀⣀⣼⣄⣤⡿⠀⢀⠀⠀⣀⠀⠀⠀⣿⣿⡄⠀⠈⣻⡏⣇⢠⡤⢀⣤⡀⣠⣄⠀⠀⠀⣠⣤⡀⢠⣤⣄⢻⣆⣹⣷
⠀⠀⢠⠿⣿⣿⣿⡿⠗⠋⠅⢨⡟⠉⠀⢄⣠⣗⣶⣓⠢⡃⠀⠹⣟⠁⣀⣀⡙⣀⠇⠞⠐⠋⠀⠀⠆⠉⠀⣤⡀⢿⣼⡷⣿⣅⣽⡦⠛⠛⢻⣇
⠀⠀⣼⠀⠙⢿⡁⡀⠈⠀⣠⣿⠀⢸⡀⠸⢤⣨⣙⣅⡴⠋⠀⠀⠈⠛⠻⠿⠛⢁⡀⠀⡀⣤⠀⣴⡿⢿⣆⢿⣇⣀⣭⡀⠘⢿⣿⡷⠀⠀⠀⠁⡀
⠀⠀⢿⠀⢀⠋⠙⢿⣽⣻⣿⣿⣷⠈⠳⣤⣰⡈⠉⠁⠀⣀⣠⠴⢆⣀⡀⢴⣧⢸⣷⢺⣿⣿⣇⢿⣧⣼⣿⠸⣿⣿⠿⠃⠀⠀⣭⣴⣶⣿⡇⢘⡇
⠀⠀⠘⣧⣈⠀⠀⠀⠈⠙⢛⣿⠟⠀⠀⠘⠛⠁⠀⣀⣠⠉⠛⠀⣿⡟⠻⠿⣿⡟⢿⡞⣿⡻⣿⠎⠛⠛⠁⠀⠀⢠⡀⠀⠀⠀⢿⡏⣉⣈⡇
⠀⣀⣀⣸⡛⠷⢶⣴⠴⠖⠋⢁⣠⣄⠰⠀⠐⣾⣿⣿⠛⣤⣶⣛⣹⣷⣀⣶⣽⡷⠘⠃⠉⠀⠀⠴⠞⢨⡄⠀⢀⣀⡧⠀⠀⢶⣿⣍⣼⣿⣿⣿⠇
⠀⣿⣿⠿⢿⣶⣾⣿⣿⡆⢐⠂⠉⠀⠈⠉⠁⠀⠈⣿⣇⢹⣿⣻⣅⠙⠛⠛⠀⠀⣀⠶⡀⠀⠱⣐⠀⠄⣩⠄⠀⠁⠀⠀⠀⠀⠛⢿⣿⣿⣿⠏
⠀⣿⣿⠈⠀⠀⠀⠀⢰⠃⢺⡀⠀⠀⠀⠀⢤⡃⠀⠸⠟⠀⠛⠉⠁⠀⢀⡰⢦⣄⡀⠨⠑⠀⠀⠙⠔⠉⠀⣠⢶⣻⣿⣿⣿⡗⠀⠀⠙⠿⠋
⠀⣿⡏⣦⠀⠀⠀⢀⡏⠀⠈⠓⣀⢀⡄⡰⠑⠀⠀⢀⡠⠴⠶⠃⠀⠀⢹⣿⣿⣶⣶⣤⣄⣀⠀⠂⠀⠀⠘⠷⣯⣷⣾⣿⣿⠀⢀⠞⢦⣄
⠀⠈⠛⠻⠶⠶⠖⠊⠀⠂⠀⠀⠀⠈⣀⣤⡤⠖⠋⠁⣀⣤⣴⣶⣾⣿⣿⣿⣻⣿⣼⣿⡿⠋⠆⠲⠀⠀⠀⠀⠀⠛⠿⣛⠃⠀⣨⣦⣀⡉⢠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⡀⠑⣶⠀⢉⣀⣤⡶⣾⣿⣿⣿⣿⣿⣿⣾⠿⢿⣿⣿⡿⠋⠀⠀⢈⠧⠴⠀⠀⢠⣶⡀⠈⣿⠀⠀⣿⣿⣿⠇⢨⣿⠃
⠀⠀⠀⡄⠀⠀⠀⠀⠱⠼⠀⠀⣵⣾⣿⡿⠿⠟⠛⠛⠉⠉⠁⠠⣀⠄⠀⠈⡿⠋⡀⡀⠈⠂⠁⠀⢰⣤⡌⠿⠿⠿⠀⣹⡀⠀⠉⠉⠀⠀⠨⠏
⠀⠀⠀⢀⠀⠂⠐⠀⡀⠀⢀⡠⢬⣤⠤⢤⡀⠠⠀⠀⠀⣤⣄⣰⡿⠀⠀⣄⡠⠀⠁⢒⡀⠀⣴⠲⡟⠿⠛⢠⠴⠚⣉⣉⡉⠲⡄⠀⠀⡀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡖⢛⣠⣬⠷⣶⣒⣘⣦⡁⡄⠀⠈⠛⠏⡀⠄⠀⠀⠈⠉⢰⡋⠱⣄⣟⠀⢹⠀⣰⠃⣴⣿⣿⣿⣿⣷⣼⡀⠀⠼⠾⢧
⠀⠀⠀⢀⣄⠈⢻⠀⣾⣷⣿⠷⢿⡟⠉⠉⠉⠉⠳⣶⡍⠂⢈⠄⢀⣠⣾⣿⣿⣶⣆⡻⣦⣀⣻⣿⡏⠀⣿⠸⣾⣿⣿⣿⣿⣿⡿⡇⠀⢸⣯⣽
⠀⠀⣴⣿⣿⣆⠀⠀⣿⠉⡄⠀⠈⣧⣀⡀⠐⠶⠇⣸⣷⡄⠘⡆⢺⣯⣭⣿⠉⣯⢹⣷⠀⠙⣿⡿⢿⣄⢸⡄⠙⠿⣿⣿⡿⠟⢁⣧⣄⡘⠋⠉⠁
⠀⠀⠈⣿⡏⠉⠀⢸⣿⣾⠋⢀⣾⣿⣿⣿⣶⣠⠔⠁⠘⣿⡌⢢⢹⣿⣭⣽⣤⣧⣼⣿⠀⠀⢿⡖⡱⣹⣿⡿⠒⢠⣤⢤⣴⣎⣥⡀⣷⣯⠷⡄
⠀⠀⠀⣿⡇⠀⠀⣿⠃⠈⠛⣾⣿⣿⣟⣽⡟⠙⡆⠀⠀⢸⣧⠱⠸⣿⢨⡃⡇⡷⣹⣿⡆⢀⠀⠻⣧⣧⣹⡗⣏⡵⣄⣶⣶⠰⣲⢷⠸⣿⡭⢽
⠀⠀⠀⣿⡇⠀⢸⣿⡀⠀⠀⠹⢮⣭⣛⡋⠤⠞⠁⠀⢠⡞⡝⢲⡀⣿⡟⠟⣿⠿⢹⣿⣇⢈⠆⠀⠈⠛⠻⡇⠫⣕⡁⠙⠿⢀⡠⠊⢀⣿⣿⣿
⠀⠀⠀⣿⡇⢸⠏⢐⣽⣦⠀⠀⠀⡴⠒⠉⠉⡇⠀⠀⢸⣿⡖⡌⣷⢸⣷⠴⠿⡾⠲⣿⣿⡌⡦⠀⠀⠀⠀⣿⣦⣤⣬⣭⣭⣥⣴⣾⣿⢿⡏⢹
⠀⠀⢸⣿⣇⠸⣇⣻⠸⡿⠀⠀⢀⣇⣀⠀⢰⠁⠀⠀⠈⠛⠃⠈⠁⣿⣿⣇⣺⣿⠻⣿⣿⡇⢧⠀⠀⠀⠀⢸⣟⠛⢿⣿⠿⢿⣿⣋⠽⡎⠷⠼
⠀⠀⣾⣭⣿⡀⠉⠁⣴⣾⠷⠐⠀⠀⡇⠀⠈⣹⠁⣤⣤⣿⣄⡀⠀⣿⡟⣻⣻⡏⢻⡏⣿⡷⢮⠀⠀⠀⢀⣸⣿⣭⣭⣼⡆⢸⣿⣿⣿⣿⣶⣄
⠀⢰⣿⣉⣿⣷⡀⢀⣩⠀⢼⡷⠀⠄⠋⢙⡴⠁⠀⠀⣿⢿⡏⠀⠀⣿⣷⠸⢇⡇⣦⣀⣿⠇⢸⠃⠀⠀⣿⣍⣽⣿⣿⣿⡇⢸⣿⣿⠿⠿⠿⣻⠆
⠀⠀⠉⠉⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠈⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠛⠛⠙⠛⠛⠋⠁⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⠉⠉⠉⠉⠉⠉⠙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⣿⢿⢿⣿⣿⣿⣿⣷⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⣷⣾⣷⣶⣿⣿⣿⣿⣷⣶⣿⣶⣷⣿⣷⣶⣾⣾⠇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣌⣉⡛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢛⣉⣡⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠲⠶⠶⠶⠶⠖⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡀⢀⡀⢀⡀⣀⣀⡀⣀⢀⢀⢀⡀⣀⠀⣤⢠⠀⡀⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠊⠘⠙⠍⠃⠛⠋⠃⠋⠫⢉⠏⠛⠁⠃⠀⠋⠘⠒⠛⠸⠚⠛

