⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⠐⠂⠐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂
⠨⠅⠨⠅⠨⠅⠨⠅⠨⠅⠨⠅⠨⠅⠨⠅⠨⠅⠨⠅⠈⢁⣀⣤⣶⢶⣖⣛⣛⣛⣛⢷⢶⣶⣤⣁⠈⠡⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡
⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⠐⠂⣤⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣝⣻⣦⡀⠐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂
⠨⠨⢑⠌⠡⡊⢑⠌⠡⡊⢑⠌⠡⡊⠑⢈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣷⡄⢈⠡⡊⢑⠌⠡⡊⢑⠌⠡⡊⢑
⠰⠌⠡⠕⠨⠄⣢⠵⠬⡄⠢⠕⠨⡀⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡺⡵⡻⡄⠌⠄⠢⠕⠨⠄⠢⠕⠨⠄⠨
⢐⡂⢐⡂⢐⠢⢠⠋⢙⡌⡐⠂⢀⡿⡾⣽⣯⣽⣯⣽⣯⣽⣯⣽⣯⣽⣯⡽⣯⣽⣯⣽⢿⣯⣯⢽⣯⣽⣯⣷⣝⣞⡽⡀⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐
⠨⠅⠨⢅⡂⠐⡢⢥⠻⣞⠌⢀⣟⣿⣿⡿⣼⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣻⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⠈⣿⢽⣷⡀⠨⠅⠨⠅⠨⠅⠨⠅⠨
⢐⡂⠄⠨⠑⠨⠅⢸⠸⣸⡀⣿⠁⣿⡿⣴⢏⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣚⣟⣄⣿⣿⣿⣯⣷⣏⡆⢐⡂⢐⡂⢐⡂⢐⡂⢐
⠨⢅⡐⠂⡐⢂⡐⢂⡐⠂⣼⣿⣶⣷⣱⡟⠏⢿⣿⣿⣾⢻⢉⣿⡟⣿⡏⣿⢹⢹⢽⣿⣿⣷⣯⣷⢿⢿⣿⣿⣿⣿⢸⢺⢻⡀⠌⠡⠌⠡⠌⠡⠌⡁
⢐⠨⢕⠪⠅⠨⠅⠨⠅⢀⣿⣿⣿⡗⣿⣸⣿⣿⢽⢯⣿⣾⣾⣿⣿⣿⢹⣷⣿⢸⢸⣮⣿⣿⣿⡊⡎⡮⣿⣿⣿⣿⡇⡏⣷⢧⠐⡂⢐⡂⢐⡂⠌⡑
⠨⡂⢈⠠⡂⢑⠌⠠⠌⣸⣻⣿⣿⡃⡟⣿⣿⠯⣾⣮⢸⣿⣿⣿⣿⣿⣾⠘⡜⡌⡳⠸⡜⡿⣿⣟⣿⣿⣿⣿⣿⣿⣯⣿⣟⣧⣷⠈⠅⠨⢅⡂⠨⢅
⢐⢑⡂⠐⠑⡈⢄⡂⠄⣿⣿⣿⣿⡃⡇⣿⡿⣼⢸⢹⠘⣏⡞⣿⣿⣿⣿⡀⠙⣦⣷⠹⡻⣯⠻⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣮⢗⢿⡀⠐⠊⠡⢂⡑
⠨⠅⡈⢐⡂⠠⢌⡐⢀⡗⢺⣿⣿⡆⡇⣿⢫⠓⢄⣼⡀⣯⣿⢻⣿⣿⢸⡀⡤⠊⠛⠷⠈⠿⣍⢶⣼⡇⡿⢿⣿⣿⣿⣿⣹⢿⣿⣾⠾⠁⠢⠅⠨⠅
⢐⠌⠡⠌⡑⠢⠌⣠⣿⣹⢸⣿⣿⣗⣷⠏⡿⡀⡀⠘⡏⠞⣼⢧⢿⣿⡘⡀⣀⠤⠖⠒⢒⣀⣀⣀⣠⣷⠾⣯⣿⣿⣿⣿⣿⡀⢄⢄⠢⠌⡑⢂⡐⠪
⠨⢐⡂⠄⡈⠄⠻⣍⣬⣿⣇⣾⣺⣯⣹⣿⠃⣀⣀⣙⣋⣙⡛⠆⠷⣶⣦⣷⢐⣯⣿⣿⣻⠿⣿⠉⡗⡧⣿⣿⣿⣿⣿⣿⡿⡀⠢⢂⡐⠪⠅⠨⢕⡂
⢐⠌⡑⠨⢐⠪⠂⡀⡀⡀⣿⣿⣿⣷⡍⣿⢸⡛⠛⠛⢿⣿⢿⡀⡀⡀⡀⡀⡀⡀⣴⡹⢓⡼⠁⠰⠁⣯⣿⣿⣿⣿⣿⣿⣗⡆⢂⠨⢕⡂⢐⡢⠅⠨
⠨⠂⠨⠅⠨⠅⠨⠅⠠⠌⢹⣿⣿⣿⣷⣿⡀⢷⡀⠙⢤⣉⠟⡀⡀⡀⡀⡀⡀⡀⡀⣀⡀⡀⡀⡀⡀⣟⣻⣻⣻⣻⣾⣿⢟⣇⠨⡂⠨⠅⠨⢅⡐⠡
⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢸⣿⣿⣿⣿⢸⣿⡀⡀⡀⡀⠃⡀⡀⠃⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⣸⣿⣿⣿⡿⣿⡏⣹⣽⡀⡐⢂⡐⢂⠄⢐⠢
⢨⠅⠨⠅⠨⠅⠨⠅⠨⠅⣸⣯⣽⣯⣽⢸⣿⡇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣸⣿⣯⣽⣯⠇⣇⢇⣿⠈⢧⠨⠅⠨⠅⡐⠡⠌
⠨⢂⡐⢂⡐⢂⡐⢂⡐⠂⢹⣽⣷⢿⣿⡅⣿⣿⡀⡀⡀⡀⡀⡀⠐⣄⡀⢀⠞⡀⡀⡀⡀⡀⢀⣾⡇⣿⣿⣿⣿⣸⣿⣜⠇⡈⠨⡂⢐⡂⢐⡂⢐⡂
⢐⠡⠌⠡⠌⠡⠌⠡⢌⡀⣟⡿⠸⡘⣿⣷⣿⢙⣿⣤⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣴⡟⣿⣸⣿⣿⡿⢡⣿⣇⠟⡀⡑⠨⠅⠨⠅⠨⠅⠨⠅
⠨⢐⡂⢐⡂⢐⡂⢐⢁⠖⠟⠁⢷⢻⡝⡿⡸⡸⣮⢿⠻⣿⣷⣦⣄⣀⡀⡀⣀⠤⠂⠁⣾⠟⣴⣵⣫⣿⡻⣮⣿⣿⡀⢐⠨⢑⡂⢐⡂⢐⡂⢐⡂⢐
⠨⠅⠨⠅⠨⠅⠨⠅⠨⢅⡂⠨⡀⠳⣿⣷⣧⣷⡛⢸⠐⠦⣭⡀⣉⠆⡀⡀⡀⡀⡀