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣀⣴
⠀⠀⠘⣧⢀⣿⡆⣰⠇⣾⣀⣀⣾⠀⣿⠀⣞⣛⡳⠀⣿⣠⠞⠃⠹⣦⣴⠏⠀⠀⠀⠀⠀⠀⡷⠋⣧⡼⠃⣷⣀⣰⠂⣶⢠⣖⣒⠂⢷⣴⣁⠀⠈⠻⠄
⠀⠀⠀⠸⡿⠁⢻⡏⠀⣿⠉⠉⣿⠀⣿⠠⣬⣭⣽⠂⣿⠙⢷⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠇⠀⠽⠀⠿⠀⠮⠽⠇⠘⠃⠉⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠂⠐⠀⠂⠀⠐
⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠾⠆⠰⠆⠰⠆⠐⠆⠀⠶⠀⠰⠆⠰⠆⠐⠆⠰⠇
⠀⠀⠒⡀⢒⢠⣤⣶⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣦⡤⢐⡊⡰⠂⠀⠀⠀⠀⠀⠀⠀⣀⣶⣤⠀⠄⠀⠀⠀⠀⠀⠠⠐⣶⢾⣄
⠀⠀⠀⠃⢨⠓⢻⡌⠿⠍⠝⡫⠗⠚⣺⠭⡆⠒⠺⡝⠽⠹⠟⣡⠛⢎⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠘⠂⠤⠭⠾⠥⠤⠒⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠰⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⣤⢤⡄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠾⠶⠤⡄⠀⠀⠀⠀⠀⡀⠀⣀⣤⣴⣾⣦⣀⣀
⠀⠀⡀⠀⡀⢀⣀⢠⡞⢙⡆⢧⣤⠇⠿⠻⠇⢿⣿⡇⣞⠙⣷⢀⡀⠀⠀⢀⠀⠀⠀⠀⢀⣐⡒⠛⠂⢀⠀⠘⠓⠀⠁⣀⣀⡉⣘⣋⡁⢀⣉⣟⢿⣓
⠀⠀⢳⠀⠐⢿⣞⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠡⠋⣇⡴⠀⢴⠁⠀⠀⠀⢸⠒⣿⢸⣏⢉⡗⣿⠀⣻⢸⡷⣾⠋⣿⠚⣏⢿⡁⣹⠟⡟⢦
⠐⢢⡘⣜⠄⠀⠁⠰⠀⠶⠀⠰⠆⠀⠆⠰⠆⠐⠦⠀⠲⠐⠆⠀⠋⢠⢾⠊⡐⠂⠀⠀⠈⠉⣁⠀⠉⠉⠀⠈⠉⠁⠈⠀⠈⠁⠉⠉⠁⠀⠉⠁⢀⠁
⠀⠐⠄⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀⠆⠀⠀⠀⠀⠀⠠⡄⠀⢠⣤⡤⢀⠀⣀⡀⣀⠀⡀⢤⣤⣤⠀⠀⡄
⠀⠀⠀⠒⠀⢾⣶⣤⣄⣰⡾⠟⠛⠒⣤⢠⡔⠛⠛⠳⣆⣀⣤⣴⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠉⠉⠃⢀⣀⣁⣀⣈⣀⠀⡘⠃⠉⠉⠐
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⡟⠁⢠⡄⠀⠀⠄⠈⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠄⢠⠀⠄⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⠳⣄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢤⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡠⠚⠛⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠘⢿⡿⠃⠀⠀⢀⣀⣼⣄⣀⣀⣧⣀⣀⣸⣇⣀⣀⣼⣀⡀⠀⠀⠀⠈⠻⡿⠃⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡇⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⡇⠁⠉⠉⠁⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣅⣀⣀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡧⠤⠤⠤⠤⠤⢴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡀⠀⠀⠀⠀⠙⠿⢿⠿⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⣤⣶⣄⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⣠⠞⠀⠀⣤⣷⣄⠀⢸⡇⠀⠀⠈⠉⠉⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠒⠚⠁⠀⠀⠀⠿⣿⠟⠀⠘⢧⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⡆⠀⠀⢸⣿⢸⣿⠀⠀⠀⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣴⡆⣿⣿⢸⣿⣿⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⣄⣴⣿⣿⣸⣿⣿⡷⠶⠾⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣏⣽⣿⣯⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣰⣿⣼⡟⣿⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠿⣺⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣷⡖⣻⣿⡇⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⡇⣿⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡖⣶⣼⡏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⣿⣶⣯⣿⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⢸⣏⣻⣿⣟⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡶⠛⠸⣿⣿⢹⣿⣿⡷⠶⢶⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠻⠇⣿⣿⢸⣿⣿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠸⠃⠀⠀⢸⣿⢸⣿⠀⠀⠈⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢀⣀⣀⠀⠀⣶⣿⣦⣀⣀⣀⣀⣀⣀⣶⣿⣦⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢿⣿⣿⠆⠀⠻⠿⠛⠀⠀⠀⠀⠀⠀⠻⠿⠏⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡞⠁⠀⣀⣀⡀⠀⠉⠉⠙⠦⣄⣀⣀⣀⣀⣀⣀⣀⣴⣶⣦⠀⠀⣼⣿⣿⡆⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏⠀⠐⣿⣿⣿⠖⠲⠦⣄⠀⠀⠉⠉⠉⠉⠉⠉⠉⠻⠿⠟⠀⣠⠞⠛⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⢱⡆⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠞⠁⣰⣾⣷⡄⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⢀⣴⣶⡄⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⢀⣴⣶⣇⠀⠀⠀⠀⠘⢿⠟⠁⣴⣶⣶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⠀⠘⢿⡿⠿⣄⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠘⠿⡿⠏⠀⠀⠀⠀⢠⠞⠀⠀⠻⠿⠟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠓⠢⣀⣀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣼⣿⣷⡄⢀⣤⣤⡀⠈⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠉⠛⠉⠀⠀⠀⠀⠙⠛⠛⠀⢸⣿⣿⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢋⣤⣦⡄⠀⠀⢠⣶⣶⣄⢀⣀⣠⠞⠁⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠘⠿⡿⠏⠉⠉⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⢤⣄⣀⠀⠀⠀⢠⠞⠛⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢀⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢿⡿⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢻⠳⢤⣖⠉⠀⠠⡇⠀⠉⣲⠤⠚⡟⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⢸⠀⠀⠈⢱⠀⠈⡇⠀⡏⠀⠀⠀⡇⠀⣤⣀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⣿⣿⣿⣦⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⣇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠢⣄⡀⢸⠀⢀⡇⠀⡇⠀⣀⠼⠿⠧⡈⠙⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠔⠊⠀⠀⠀⠀⠀⢉⠿⠀⣨⣏⠰⣷⣉⠀⠀⠀⠀⠀⠑⠠⢄⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢁⠀⠀⠀⠀⢀⡠⠔⠊⠀⣠⠔⠻⠟⠢⣄⠈⠑⠢⣄⡀⠀⠀⠀⠀⡨⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠤⠒⠁⢀⡠⠖⠉⠀⣀⢴⣦⣀⠀⠉⠲⢤⣀⠉⠲⠤⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠄⠊⠁⢀⡠⠔⠈⠀⠐⡇⠈⠙⠢⢄⡀⠈⠑⠦⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡉⠀⠀⢠⠂⠁⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠉⠲⡄⠀⠀⢙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢼⠀⠀⠀⡠⠔⠊⠉⠉⠙⠢⢄⡀⠀⠀⡧⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⢀⠠⠐⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢀⢤⣄⡧⣩⣴⣥⣍⣄⢁⠒⠀⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⢨⣐⡲⢦⢹⣿⡿⠧⠼⠶⠎⠾⠾⠿⠫⠶⠶⢂⣄⣤⣀⡀⠄
⠀⠀⠀⠀⠀⢀⣐⢶⡸⣜⠎⠓⣑⢴⠦⠀⠀⠀⢠⣤⣤⡄⠀⠠⢀⡈⠉⠉⠢⣦⣴⠆⣚⢁⣂⡀
⠀⠀⠀⠀⡈⢀⠡⠙⠃⠛⠛⠉⢀⠄⠀⠀⠀⠀⠚⠛⠛⠃⠀⠰⠊⡁⠾⠋⣗⠒⠒⣒⠮⠍⠁
⠀⠀⠀⢐⠨⠲⠥⠖⠴⠶⠶⠦⢁⣠⢖⢄⣤⣤⣤⣤⣤⣤⣤⣔⣦⣉⣀⡐⣙⣛⢉⣥⡓⢈⡃⢒⣒⡂
⠀⠀⠀⠀⢁⣴⠳⡎⣿⡡⡋⠛⠛⠪⠓⢉⠨⣻⣾⢛⠛⡹⡛⣟⣒⠒⣲⠭⢤⣔⢮⢲⡆⣷⡽⣎⡛⠟
⠀⠀⠀⠀⠈⠉⠑⠛⠣⢪⡪⣉⠋⠧⣒⡵⣪⠵⠟⣸⠻⡝⣦⣤⡦⣿⡦⢹⡏⣿⡜⣦⢹⣬⣁⠈⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢇⡟⣾⡞⣵⠊⣵⡇⣿⡿⢃⣧⢙⡏⡗⢿⣁⣿⣇⣿⡇⣹⣧⣉⡭⢳⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢻⡇⢻⣆⢹⣧⠘⠿⠸⠿⠿⣤⠃⣮⡙⠛⠉⠉⠁⠉⠉⠉⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠺⢉⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⠀⣿⡇⣿⣿⣿⣿⣿⢠⣶⡆⢀⣀⣴⣾⣿⣿⣯⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢸⣿⣾⣿⣶⣿⣶⣿⡇⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣼⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⢸⣿⡇⠻⠿⢿⣿⣿⣿⣿⣿⣿⣩⣩⣭⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏⠀⠋⠉⠉⠉⠋⠀⠀⠀⠀⠀⢀⣍⣉⣉⣉⣉⣉⣉⣉⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⣉⣉⣉⣉⣉⣉⣉⣙⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡀⣰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣛⣙⣛⣿⣿⣿⣿⣿⣿⣷⣶⣦⢸⣿⡇⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⢸⣿⠿⣿⠿⣿⡿⣿⡇⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⣻⣿⣿⡿⠟⠉⠁⠸⠿⠃⣿⣿⣿⣿⣿⢸⣿⠀⣿⠀⣿⡇⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⣿⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡀⠀⠀⠀⠰⡆⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠀⡗⠀⠀⡇⠀⢸⠂⢸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠳⡈⢢⠀⡇⡴⠋⡔⠋⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡔⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣟⡍⣭⢹⣭⡍⣭⣩⣩⡝⣿⣿⣀⣀⣀⣀⣀⡤⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⣀⣀⣀⣀⣿⣿⣯⣥⣭⣬⣭⣥⣭⣭⣬⡅⣿⣿⣀⣀⣀⣀⣀⠔⠉⠉
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠉⠉⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⠉⠉⠉⠉⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠜⠀⡇⠳⣄⠣⡀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣇⠀⡧⠀⠀⡇⠀⢸⠄⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠈⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⣿⣛⣻⣿⣿⣻⣛⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⣿⣷⣿⣿⣉⡿⣷⣟⢹⣛⠿⣾⣿⣻⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣬⢿⣯⣟⢻⡹⣿⢷⣻⡿⣽⣿⣻⣾⢛⣯⣯⣙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣹⡟⣻⠟⣭⢯⣷⡿⣿⣿⣩⣷⣿⣿⣿⣿⣿⣵⢿⣜⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣼⣿⣛⣿⣟⣟⣿⣶⣿⢽⣿⢿⣾⣏⣥⣽⣿⣿⣭⣯⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣥⣭⣿⠿⣿⣿⡞⢿⢿⣿⣻⡿⢿⣽⣿⣿⣟⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣯⣿⣾⣿⣶⣿⣟⣿⣿⣶⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠛⣆⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢻⡀⢸⡇⢸⡴⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⡇⠸⡇⠘⣇⠀⣷⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢷⠀⣷⠀⢿⠀⢻⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡁⠀⠰⡏⠳⣸⡀⠘⠀⠈⠀⠈⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣄⠻⠃⠀⠀⢻⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠳⣌⢧⡀⠀⠀⠀⢳⡀⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠈⢧⡙⢦⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⠷⠖⠉⠀⠙⢲⣀⣀⣀⣤⠤⠤⠿⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⣼⠭⠤⠶⠒⠒⠛⣉⡉⡇
⠀⠀⠀⠀⠀⠀⠰⣇⣤⠞⠁⣠⠶⠀⠀⠀⠀⢀⡀⠀⡴⠳⢤⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠛⠃⢿
⠀⠀⠀⠀⠀⠀⢠⡞⢁⣴⠞⠁⣠⠞⠃⣠⢶⠏⢀⡞⠁⠀⠀⣸⢳⣄⡤⠶⠟⠶⠶⠤⠤⠤⣤⣄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠈⡽⠋⢁⣴⠟⢁⡤⠚⢱⠇⣰⠋⠀⠀⠀⢰⢃⡞⠀⠀⠀⠀⠀⠰⠶⣤⣤⠤⠞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠳⠞⢿⣁⡴⢯⣀⡀⠈⠉⠁⠀⣀⡀⢀⡏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠓⠦⢤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣄⣛⠃⣼⣰⣃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠙⠲⠶⣤⣌⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠁⠈⠳⢤⣀⠀⠀⠀⠀⢀⡈⠙⠓⠶⣤⣄⣈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣀⡉⠛⠶⢦⣤⣈⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠴⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢠⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠀⡇⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⡴⠋⠀⢸⢸⠀⣨⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡇⢸⢸⠀⡇⠀⠀⠀⡼⠁⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⢳⠀⠀⢰⠃⠀⠀⢸⠈⣫⠴⠊⢹
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠀⡇⡇⢸⢸⠀⡇⠀⠀⢠⢣⡄⠀⠀⡿⡄⢶⣄⠈⢇⠀⠀⡀⡇⠀⠘⣆⣤⡀⠘⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⡇⡇⢸⢸⠀⡇⠀⠀⢸⢸⠁⠀⢸⣷⣟⢼⣎⣗⣾⡄⠀⡇⢸⠀⠀⢿⠀⣗⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠴⠧⠾⠼⠴⠷⠧⠼⠾⠤⠧⠄⠀⢸⢸⡀⢀⣇⣘⣠⠋⢧⣘⣀⣇⠀⡇⢸⠀⣴⣚⣈⣓⡍⠉⠁⠀⠀⠀⠀⢰⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⢧⣸⣆⠀⢀⣐⣀⠀⢀⠿⡀⣇⡞⠀⠀⠀⠀⠀⠀⠀⣰⢦⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⡷⣄⠀⠀⠀⠀⠘⢮⡟⣨⡳⡤⣉⡡⡴⢋⣤⣱⡟⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⠓⣤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣛⣀⡉⠙⡇⠀⠀⠀⠀⠀⠈⠁⣹⠇⠀⠀⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠯⠇⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⡠⠖⠒⠦⣼⠀⠶⠶⠆⠀⡇⠀⠀⣠⠖⠚⠻⣋⢷⠀⠀⠊⢱⢋⡻⠒⠲⠤⣀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⣀⣈⣉⣁⣀⡇⠀⡜⠁⠀⠀⠀⠈⠹⡖⠦⠶⡞⠉⠀⠀⠀⠀⠘⡆⠀⠀⢸⣉⣉⣉⣉⣉⣉⣿⣏⣹
⠀⠀⠀⠀⢀⡹⠀⠀⠀⡆⠀⠀⠈⣇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢃⠀⢀⠃⠀⠀⠀⣤⠀⠀⢹⠀⠀⢸⠀⠀⠀⡴⠦⡄⠀⠀⢸
⠀⠀⠀⠀⡎⠀⠀⠈⠳⡷⠊⠀⠀⠈⢧⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠸⡄⡼⠀⠀⠀⠀⣇⠀⠀⠀⣇⠀⢸⠀⠀⠀⠳⠶⠧⠀⠀⢸
⠀⠀⠀⠀⠱⢄⣀⣀⣀⣀⣀⣀⣀⡠⠏⠀⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⣿⠀⠀⠀⢹⡀⢸⠀⣒⣒⣒⣒⡒⠒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠸⣤⣤⣤⣤⣤⣤⣤⣤⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠒⠦⣾⠀⠀⠀⠀⠀⠷⠇⠀⠀⠀⠀⣯⡤⠤⠶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣲⣿⠭⢬⣣⣴⠃⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣼⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠈⠉⣽⣷⡾⠋⠀⠀⠀⡵⣝⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⠚⠻⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠧⠤⠤⠴⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⢠⡄⠂⠀⠀⠤⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⢀⣼⡅⠀⠀⠀⠀⠀⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣮⣽⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⣾⡇⣧⡄⠀⠀⠀⠀⠀⠀⡛⠛⠛⠒⠢
⢸⡇⢄⢸⡇⢠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⢀⣿⠠⣿⠇⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠄


⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣰⡾⠛⠙⠻⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⣽⠖⠲⡿⢦⠀⠀⠀⠀⠀⢀⣞⣉⡇⢹⠱
⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣟⣽⣿⣿⠅⠀⠀⠀⠀⢸⣸⡅⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣲⢖⡃⡺⢄
⠘⢿⣶⣴⣾⠗⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⢯⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢩⣷⣻⠗


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⣤⣤⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣼⡆⢀⢈⣿⢀⠄⠀⠀⠀⠀⣠⡀⢁⢂⣠⣶⡤⠢⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢
⣿⣿⣧⣤⣾⣿⡇⠀⠀⠀⠀⠀⢻⡇⠈⠘⡿⢀⠀⠀⠀⠀⠀⠸⠱⣦⡦⢫⢔⠔⠳⠄⠀⠀⠀⣯⣱⣾⣿⣶⣶
⠛⠛⠛⠻⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠛


⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢀⣀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⡇⣠⠿⢿⡃⠀⠀⠀⠀⢨⣭⢨⣭⠈⠉⠁⠀⠀⠀⠀⠀⢀⡀⣴⢰⣿⢸
⢿⣿⣯⣽⣿⣿⠇⠀⠀⠀⠀⠀⡿⠛⢾⣿⣦⣾⡇⠀⠀⠀⠀⠰⠶⠰⠶⠰⠶⠲⠶⠆⠀⠀⠀⢸⡇⣿⠨⣿⢸
⠀⠏⢀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠿⠶⠿⠿⠿⠿⠃⠀⠀⠀⠀⠘⠛⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠀⠋⠘
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⡤⠤⠤⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⣶⣶⣦⡀⠊
⠀⠀⠀⠀⠀⠀⣀⣀⢠⡏⠀⠀⠀⠈⡆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣼⣿⣿⣿⣿⣿⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠼⢧⠀⠀⠀⣠⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠹⣿⣿⣿⣿⡿⠡⣄
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢳⣀⣸⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡠⠂⠘⣿⣿⡟⠀⠲⡌⢳⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⣶⡖⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢒⣒⠂⠀⠀⠀⠀⢷
⠀⠀⠀⢀⠖⠛⠓⢆⠀⢀⡤⠤⠤⡀⠀⣰⠋⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣴⣶⣦
⠀⠀⠀⢸⡀⠀⠀⣸⠀⡟⠀⠀⠀⢸⠀⣳⣀⠀⣠⣏⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠀⠀⣼⣿⣿⣿⡄⠀⠸⣿⣿⣿⠃
⠀⠀⡴⠋⠉⠛⠋⠉⣳⠿⢤⣀⡠⠾⢏⠀⠈⠉⠁⠀⢳⠀⠀⠀⠀⠀⠀⣠⣦⣭⣯⣵⣦⠀⡻⣿⣿⠿⡃⢰⣾⣶⣿⣶⣷⡄
⠀⠀⡇⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢣⣾⣿⣷⣶⣾⣿⣦⢻⣿⣿⣿⣿⣿
⠀⠀⠧⣤⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⠼⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠸⢤⣤⣀⣀⣀⣠⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⠲⠒⢁⣀⡘⠒⠖⠛⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣶⣿⣿⣿⣶⣶⣿⣦
⠀⠀⠀⠀⠀⠀⣀⣠⠏⣠⠖⠋⢉⣄⡉⠀⠲⠄⠹⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡿⣫⣷⣾⠿⣿⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⢸⡉⠁⡼⠁⡴⢺⣁⣤⡞⠓⢦⠈⢆⠈⢙⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣾⡟⢻⣁⣤⣞⠉⠻⣿⡽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⣧⣸⠁⠀⢸⡗⢾⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣇⣸⣿⣿⣿⡟⠲⣿⣷⣿⡏
⠀⠀⠀⠀⠀⢰⠋⠀⢧⠀⢧⣈⣱⠖⢺⣇⠼⠀⡞⠀⢙⡆⠀⠀⠀⠀⠀⠀⠰⣿⣿⣟⣿⣇⡈⣙⠿⠛⣇⣠⣿⢧⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠛⠳⡄⠳⣄⡈⠙⠒⠋⢁⣠⠞⢠⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣮⡻⣿⣷⣦⣶⣿⢿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣤⣉⡙⠛⢉⣉⣄⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⣷⣿⣿⣿⣾⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠳⠤⠞⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⠿⠟⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⡄⠠⡤⠀⡄⠀⠀⡤⠄⡠⡄⡀⢠⠤⢠⣀⠀⡤⡄⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠼⠰⠿⠀⠇⠰⠿⠀⠀⢭⠆⢧⠄⠇⠸⡁⠸⠹⠀⠧⠄⠯⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⣄⠀⠀⣼⣿⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⢿⣷
⠀⠀⠀⣿⡏⠀⠀⠀⠀⣀⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⡏⠉⣿⣿⣿⣶⣄⠀⢸⣿
⠀⠀⠀⣿⡇⠀⢀⣴⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠙⣿⡇⠀⣿⣿⠀⣿⣿⣤⣼⣿
⠀⠀⠀⣿⡇⠀⢸⣿⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡇⠀⣿⣏⠀⣿⣿⠛⢿⣿
⠀⠀⠀⣿⡇⠀⠀⠙⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡇⠀⣿⣿⠀⣿⣿⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢠⣾⡿⠿⣿⣿⠀⠀⠀⠀⣀⡀⠀⢸⣿⡇⠀⣿⡇⠀⣿⣿⠀⣿⣿⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣩⣽⣿⡿⠟⠀⠀⠀⠀⣠⣾⡿⠁⠀⣿⣿⠀⠀⢰⣿⡿⢿⣷⣸⣿⡇⠀⣿⡇⠀⣿⣿⠀⣿⣿⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⢁⣀⣤⣤⣶⣾⣿⠿⠛⠁⠀⠀⠘⢿⣿⣾⣿⣿⡆⠈⢿⣿⣿⡇⠀⠉⠁⠀⠉⠁⠀⠈⠁⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟
⠀⠀⠀⠀⣠⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⢀⡀⠀⠀⡀⠀⠀⡀⠀⢸⣿⣿⣷⡀⠸⣿⣿⡿⣿⣷⣄⠀⠀⠀⣠⣶⣿⡿⠿⠛⠛⠉⢁⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⣾⣿⠀⢸⣿⠀⢸⣿⡏⢿⣷⣶⣿⠇⠀⠀⣿⣿⠀⢀⣾⡿⠋⠀⠀⠀⠀⣴⣾⣿⣟⣋⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⣿⣿⠀⢸⣿⠀⢸⣿⡇⠀⠉⠉⠁⠀⠀⠀⣿⣿⣶⣾⣿⠃⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⣽⣿⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣷⣄⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣷⣤⣿⣿⠀⢾⣿⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⣿⡇⠀⢸⣿
⠀⠀⠀⠀⣿⡿⠛⣿⣿⠀⣹⣿⠀⢸⣿⡀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠹⢿⣿⣿⣿⡀⣸⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⣿⣿⠛⠋⠁⠀⠀⠀⣸⣿
⠀⠀⠀⠀⢿⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿⡟⠀⠀⠹⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣿⠟
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣄⣀⣀⠀⢀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⡿⣯⡶⠿⢾⣝⢿⠠⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀
⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠰⣷⠀⣿⢾⣷⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⣧⡿⢦⣤⡼⣿⣾⠁⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠻⣿⠛⠉⣋⡼⣿⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡃⢶⠄⣄⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣷⣶⣾⡿⠂⢄⠀⠀⠙⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠁⠄⠀⠘⢦⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⠄⠐⢃⣀⠭⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠔⠚⡈⠁⠀⠐⠢⣶⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠄⠁⠘⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⢒⡒⠒⠒⠒⠆⠀⠀⠀⢠⠒⠒⠒⠒⠒⢦⠀⠀⠀⠀⠀⡴⠲⠿⠖⢢⠀⠀⠀⠀⠀⢠⣶⣿⡷⠐⠄
⠀⠀⠀⠻⠷⠀⠀⠀⡆⠀⠀⠀⢸⠀⠤⠤⢾⠉⣛⠀⠀⠀⠀⠀⡟⠿⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣣⣄⣈
⠀⠀⠼⠿⠿⠽⠿⠿⠧⠀⠀⠀⠈⠉⠩⠿⠏⠉⠙⠂⠀⠀⠀⠀⣧⣤⣤⣶⣸⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣠⠶⡶⢦⡀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠆
⠀⠀⡇⠀⣄⢀⣄⡀⣿⠀⠀⠀⠀⣿⠒⣿⢚⡇⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣤
⠀⠀⣇⣺⣛⣟⣟⣇⡿⠀⠀⠀⠀⠈⠓⠛⠛⢧⡀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠋⠀⠀⠀⠀⠀⠀⠺⠛⠒⠛⠻
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣤⣀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣠⡀
⠀⠀⣀⣰⣋⡠⠿⣶⡶⠀⠀⠀⠀⣰⠏⠁⠀⢛⢳⡄⠀⠀⠀⠀⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠴⢒⣄
⠀⠀⠉⠉⠻⠥⠴⢇⠀⠀⠀⠀⠀⢿⡠⠶⠴⠿⣸⠇⠀⠀⠀⠀⠸⠴⢤⡤⠦⠄⠀⠀⠀⠀⠀⡟⢖⣛⣜
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠈⠛⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠰⠾⠷⠀⠀⠀⠀⠀⠀⠀⠳⠶⠴⠶⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡿⠿⠿⠿⠿⠿⣟⠀⠀⠀⠀⡞⠉⣩⡿⡆⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⣿⠀⠀⠀⠀⠀⡠⡼⠩⠍⢧⢄
⠀⠀⡤⣤⣤⣔⣩⣕⣾⠀⠀⠀⠀⢷⣛⣛⣳⡃⠀⠀⠀⠀⠀⠀⣿⣁⣉⣀⣿⠀⠀⠀⠀⠀⠂⡇⠐⡂⡰⠐
⠀⠀⠦⠤⠤⠬⠵⠭⠮⠀⠀⠀⠀⠀⠈⠉⠀⠹⣦⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⠭⣈⣣⠴⠃

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



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⢦⡀⡀
⠀⠀⢀⡀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣝⣤⣚⡁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣹⣳⣾⣯⣉⡇
⠀⠀⠄⠰⠐⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⡳⡋⣶⡎⡷⠉⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣹⣾⣿⣿⣹⣎⢙
⠀⠈⠈⡐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⣛⠶⣛⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⢻⣻⢿⡟⠙⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣠⣊⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣣⣴⣉⣉⣁
⣿⣿⣋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⢲⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⠈⡌⢫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠁⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣖⣒⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⢔⡳⢸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⣄⠀⢘⡙⠛⡛⡋⡋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⣀⢍⠉⣡⢠⠄⡄
⠀⠀⠀⠀⠀⡯⢸⠇⠣⠅⠹⠻⠃⢱⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠟⠡⡘⠄⠏⠀⡇⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣄⣤⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣿⡿⣿⢻⡿⣿⢻⡿⣿⣻⣿⢿⡟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣽⣽⣷⣿⣸⣿⣶⣾⣷⣿⣾⣷⣽⣾⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠟⠛⠻⠿⠿⠟⠋⠈⠉⠉
⠀⠀⠀⠀⠀⣿⣿⣿⣥⣽⣿⡇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣯⣷
⠀⠀⠀⠀⠀⣀⠈⠀⡀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢿⣷⣿⣾⣭⠟
⠀⠀⠀⠀⠀⠎⠰⠴⠳⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢶⠖⠓⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣀⣶⣙⠀⠀⠀⠀⠀⢸⡎⣿⡀⣼⣀⢺⢣⠹⡄⢹⢔⡦⣿⡀⣼⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡍⠿⠉⠀⠀⠀⠀⠀⠘⠁⠁⠉⠀⠉⠈⠈⠀⠁⠈⠀⠀⠁⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠒⢰⡄⣀⢠⡔⠐⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠢⠻⠃⠸⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣀⡤⢾⠉⢀⣠⠴⢊⡁⠈⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣿⣿⣿⡿⠟⣉⡀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠖⠉⣀⠤⣄⡈⠓⢦⣄⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸⡿⠋⢁⡤⠤⣀⠙⠲⣤⡀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⡞⠧⣄⡤⢻⠀⢸⠀⠙⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⠻⢤⣠⠜⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡧⣄⡛⠀⠳⣄⣸⣀⡼⠃⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣦⣘⠇⠸⢤⣀⣇⣠⠿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣇⠀⠉⠒⢤⣀⠉⢁⡠⠔⢸⠀⣀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣄⡉⠉⣁⡴⠂⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡬⠛⠉⢀⣠⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠟⠋⠁⣀⡤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢀⡀⢤⠄⢠⠀⠀⡤⠄⡠⡄⡄⡤⠄⣄⡄⠠⠄⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠞⠜⠣⠸⠀⠟⠆⠀⠬⠇⠣⠆⠇⠯⠄⠏⠇⠰⠄⠸⠅

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣴⣶⣦⠀⠀⠀⠀⠀⠀⣴⣿⣅⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⠉⠁⠀⢀⣠⣀⠀⠀⠉⢉⡹⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⢠⣤⠏⠉⠉⣷⣄⠾⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠘⠛⣧⠀⢰⡟⠋⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠛⡆⢀⡀⢿⣦⠿⣶⢀⠀⠘⠛⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⢼⡇⠁⠁⠀⠀⠀⠀⠈⢐⣀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠶⠿⠿⠇⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠇⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⡆⠀⣿⠀⠀⠀⠀⣠⣾⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣠⣾⠟⣳⠀⠀⣰⡾⣛⣭⣽⡻⣷⡄
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡄⠀⣿⡇⠀⣿⠀⠀⠀⣸⣿⣿⣿⢟⣭⡻⣿⣿⡄⠀⠀⠀⣿⡿⠿⠿⠿⣿⣫⣾⠟⠁⠚⠁⠀⢰⣿⣸⣿⣿⣿⣿⡞⣿
⠀⠀⠀⢰⡆⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠀⠀⢻⣿⣿⣿⠻⠿⢇⣼⣿⣶⠀⠀⠀⣿⡿⠿⠿⣿⣣⣬⣷⠀⠀⠀⠀⠀⠘⣿⡜⣿⣿⣿⡿⣳⡿
⠀⠀⠀⢸⠇⠀⢿⠀⠸⡇⠀⢿⠇⠀⠿⠀⠀⠀⠈⢿⢟⣵⣿⣿⣿⢟⣱⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣷⠾⢛⣵⣤⡀
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠈⠙⠓⠲⠚⠋⠁⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⣿⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠻⢿⣿⣿⣿⠀⠀⠀⠋⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣌⣉⣉⣀⣤⡴⠟⠉⢳⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣤⣤⣉⣉⡁⠀⢠⣾⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣦⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠘⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⠃⠀⠈⠛⠛⠛⠛




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣶⡆⠉⢡⣀⣴⡄⠀⢀⠔⢲⣶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡟⣿⣿⡦⡤⠄⠠⣼⢀⡎⠀⣠⠟⠒⠲⢬⡙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢸⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣾⠁⠀⠁⡀⠀⠀⠀⢹⡿⣏⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⣝⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡏⠀⠀⠀⣸⠇⣹⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢤⠈⣽⣿⣿⣿⡾⠚⢻⣿⣿⣟⣿⣿⡿⠀⠐⢾⡁⠀⠀⠀⠉⢳⡟⠀⣀⣼⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⢸⣿⣏⣿⣿⣿⣟⣠⣤⠬⣧⡀⠀⠀⠀⢈⣇⠀⠈⠙⣷⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⣦⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⡟⣾⣿⣿⢻⡏⠀⠀⠀⠀⢀⣤⡴⠶⠾⠿⢄⡀⠀⠸⣇⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠈⠙⠲⠾⠿⣿⣿⣿⠀⠀⢸⣱⣿⣿⠁⢨⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠂⠀⣿⢰⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠖⣀⡚⠚⢷⡤⣼⡇⠀⠀⢰⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⡟⠁⠀⠀⠀⠙⠃⣤⡈⠳⡀⠀⢸⣿⣿⣿⠀⢸⡷⠶⠶⠒⠚⠾⠅⠀⠀⠀⠀⢀⣦⡤⠟⠀⢠⡾⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡛⠀⡰⠀⠐⢤⠀⠀⠀⠁⠀⠙⣦⡼⠿⢿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⠛⠓⠀⠀⠀⢿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠾⢄⠔⠁⠀⣡⡀⠀⠀⠀⠰⣿⡀⠀⠈⣿⠀⢸⡇⠀⠀⠀⠀⠀⡀⢀⣠⠇⠀⠀⠀⢀⠀⠀⠈⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠠⡖⠁⠀⠐⠀⠀⠀⠀⢹⣧⠀⠀⢻⠀⢸⡇⠀⠀⠀⠀⢀⡿⠚⠁⠀⠀⠉⠋⠉⠉⠓⣆⠀⠚⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠰⣀⠤⠐⡇⠀⠀⠀⠀⠿⠀⠀⠸⠀⢸⣿⡶⠶⠶⠶⣿⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⡇⠀⠀⠀⠀⢀⠀⠀⣸⠀⠀⣀⠀⠀⠇⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⠙⠶⠦⠤⠤⠤⠞⠀⢠⣤⠟⢰⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠸⠟⣟⣹⡆⠸⣀⡅⠀⢰⠀⠀⠀⢸⡇⠀⠀⠀⢸⣦⠀⠀⠀⢀⣄⠀⠀⠀⢨⣿⡀⠘⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⡿⣿⣿⡇⠀⠉⠀⠀⢸⠀⢀⠀⢸⡇⠀⠀⠀⣸⠏⠙⠛⠛⠛⠉⠛⠚⠚⠋⠙⢿⣞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠐⠧⣄⣹⠃⠀⢠⠀⠀⣼⣴⣾⣧⣸⡇⠀⠀⣼⠏⠀⠀⣰⣄⡀⡴⠖⠛⠳⣄⠀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣄⣀⡜⠳⢤⡝⠀⢀⡄⠀⢀⠟⢿⣿⣿⣿⣇⣠⣿⣏⢀⣠⠴⠋⠈⢻⡅⠀⠀⠀⢹⣶⡾⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣏⠻⢦⣾⠁⣠⡿⢀⢀⣾⣆⣼⣿⣿⣧⡟⠁⠀⠉⠉⠁⠀⢀⣰⣾⠃⠀⠀⢐⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣙⣣⣏⣴⣿⣿⣿⣿⣿⣮⣻⡿⡇⠀⢀⢀⣹⣷⡾⠿⠋⠁⠀⣰⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣾⣟⢿⡿⣿⣿⣿⣿⠃⣟⠒⠛⠋⣉⠀⠀⢀⣆⣠⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠽⢿⣿⠟⠃⠀⠘⢦⣤⣴⣿⣤⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣧⡀⣨⡿⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠈⠛⠉⠀⠀⠈⠻⣦⠀⠀⢠⡄⢠⡄⢠⡄⢀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣤⠴⠦⣤⣤⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣠⣤⣤⡴⠶⢦⣤⣌⠁⠶
⠀⠀⠀⠀⠀⣤⠉⣰⠟⠉⠀⠀⠀⠀⠀⢀⣿⠋⠛⠶⣦⣄⡀⠀⠀⢀⣠⣴⠶⠛⠉⢿⡀⠀⠀⠀⠀⠀⠉⠻⣆⣀
⠀⠀⠀⠀⢠⡄⣸⠏⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠉⢻⣶⣶⡛⠉⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣼⠋⠉⢿⡄
⠀⠀⠀⠀⢤⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣠⣾⢛⣁⣈⡛⣶⣄⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠹⢦⣴⠟⠁
⠀⠀⠀⠀⢰⠄⣿⠀⢠⡾⠛⢳⣦⣤⣿⠷⠶⢛⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡛⠶⠾⣷⣤⣄⣀⡀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣸⣧⡾⣧⣄⣴⠏⢰⡟⢀⣴⠟⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠻⣦⡀⢻⡆⠈⠉⠛⠳⢶⣼⣇
⠀⠀⠀⢀⣤⠾⠋⢿⡄⠀⠉⠀⠀⢸⣷⠟⠁⠀⣴⠟⠋⠉⠉⠉⠉⠉⠉⠉⠛⢷⡄⠈⠻⣾⡇⠀⠀⠀⠀⢠⡿⠙⠷⣦⡀
⠀⠀⣰⠟⠁⠀⠀⠈⢿⡀⠀⠀⣠⣿⠁⠀⠀⠀⣿⢶⣤⣄⣀⣀⣀⣀⣀⣤⣴⢾⡇⠀⠀⠈⣿⣄⠀⠀⢀⡾⠁⠀⠀⠈⠻⣆
⠀⢸⡏⠀⠀⠀⠀⠀⠈⢿⣄⣼⠋⣿⠀⠀⠀⠀⣿⠀⠀⣌⠉⡍⠉⡍⢉⡄⠀⢸⡇⠀⠀⠀⣿⠙⣧⣠⡾⠁⠀⠀⠀⠀⠀⢹⡇
⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⣿⠀⠀⠀⠀⣿⢦⣤⣀⣀⣀⣀⣀⣀⣠⣤⢾⡇⠀⠀⠀⣿⠀⣸⣿⡅⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠘⣧⡀⠀⠀⠀⠀⢠⡟⠀⠙⣧⣿⠀⠀⠀⠀⣿⠀⠈⡉⠉⡉⠉⡉⠉⡁⠀⢸⡇⠀⠀⠀⣿⣼⠏⠈⢻⡄⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠘⢷⣄⡀⠀⢠⡟⠀⠀⠀⠈⢿⣆⠀⠀⠀⠻⣤⣄⣁⣀⠁⠀⢁⣀⣁⣤⡾⠃⠀⠀⣰⡿⠁⠀⠀⠀⢿⡄⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠉⠻⢶⣿⡁⠀⠀⠀⠀⢸⡟⢷⣄⠀⠀⠀⠉⠉⠉⠛⠛⠛⠉⠉⠁⠀⠀⣠⡾⢻⡇⢀⣤⣤⣄⢈⣿⡶⠟⠉
⠀⠀⠀⠀⠀⠀⣸⡏⠙⠻⠶⣤⣤⣘⣷⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣾⣃⣿⡁⠀⣹⠏⠹⣇⢀⡀
⠀⠀⠀⠀⢠⡾⠛⢳⡆⠀⠀⠀⠈⠉⢻⡟⠛⠻⠿⠷⣶⣶⠶⠶⠶⠶⣶⣶⠾⠿⠟⠛⢻⡟⠉⠉⠛⠛⠋⠀⠀⣿⠀⣁
⠀⠀⠀⠀⠘⣧⣤⣼⠇⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠈⠛⢶⣄⣠⡶⠛⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣿⢀⡅
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⣀⣤⠾⠛⠛⠶⣤⣀⠀⠀⠀⣰⡏⠀⠀⠀⢀⣀⠀⠀⣼⠏⣤
⠀⠀⠀⠀⠀⠀⠀⡘⢷⣤⣀⣀⣀⣀⣀⣀⣿⣶⠾⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠶⣶⣿⣀⣀⣀⣼⠋⠙⢷⡞⠁⠴
⠀⠀⠀⠀⠀⠀⠈⠁⠴⠌⣉⠉⣉⠉⠉⠉⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣴⠟⠀⠉⠉⠉⠻⢦⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠠⣿⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠞⠛⠷⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡟⢷⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡟⢿⡇⢹⡇⢸⠆⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣿⣭⣭⣭⣭⣭⣭⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⡇⠻⠃⠘⠁⠘⠁⢸⡏⠉⣉⠉⠉⠉⠉⠉⠉⢻⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⣷⠟⠛⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠉⠁⢀⡾⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⣤⣤⣤⣤⣤⣤⣾⣦⣄⡀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢶⣄⠀⠙⢷⡄⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠉⠻⠶⡾⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡶⠶⣦⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣤⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢷⣄⠀⠙⠷⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠃⠀⠀⠈⠛⠻⡿⠛⠛⠛⠛⠛⠛⢛⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿
⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⣠⡾⠁⢀⣀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣄⣴⠿⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣀⣀⣀⣀⣉⣀⣸⡇⢠⡄⢀⡄⢰⣦⢸⣧⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣛⣛⣛⣛⣛⣛⣿⡟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡇⢸⡇⢸⣇⢸⣷⣼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⢷⣼⠟⠛⠁

⠀⠀⠀⠀⠀⠀⡖⠒⢲⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⠂⢐⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⢰⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢠⢁⠞⠁⡠⠄⠈⠢⠑⡄⠀⠀⠀⠀⠀⡀⠤⡀⡀⠿⠸⠸⢂⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠠⢤
⠀⠀⠀⠀⠀⡂⡯⠭⢽⠀⠒⠒⡆⠀⠀⠀⠀⢘⠁⡆⠀⡠⠄⡇⠀⠀⠀⠀⠀⡼⠤⠂⠘⡈⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠠⠠⠤⠠⠤
⠀⠀⠀⠀⠀⠄⣏⠉⣿⢰⣄⣠⡇⠀⠀⠐⡈⢮⡀⠅⠀⣇⡴⢠⠂⠀⠀⠀⠀⠈⣄⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⠑⠂⠠⣄⠔⡱
⠀⠀⢸⠈⢹⠅⠏⠉⡿⠸⡏⢀⠇⠀⠀⠀⠈⠢⠍⣁⡉⠡⠴⡣⠑⠄⠀⠀⡔⠁⠀⠎⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠗⠠⠀⣈⣀⠠⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠈⠀⠈⠈
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠔⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⡒⠀⠀⠀⠠⠂⠀⠀⠀⡠⡀⠈⠆⠀⠀⠀⠀⠀⠀⢀⠄⣒⣂⠠⣀⠆⠸
⠀⠀⠀⠋⠀⠊⠀⡄⡂⣀⢇⠀⠀⠀⠀⠀⠀⢀⠔⣉⠢⠔⡠⠲⠁⠀⠀⠀⠀⢄⡀⠀⠀⠀⣇⣠⠃⠀⠀⠀⠀⠀⡐⡐⢁⢄⢀⠐⡌⠎⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡆⠆⠀⠀⠀⠀⠴⡡⠊⠀⠑⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠜⢌⠀⠃⠁⠗⠀⠀⠀⠀⠀⡁⢇⠔⠢⡥⠊⡀⡀
⠀⠀⠀⠀⠀⠀⠈⠊⠤⠌⣜⢀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡂⠀⠀⠀⢄⠙⠪⣂⠀⠀⣊⡔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠤⠤⠧⠠⠤⠸⠤⠤⠧⠤⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒⠁

⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢩⢩⡍⣭⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⠐⠂⠐⠒⡄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⣔⡄⢀⡢⠈⠀⠀⠀⠀⠰⠒⠒⠒⠒⠖⠶⠲⠖⠲⡁⠀⠀⠀⠀⠀⣀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠰⠳⠣⠇⠶⢰⠐⠞⢆
⠀⠀⠀⠀⠀⠙⠀⠘⠝⠀⢀⠀⠀⠀⠀⢀⣘⣈⣃⣛⠄⠀⠠⡐⣄⠇⠀⠀⠀⢀⣀⣀⡀⠁⣀⣀⣀⠀⠀⠀⠀⠆⠤⠴⠤⢤⢔⠢⢑⠾
⠀⠀⠀⢆⣀⣀⣀⣄⣀⣄⣀⠲⠀⠀⠀⠀⢤⠠⠄⠈⠀⡀⠀⠐⡈⡆⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠡⡴⡤⡄⣼⢀⠀⠀⡁⠁
⠀⠀⢘⠘⠒⠒⠒⠒⠒⠒⠒⠓⡆⠀⠀⠈⠀⠀⠀⠓⠉⠒⠐⠚⢝⠇⠀⠀⡏⠉⠈⢰⠁⠀⠁⠈⠀⠈⠀⠀⠀⠀⠈⠳⠥⠬⠶⠥⠄⠪⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠁⠁⠈⠁⠈
⠀⠀⠀⢀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠈⠔⠈⠉⠁⢢⠀⠀⠀⠀⠀⠀⠱⠆⠒⠀⠂⠒⠀⠐⠂⠶⠃⠀⠀⠈⡤⠤⠄⠠⠤⠤⢬⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠀⢀
⠀⠀⢠⠤⠥⠔⠠⡀⢰⠠⠖⢄⡀⠀⠀⠀⠀⣀⣀⠉⠀⠀⠔⡄⠀⠀⠀⠀⠀⠀⠀⡄⢀⢄⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⣽⢛⣙⣫
⠀⠀⠘⠒⠒⠢⠐⠁⢠⠒⠦⠊⠁⠀⠀⠀⠀⣃⣸⣀⣖⣲⣀⡇⠀⠀⠀⠀⠀⠔⡆⡇⠀⣄⡀⢌⠘⠀⠀⠀⠀⡄⠀⠀⢤⠀⠀⠠⠠⠀⠠
⠀⠀⠀⠀⠢⠠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠤⠤⠤⠤⠎⠀⠀⠀⠀⠈⠁⠁⠘⠝⠛⠫⡞⢄⠀⠀⠀⣇⣋⣀⣸⠈⠁⢃⣉⣀⣀
⠀⠀⠀⠠⠄⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠤⠈⠤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠎⠁⠉⠱⠀⠀⠰⠉⠈⠱

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⣛⣛⠿⠿⠛⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⣠⣾⡿⠀⣴⣶⣶⣶⣶⣾⣿⣿⣶⡄
⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⡤⠤⠤⢤⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⢠⡤⠤⢤⣄⣠⣤
⠀⠀⠀⠀⠀⠀⠀⣠⠷⠴⠃⢀⣠⣄⡀⠘⠦⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠞⠀⢀⣀⡀⠀⠳⠼⢃⡀
⠀⠀⠀⠀⠀⠀⡼⠁⣀⡤⡞⠉⣀⣤⠛⠲⢤⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⡄⣾⡿⣟⢭⣶⣦⣀⠀⠹⡄
⠀⠀⠀⠀⠀⣈⡁⠀⡇⠀⣷⣏⠁⠈⣱⣦⣄⣿⠀⢘⣆⠀⠀⠀⠀⠀⢀⣉⠀⠀⣿⡇⡱⢾⣿⡷⢎⢙⡿⠇⠀⣻⡀
⠀⠀⠀⠀⠸⢤⠟⠀⣧⣄⡇⠈⢹⠏⠀⣿⠀⣿⠀⠫⡬⠇⠀⠀⠀⠀⢯⣼⠃⠀⡻⠇⣿⣷⣤⣾⣿⢸⣿⠂⠘⢧⡽
⠀⠀⠀⠀⠀⠘⡆⠀⢧⣀⠉⠲⣼⡤⠚⣿⣀⡿⠀⣰⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢿⣷⣭⣛⠛⣛⣭⢸⡿⠂⢀⡖
⠀⠀⠀⠀⠀⠀⠘⠆⠀⡈⠑⠻⣅⣠⠔⠋⣁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⡈⠉⠵⣿⠿⠛⢀⡀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢮⣉⣧⣀⣀⣀⣀⠸⣉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣽⣄⣀⣀⣀⡀⢯⣹⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡆⣴⡀⢳⠀⣶⠀⠀⢞⡀⡞⠂⡆⣾⠁⣶⣴⢰⠓⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉⠁⠈⠈⠉⠀⠀⠓⠁⠙⠁⠁⠑⠂⠁⠉⠈⠋⠘⠂

⡶⠒⢲⠶⡶⠶⠶⢶⠶⠶⠶⢶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣒⠒⡖⣢⠨⣡⣶⡔⠦⠃⢀⠀⠂⠀⡤⠀⠒⠒⣂⣀⡐⠒⠒⠂
⠀⠀⠀⠀⣀⠤⣺⠁⢠⣤⣤⣤⣶⣶⣶⣾⠀⠀⣾⣦⣴⣿⣿⡧⠀⠨⢎⠌⠜⡼⠠⣖⡻⠷⣔⠃⡎⠀⠀⡀⢰⣷⠀⠁⢻⣿⡇⠀⠿⠿⠿⠿⠗⠐
⠀⠀⠀⠸⢐⠥⠚⡁⢸⣿⣿⣛⣟⣻⣿⣿⠀⠀⠙⢿⣿⣿⡟⠁⠀⣐⣠⣂⣊⣾⡀⠢⠄⠉⣹⡶⣄⠀⢀⠁⠸⠿⠀⢠⠘⠛⣁⣤⣤⣦⣤⣄⠀⠀⡀
⠀⠀⠀⡋⠤⢂⠥⡇⠈⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⠄⠙⠉⠀⠀⣸⡿⠿⠿⠿⢿⣧⣀⠀⢀⡟⠃⠙⠆⠘⠀⢠⣶⣦⠸⠀⣼⣿⢟⣩⣍⡝⠻⣿⣄⠁
⠀⠀⠀⡇⠊⡡⠔⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⣼⡟⠁⠀⢀⡀⠀⡉⢻⣧⠈⠁⠆⠀⠀⠀⠀⠈⠻⠋⠀⢸⣿⡇⣾⣿⣿⣿⣇⢹⣿
⠀⠀⠀⡇⣈⠔⣊⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠹⣿⣇⠀⠀⢘⡁⠉⠁⣸⡟⠀⠀⡃⠀⠀⠀⠀⠀⠀⢠⠀⠘⣿⣧⡹⠿⣿⠿⣣⣿⡟⡀
⠀⠀⠀⣋⡠⢊⠅⠘⠼⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣼⠀⠀⠙⢿⣷⣤⣨⣁⣠⣴⠟⠁⠀⠀⠃⠀⠀⢠⠀⠀⠀⠈⠀⠀⠈⠻⢿⣷⣶⣿⠿⠋⠀⠂
⠀⠀⠀⠧⢈⣤⢊⣠⡀⠀⠀⠀⠀⠀⢀⢼⠀⠀⡒⠄⡁⠠⠐⠀⠀⠈⢻⡻⠻⠟⣿⠀⠀⠀⠀⡆⠀⠀⠀⢄⣀⣀⣀⣠⡄⣠⡠⠠⠤⠤⠤⠤⢠⠲
⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠐⠊⠀⠀⠈⠢⣿⠤⠚⠀⠀⠀⠘⠒⠀⠒⠞⢀⡴⣤⠀⠘⠀⠠⡶⣦⠈⠓⠓⠚⠓⠒⠒⠂⠋⠂⠈⠈⠁
⠀⠀⠀⠋⠀⠀⠀⣀⠄⣆⣂⣖⡠⡀⠀⠀⠀⡌⠁⡀⡀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠚⠿⠂
⠀⠀⠀⠀⠀⠠⡎⢰⠊⠉⠙⢿⣿⣮⣢⠀⠈⠀⠁⠠⣿⡴⠂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣥⣥⣤⣤⡀⢱⡀⠀⡊⠁⠰⠈⠀⣧⢀
⠀⠀⠀⠀⣐⢃⡡⠁⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⣠⣤⣿⢀⡀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⣉⣉⡉⠉⠙⠛⢻⣿⡇⢸⡇⠀⠀⡀⠀⠀⣰⠏
⠀⠀⠀⠀⡉⢀⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢸⣿⣿⣿⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⢷⣆⠀⢸⣿⡇⢸⡇⠀⢀⠀⢠⡴⠃
⠀⠀⠀⢠⡁⣈⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠀⠈⠛⠛⠁⠀⠀⢀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⠀⠸⣿⡇⢸⡇⢀⠀⠀⣸⣿⠀⠻⠃
⠀⠀⠀⠀⡁⢌⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⠀⢠⣄⣰⡆⢀⠀⣿⣿⠀⠀⠀⠀⠐⠘⢿⣷⣿⣽⣿⡛⠋⠀⠀⣿⡇⢨⡇⢸⠀⠀⣿⣿⡆
⠀⠀⠀⠀⢅⠈⣭⣉⠛⢶⣄⠠⠐⠂⢩⣙⢻⣿⡄⠀⠈⢿⡿⠃⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣿⡇⢠⡇⠸⠂⠀⣿⣼⠇
⠀⠀⠀⠘⠂⠁⠈⢿⣷⣄⠻⣧⠔⢠⣿⣿⡆⣿⣷⠀⠀⠀⠀⠀⠀⢄⠻⠿⠿⠿⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣾⠿⠿⠿⢃⣸⠇⠀⠀⠄⠀⡀
⠀⠀⠀⠀⢰⣾⣿⣆⠻⣿⡄⢻⣇⣿⣿⣿⡇⣿⣿⠀⠁⠀⠀⠀⠄⠂⠀⠀⠈⠉⠁⠁⠈⠻⢿⣿⣿⣷⣾⣟⣃⣉⣀⣀⣉⣑⣒⡄⠀⠀⠸⠀⠰⠁
⠀⠀⠀⠀⣿⣿⣿⣿⡆⢹⣷⢸⣿⣿⡿⠏⣰⣿⡟⠀⠀⠠⠀⠀⢷⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠠⠀⠐⠀⠈
⠀⠀⠀⠀⠻⣿⣿⣿⡏⢨⣟⣿⣧⣤⣴⣾⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⣲⠄⣀⡲⠄⢠⠰⠤⠀⣀⣀⡀⠀⠀⠀⢀⠠⠐⣒⣒⣒⡀⠄⠁
⠀⠀⠀⠀⠄⠈⠛⠛⠴⠛⠋⠀⢀⠉⠁⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠘⠛⠀⠀⢹⣿⣷⠀⠁⠀⠓⣿⣿⠿⣿⣿⠿⢷⣾⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢠⠂⠚⠀⠠⡎⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⡆⠀⠀⠀⣿⡇⠀⣿⡏⠀⣾⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠨⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠡⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠘⣿⠀⢹⣷⠀⢸⣇⣼⠏
⠀⠀⠀⠀⠀⠀⠒⣴⣶⣶⢽⣿⢿⡍⠃⣉⣶⣶⣿⡙⠻⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠀⢀⣿⠀⣸⣿⠀⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣼⣿⣽⡧⠧⣿⣿⣿⣿⡷⠀⠀⢐⢂⠀⠀⠀⠀⠀⠉⠉⠈⣈⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣴⣾⣧⣀⣿⣧⣸⣿⣷⣦⡀
⠀⠀⠀⠀⢀⠀⠀⠙⠛⠛⡉⢩⣉⣠⡂⠙⠻⠿⠛⠁⢠⠀⠈⠀⠀⠀⡦⠠⠤⠀⠤⠤⠤⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠒⠐⠂⠂⠒⠒⠒⠓⠚⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠷⣤⡤⠞⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠤⠤⠀⠀⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠶⣄⠀⠀⠀⢠⠀⠀⠀⢀⡴⠖⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⣹⠀⠀⢀⣼⣄⠀⠀⢸⡁⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠶⠶⠞⠛⠳⣄⠉⠀⠈⢁⡴⠛⠛⠶⠶⠞⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⢀⣀⣀⠀⠀⠀⠉⠙⠲⢤⣀⠀⠀⠀⠀⢾⠀⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⢀⡴⠋⠻⢤⠈⠉⠳⣄⠀⠀⠀⠀⠈⠑⢦⡀⠀⠈⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡞⠲⠤⠞⠋⢀⡴⠏⠮⣇⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡴⠋⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⣠⣞⣓⣒⣒⣒⣒⣚⣓⣒⣒⣛⣢⣀⠀⠀⠀⠀⠀⠀⠙⣌⢧⡀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⣆⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⣺⠉⡇⠀⡴⠊⠒⣄⡤⠤⠤⣄⡔⠊⠒⡄⠀⡏⢙⡆⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠻⢤⡇⠀⢧⣀⣠⠟⡇⠀⠀⡏⢧⣀⣠⠇⠀⣧⠴⠃⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠲⠐⠔⣴⡃⠀⠀⢳⣔⠠⠴⠖⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⣷⣤⣤⣥⡸
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢰⠖⠒⢶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡖⠒⢲
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡞⢠⠦⣾⠀⠀⠀⢀⣆⢦⣦⢦⠀⠀⠀⢸⠦⢶⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡸⢁⠇⠀⢸⡀⠀⠀⠸⠜⠜⠞⠏⠀⠀⠀⣸⠀⠀⢇⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢮⠀⢸⠂⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁⠀⠀⢸⡀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⡼⣉⢣⠀⠀⠀⢸⢹⠀⠀⠀⠀⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠓⢤⠙⠲⠤⣄⣸⢡⠛⡎⣇⠀⠀⣸⢸⠀⠀⢀⠴⠓⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⡇⠀⠀⢠⠇⠿⠖⠃⠸⡆⠀⣿⢸⠀⠀⡏⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⢀⣏⡞⠉⠉⠙⢦⣹⡀⣿⣸⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⠶⣶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⠆⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⠀⠀⣿⠀⠈⢻⡀⠀⠀⠀⣤⠀⠀⠀⠉⠙⢧⡀⠀⠀⠀⣸⣏⣹⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⣴⠟⠳⢦⣼⠇⠀⠀⠀⣿⠀⣤⣤⣤⠀⢨⡟⢳⡶⠛⠉⠈⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢾⣅⣀⣠⡴⠋⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⢀⣛⡛⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⣿⠀⡿⠀⣿⠀⣿⠀⣿⠀⣾⠛⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⣤⣤⣤⡤⠠⣤⣤⣤⡄⠀⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡽⠋⠉⠉⠉⠉⠉⠉⢿⡍⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡯⠈⠀⣾⣧⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠇⣨⡝⠂⣸⣿⡏⠀⠀⠀⢋⠁⢤⠤⠒⢂⣷
⠀⠀⠀⢀⡀⠀⠀⠐⠀⢠⠥⠄⢹⣿⣿⣿⣿⣿⡿⠀⠀⠒⣞⠀⠈⡀⢠⣿⣿⠁⠤⢤⣄⡐⢠⢯⢐⣦⣍⡿
⠀⠀⠘⡄⠀⠀⠀⢀⣂⣀⣭⣵⣀⣿⡿⠟⠋⠁⣀⣀⣀⣀⠈⠉⠒⠋⠚⠛⠁⠀⠀⠀⠀⠫⠉⠭⠜⠛⠉
⠀⠀⠀⠙⠛⡛⢛⡻⠛⠉⠀⣹⠛⠛⢋⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠀⠀⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⢠⠉⣐⢎⠐⠁⠀⠀⠀⠀⡇⢠⣿⣿⣷⣶⣶⣶⣶⣦⣤⣬⣤⣤⡀⠀⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢸⢰
⠀⡼⠣⢍⡁⢱⠀⠀⠀⠀⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡿⠟⠻⣧⣐⣲⣆⡼⣸
⡘⢠⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣨⠛⣙⣤⣶⣿⣿⣿⢟⡠⠋⠔⠁
⠇⢸⡀⠀⠀⠀⠀⢀⣀⡀⣸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢾⣟⠁⣿⣿⣿⣿⡟⠉
⠈⠀⢱⢤⡒⣈⣭⣤⠄⠀⢀⠗⠘⠛⢛⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣶⣿⣿⣿⢤⣤
⠀⡔⠁⠀⠚⠛⠋⣁⡤⠖⠉⠛⢶⣤⣤⣀⣈⣉⠉⠙⢌⠻⣿⣿⣿⣥⠖⣺⣿⣿⣿⢿⣫⣷⣿⣿⠀⣀⡀
⠀⠈⠒⠒⠒⠛⠛⠳⠤⠄⠀⣶⠻⠿⣒⣚⠛⠛⠛⠓⣚⣓⣍⠻⣿⣿⣷⠞⠛⣫⣵⣿⣿⣿⣿⣿⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣐⡒⠫⠉⠩⠉⣙⣓⠒⠓⠾⠛⠿⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠒⠠⠬⠥⢉⣑⣒⠒⠂⠨⠥⠄⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⡠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⠠⢍⣉⠑⠒⠒⠤⠬⣭⣉⣉⣉⠀⢻⣿⣿⣿⠟⠁⣀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣈⣉⠛⠓⠶⠤⣤⣄⣀⣀⠀⠀⠉⠁⠀⢸⣿⡿⢃⡴⠊⠑⣢⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⡂⠭⢉⡓⠒⠦⠤⢤⣉⣉⡙⠛⠻⠶⠶⠾⠋⠠⡏⠑⢢⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣚⠁⠀⠀⠈⢉⠚⠂⠀⠨⠉⠐⠂⠀⠀⠉⣍⣩⢿⠒⠒⢂⡄⠈⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣤⣀⣀⡉⠒⠒⠀⠀⠀⣠⢮⢟⣰⢃⢞⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣷⣶⣦⣤⣽⣷⣶⡖⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⡾⠁⠀⠀⠀⠀⠈⢷⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⢀⡿⠙⠳⢦⣄⣠⡴⠞⠋⢿⡀⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃⣀⣀⣴⣛⣛⣦⣀⣀⠘⣇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡴⠶⠚⡟⣩⡿⠋⠉⠉⠉⠉⠙⠿⣍⢻⠓⠶⢦⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢷⡀⠀⢸⡿⠋⠀⠰⠶⠶⠶⠶⠆⠀⠘⢿⡇⠀⢀⡾⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⢷⣴⢻⡇⠀⠀⢘⣛⣛⣛⣛⡃⠀⠀⢸⡟⣦⡾⠁⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⡾⠻⣼⡇⠀⠀⢨⣭⣭⣭⣭⡅⠀⠀⢸⣧⠟⢷⡀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡾⠁⠀⢸⣷⡄⠀⠰⠶⠶⠶⠶⠆⠀⢠⣾⠇⠀⠈⢷⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠓⠶⢤⣧⣙⣶⣄⣀⣀⣀⣀⣠⣶⣋⣼⡤⠶⠚⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡄⠉⠉⠻⣭⣭⠟⠉⠉⢠⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠈⣷⣠⡴⠞⠋⠙⠳⢦⣄⣾⠀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⢷⡀⠀⠀⠀⠀⢀⡾⠉⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠴⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⡀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⢀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡰⠰⠱⠀⠅⡬⢥⠀⠘⡠⢊⠀⢸⢸⠂⢸⠡⡇⢇⠀⢐

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠢⠔⠂⠤⠂⠠⠀⠀⠀⠀⠀⢠⠊⠀⠀⢸⢂⡑⣩⡄⠀⠀⠀⠀⠀⢰⡒⠒⠚⠒⠒⣢⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⡠⠊⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈⠀⡍⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⢠⠀⠀⠰⠀⠀⠀⠀⠀⠐⣄⠊⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⡊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡆⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠉⠈⠁⠁


⠀⠀⠀⠀⠀⠀⠒⠀⡅⠀⠀⢨⠀⢲⠀⠀⠀⠀⠀⠀⠤⠀⠀⠤⠀⠐⠇⠀⠀⠀⠀⠀⠀⠔⣉⢤⠄⡑⢄⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⢪⠔
⠀⠀⠀⠀⠀⠀⡁⠀⠄⠀⠀⠠⠀⢘⠀⠀⠀⠀⠀⣙⠀⠀⠀⠂⣻⠐⣁⡀⠀⠀⠀⠀⢘⠀⠅⡼⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠁⢂⢀⢄
⠀⠀⠀⠀⠀⠀⡁⠀⠆⠀⠀⠐⠀⢨⠀⠀⠀⠀⠀⠴⠈⠉⠉⠉⢼⠠⡉⠁⠀⠀⠀⠀⠈⠢⡙⠀⠐⣂⠼⡀⠀⠀⠀⠀⠀⠀⡄⡤⠣⣀⠂⢌⠈⠂
⠀⠀⠀⠀⠀⠀⠤⠀⡃⠀⠀⢘⠀⠼⠀⠀⠀⠀⠀⠈⠒⠀⠀⠒⠁⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠑⢌⠦⠀⠀⠀⠀⠀⠀⠀⡊⡁⠀⠀⢛⢑


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⢰⠀⠠⡄⡇⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢉⠀⢈⠀⡀⠀⠀⠀⠀⠀⠞⠃⠀⠀⠘⠓⠀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠆⣠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡃⠐⠀⢀⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢤⠊⠀⠀⠘⢐⠝⠀⠀⠀⠀⠀⠸⠅⠈⠀⠣⠀⠘⠀⠅⠀⠀⠀⠀⠀⠄⠈⠁⠀⡁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠢⠝⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⠀⠭⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠤⠤⠤⠀⠒


⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡤⢄⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠔⢉⣄⡉⢂⠐⡄⠀⠀⠀⠀⢰⠃⢨⠃⠄⢓⠈⠁⠠⠀⠀⠀⠀⠀⠈⡃⡰⠂⠘⢤⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡆⠒⢅⡨⠒⢒⡀⠀⠀⠀⠀⠀⠀⢸⠀⠖⠈⠁⢈⠆⡇⠀⠀⠀⠀⠘⢥⠋⠀⣀⠌⠀⠀⡀⠀⠀⠀⠀⠀⡶⠄⠇⠘⠁⢸⢨⠉
⠀⠀⠀⠀⠀⠀⢁⡨⠀⠒⠢⠀⣅⣨⠀⠀⠀⠀⠀⠐⢄⠑⠠⠤⠐⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⢄⢀⠄⢨⡀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢋⡑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢚⡙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣴⣶⣿⢟⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡻⣿⣷⣦⣻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⣡⣾⣿⣿⡿⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⢟⣴⣿⣿⣿⢋⣾⣿⣿⡟⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢣⣾⣿⣿⣿⡇⣾⣿⣿⢏⣼⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣷⣌⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣝⣋⣵⣾⣿⣿⣿⣿⣿⣦⡙⠿⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣥⣬⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠳⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⢟⣤⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇⣙⠻⣿⣿⣿⣯⣴⣿⣯⡙⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣣⣾⣿⣿⡌⢿⣿⣯⡻⣿⣿⣿⣦⡙⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢩⣾⣿⣿⡿⢋⣴⣷⡎⣿⣿⣮⡻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⣴⣿⣿⢟⣅⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠿⠿







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣭⣭⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⠴⣶⠤⣄⣠⠞⠛⠛⠛⠨⠛⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡞⠁⠀⣿⠀⠞⢳⡀⠀⠀⠀⠈⠉⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠛⠒⠒⢺⠇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⣄⡈⠳⣄⣠⠞⠀⠀⠀⣶⣶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠛⠚⠛⠛⠂⣦⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣽⡉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠿⠿⠭⠷⠧⠽⠧⠿⠾⠧⠿⠿⠾⠾⠿⠿⠮⠿
⠀⢀⡰⢢⣠⠄⠀⠀⢠⠶⠶⡄⢀⣀⡠⠀⠀⠀⠀⠀⠂⣐⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⣴⣶⣿⣦
⠀⠀⡅⣇⣆⡇⠀⠀⠻⣄⣠⣏⠘⠿⠳⣅⠀⠀⠀⠈⠸⠤⠇⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠘⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⢀⡐⠆⠐⠇⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢴⣷⠀⠀⠀⠀⠀⢠⣾⠿⣷⣄⠀⠀⠀⠀⠀⣠⡄⣿⡇
⠀⠈⢁⠻⠿⡀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠷⢠⣤⠾⠆⠀⠀⠀⢹⣧⣀⣼⡿⠀⠀⠀⣿⡇⣿⡇⣿⡇
⠀⠀⠙⠀⠀⠉⠀⠀⠀⠀⠃⠈⠃⠘⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃

⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢠⠤⠤⡄⠀⠀⠀⠀⢰⣶⢀⣀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⠀⣠⣲⣂⠄
⠀⠀⢉⡏⢥⡄⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⣿⢸⣿⢸⣷⠀⠀⠀⠸⠿⣿⠿⠇⠀⠀⠀⠈⣹⣿⣿⣮
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠚⠛⠚⠛⠚⠛⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠚⠂⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠘⠛⠛⡷⠤⠀⠀⠀⠀⣏⣉⣉⣹⠀⠀⠀⠀⢠⣋⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠖⢂⡐⠶
⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠈⠣⠤⠴⣅⠀⠀⠀⠀⠀⣐⣖⣯⡇⠀⠀⠀⠀⣆⡘⢃⣤
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡷⡧⠘⡆⠀⠀⠀⠀⢀⡄⠀⠠⠆⠀⠀⠀⠀⡔⢉⡙⢆⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⡐⢈⡐⠂
⠀⠀⣇⣄⣼⡃⠀⠀⠀⠘⠃⠁⠶⠀⠀⠀⠀⠀⠀⠣⣄⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠡⢈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⣡⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣦⡙⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠛⠿⡿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣂⡀⣴⣮⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠇⣿⡇⣾⣿⢘⣛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⣋⡻⡏⣼⣿⢸⣿⠃⣿⡇⣾⣿⢸⣿⠟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣿⣇⠁⣿⣿⣼⣿⣸⣿⣃⣿⡇⠚⠁⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣭⣭⣍⣙⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢻⣦⣤⣀⠀⠀⠀⠀⢠⡴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠁⠀⠈⠳⣄⠀⠀⢻⣄⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⢹⡷⢦⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠉⠉⠉⢷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⣄⠀⠈⠙⠋⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠸⣧⣤⡟⠀⠀⠀⠀⢀⣸⣀⣀⣀⣸⣀⣀⣀⣸⣇⣀⣀⣸⣃⡀⠀⠀⠀⠀⠘⢷⣤⡿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠉⣻⠀⠀⠀⡇⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣦⠀⠀⠀⠀⠀⡇⠀⠀⢼⡋⢙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠋⠀⠀⠀⠓⠒⠒⠒⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠃⠀⠀⠈⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⢀⡀⢀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⣨⡷⠒⠒⠒⠒⠒⠒⠒⠲⣿⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⡘⠃⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠒⠒⣿⣀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣻⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣀⣀⠀⠀⠀⠀⢿⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⠸⠧⠤⢴⡏⢉⣷⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣦⣀⣀⣠⠞⠁⠀⠀⣾⠋⢹⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠟⠀⠀⠁⠀⠀⠀⠀⠘⠛⠛⠁⠀⠈⠳⣄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠺⣇⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⠶⠶⠶⣶⣶⠶⠶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⠀⣰⣿⣿⣿⣷⡘⢿⣿⢃⣼⣿⣿⣿⣆⠀⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢻⣿⣿⠁⢰⣿⣿⣿⣿⣿⣷⡌⢁⣾⣿⣿⣿⣿⣿⡆⠀⢿⣿⡟⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢻⡏⠀⣸⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣇⠀⠘⡟⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠻⠿⠷⣶⣄⡀⠀⠀⠀⠀⠀⠀⢸⡿⠻⣿⠟⣿⡿⢿⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠰⠆⠀⠀⠀⠴⠆⠙⣿⣆⠀⠀⠀⠀⠀⠸⠷⠾⠿⠶⠿⠷⠾⠿⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⢻⣶⣤⣤⣤⣤⣤⣤⣤⣾⠟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣿⠀⣾⡟⢿⡆⢠⣶⠀⣴⡟⢻⣦⠀⣿⡋⢹⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣾⣿⠀⠙⠿⠟⠁⠀⠿⠀⠘⠻⠟⠃⠀⣿⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢀⣴⣶⠄⠠⡦⠀⢶⠀⢰⣶⣦⡀⣿⠁⠀⣠⣴⠿⠟⠿⢶⣄⣠⣴⠾⠟⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⢠⣤⣤⣤⣤⣤⡀⠀⠙⣿⠏⠀⢰⡿⠁⠀⠀⠀⢀⡙⠛⠁⢀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣸⡏⠉⠉⠉⣿⣇⣠⡾⠋⠀⠀⢸⣧⠀⠀⠀⣼⡟⢻⣧⠀⣿⠂⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠷⣶⣶⡶⠿⢿⡏⠀⠀⠀⠀⠀⠻⣷⣄⠀⣿⡿⢿⣿⠀⣿⠁⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⠶⠶⢿⣇⠀⠀⠀⠀⠀⣼⡷⠶⠶⠶⢶⣦⡀⠈⠻⣶⣌⠀⠀⠁⠀⢈⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⢋⣤⣤⣄⠀⠀⠈⢻⣆⠀⢈⣿⣶⡀⢀⣴⡿⠛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣧⣼⡿⠛⠛⠛⢿⣿⠛⠛⠁⠈⢻⣿⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠶⣶⣶⡀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣿⠏⣠⣶⠶⠶⠾⠟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⠉⢿⣦⣉⣉⣉⣉⣉⣉⣉⣉⣁⣴⠿⣧⣄⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠉⣿⡏⠉⠙⣿⠉⠙⠻⣿⣍⡀⠈⠙⠻⠛⠛⠛⠛⠛⠿⣯⣼⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⣶⣄⣠⣤⣴⡿⠇⢀⣴⢿⣦⠀⠀⠀⠙⠻⣶⣄⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣴⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡾⠏⠉⠁⠀⠀⠀⠘⢿⣶⡿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣶⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⡣⢿⡄⣼⣿⡄⢸⡇⡄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⡀⢠⣾⣿⣿⠀⢸⣧⢸⣿⣿⢧⡄⣿⣷⣶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠈⠀⣬⠉⣀⣻⣿⣿⣿⡿⣤⣷⣿⣯⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⣣⡄⠀⠈⢀⣸⣿⣿⣿⣿⠙⢻⣧⣿⣧⣿⢯
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠓⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠒⣀⣮⣿⣿⣿⣻⣿⣿⡘⣿⣯⡿⢿⣿⣿
⠀⠀⠀⠀⠈⣿⣤⡀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠤⡐⠻⠟⠉⠻⠆⢾⣿⣿⣿⣽⣿⡏⣻⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣌⠉⠲⣶⣤⣤⣀⣀⡀⠹⣷⣤⠀⠀⠀⣀⠀⠀⠀⠘⠀⠀⠀⠀⣠⠁⠀⠀⠘⠃⠀⢠⣤⡼⠃⠀⣨⣽⣿⣿⣿⣿⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⢿⡟⠳⣦⣤⣬⣤⣭⣬⣭⣽⣿⣿⠿⣶⣶⡦⠼⢦⣄⣀⣀⣀⣘⡃⠈⠁⠀⣠⣤⣀⡀⠈⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠘⢿⣶⣾⣾⣿⣿⣾⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢱⣿⣿⣿⡿⠿⣿⣿⣿⣀⣤⣤⣸⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡼⣿⣿⡁⡀⢠⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠆⠀⠞⠀⣤⣤⠀⢰⣿⣿⣧⡀⣁⠀⠙⠿⢀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣷⣿⣷⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠂⠀⠀⢠⡦⡀⣀⡀⠁⠀⠸⣿⣯⣷⣿⣯⡈⣹⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠀⠺⠗⠀⠁⠇⠀⡰⠂⣶⠢⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⣿⠿⣿⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠛⠋⠙⠉⠿⠷⠈⢿⡿⠿⠿⠆⣿⣵⣿⣿⣿⣟⣿⡟⣿⣙⣿
⣿⠿⠿⠿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠢⢈⠠⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠈⠁⡐⠀⠄⠀⢀⠀⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⣀⣀⡈⠀⢠⠂⠀⡀⠈⠤⠀⠀⠀⠎⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠲⠀⢸⡆⠚⠒⠓⠂⠀⠈⠀⠂⠘⡀⡀⠂⠀⠠⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠸⠆⠭⠭⠅⠀⠀⠐⠀⠁⠈⠂⡀⠁⠈⠀⠆⠀⠢⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠊⠀⠀⠴⠄⠠⠤
⠀⠀⠀⠀⠀⠀⡄⠀⠨⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡍⠉⠉⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠠⠀⠀⡇⢈⣉⠀⢘⡁⣉⡁⠀⠐⠀⣀⢠⣄⠁⠀⠀⠀⠀⠣⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠐⠀⠀⠀⠀⠀⠀⠂⡃⠀⠀⠰⠀⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢈⠑⠀⠀⠀⠀⠀⠀⠀⢠⠍⠈⢅⠀⠀⠀⠀⠀⠀⠄⢄⣀⠂⡀⠀⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠌⠀⠠⠀⠆⠰⠀⠀⠰⠀⠀⠦⠆⠆⠆⠀⠠⠀⠐⠀⠈⠂⠠⠊⠊⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⡆⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠆⠐⠀⠀⡀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠄⠀⠉⠈⢀⣄⠀⣀⠀⢀⡀⠀⣀⡀⠠⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢒⠒⠒⠒⠒⠒⢢
⠀⠀⠀⠀⣰⣿⡿⠃⠁⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⣿⣧⢠⢶⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣅⣿⢀⡀⣶⢸
⠀⠀⠀⠀⡏⠁⣶⣄⠘⢛⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⢼⣻⣗⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⣃⡛⠛⠘⠃⠛⢸
⠀⠀⠀⠀⠱⡀⠸⠋⣍⣬⣿⣷⣶⣢⠀⠀⠀⠀⠀⠀⢸⣿⡗⠐⠢⠄⢈⠉⢉⡡⡀⠀⠀⠀⠀⠀⠀⢸⠠⢴⡆⢹⣯⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠈⠑⠺⠀⡀⣀⣶⣀⢠⠁⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠒⠚⢉⡠⠔⠃⠀⠀⠀⠀⠀⠀⢸⣘⡒⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠥⠥⠭⠭⠜⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡠⠤⠤⠤⣀
⠀⠀⠀⠀⠀⢲⢺⡅⢰⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⢛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠿⢠⠎⠀⡶⠒⣦⠀⢳
⠀⠀⠀⠀⠚⠚⠛⠃⣼⣿⣯⣽⣿⡇⠀⠀⠀⠀⠀⠀⢀⢒⡒⡒⠺⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠛⢺⡀⢀⣷⠶⠟
⠀⠀⠀⠀⠀⠻⠛⡇⠈⠣⣀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠘⠌⣁⣉⣀⣀⣈⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⠈⠁⠄⣷⠀⠀⢠⠇
⠀⠀⠀⠀⡰⠁⢀⣙⡎⠉⢳⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⢚⡛⣛⠛⡛⠛⢓⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣐⣀⣀⣁⣿⠐⡖⠂
⠀⠀⠀⠀⠹⣿⣿⣿⣇⣀⣸⣿⣿⣏⠇⠀⠀⠀⠀⠀⠐⠬⠥⠥⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠐⠃

⠀⠀⠀⠀⠀⠂⠐⠀⠂⠐⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠈⠈⠀⠁⠈⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠉⠀⠀⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⢘⠀⠽⠠⠤⠀⢿⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠆⠀⠙⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⠁⠀⠀⢱
⠀⠀⠀⠀⢨⠀⠀⢀⠴⠤⣀⠔⣋⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠶⠸⠿⢂⡴⠃⢠⣄⠀⠀⠀⠀⠀⠀⢠⠒⢁⠔⣾⣟⣻⣷⠈⠢⡀
⠀⠀⠀⠀⠰⠀⠶⠁⡒⡆⠤⠄⣧⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡴⠋⠰⠀⠈⠉⠀⠀⠀⠀⠀⠀⢣⠀⣿⡿⣿⣝⣶⣾⠀⢀⠇
⠀⠀⠀⠀⢚⠀⣯⡇⣿⡇⣷⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠃⠀⠶⠀⠸⠯⠂⠀⠀⠀⠀⠀⠀⠀⠁⣿⠿⡟⡏⡿⢿⠃⠁
⠀⠀⠀⠀⠘⠰⠻⠷⠻⠷⠿⠳⠿⠧⠀⠀⠀⠀⠀⠀⠀⠈⠲⠒⠲⠒⠒⠒⠖⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠷⠷⠿⠾

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠐⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠂⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠈⠐⠂⠐⠂⠀⠐

⡿⠟⠋⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠀⠀⠀⢀⠤⠾⠿⠿⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⣀⣤⣶⠟⠋⠁⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⣄⣀
⠀⣠⣴⣾⠿⠋⠀⠀⠀⢀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⣽⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷
⣿⠟⠋⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⠁⠀⡿⠟⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣋⣽⣿⣿⣿⡿⠟⢿⣷⣶⣤⣀
⣿⣿⣿⣿⣿⣾⠉⠉⠛⠻⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢈⠍⢺⣿⡇⠀⢸⣿⠟⠉⠙⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣠⣶
⣿⣿⣿⣿⣿⣿⣦⣤⣶⡾⠛⠃⣀⠖⢶⣄⠀⠀⠀⣤⠿⠟⠃⣰⣄⣀⣴⡾⠛⣁⠀⠛⠃⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⣦⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣿⡿⠄⠀⢿⢿⡾⢛⣽⠟⢶⣴⠿⠀⠐⢋⣠⣍⣿⠏⢀⣼⠋⠑⠂⠀⢀⣬⣿⠶⢦⣤⣼⣿⠏⠁⢸⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡘⠁⡿⢣⣾⠿⠁⠰⠿⣶⠛⠋⢀⣄⣉⣿⠿⣿⣷⣾⣿⣿⡧⢠⣾⣿⣦⣄⣠⣿⣦⡾⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⣃⠀⠀⢠⣤⣉⣷⣶⣾⡿⣿⠷⣶⣤⣾⠋⠀⣉⡳⢾⠛⢍⣙⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣩⣿⣷⣶⠎⣛⢉⣩⡿⠀⠀⠤⢱⡌⠛⠁⣧⣀⢨⣶⡿⣷⣶⣀⣻⣿⣷⣦⣤⣩⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣭⠤⣿⣦⣩⣶⣿⢤⠄⠀⣻⡀⠈⣥⣼⣿⣭⠟⠻⠟⢋⣿⣿⣿⣿⣿⣿⡿⢻⣷⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣷⣿⣽⠶⣿⣉⢛⣿⣿⡟⣯⣾⠿⣿⣿⣿⣽⣯⣀⣀⠀⠀⠀⢉⣿⣿⣦⣭⣿⣿⡟⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣷⣿⣿⡳⡝⠲⣶⣬⣽⠟⠁⣠⣵⣏⡃⠺⣦⠟⢈⣿⠉⣿⣿⣿⣴⣾⣿⣿⣿⣿⡿⢷⣼⣿⣷⣾
⣋⠿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡳⠏⣧⣉⣙⣷⣶⠿⠷⣶⣾⣿⣿⣤⣙⢛⣛⣶⣿⠟⣷⣿⣽⣿⣿⣿⠻⠖⣿⣿⣷⣿⡋⠘⣿⣿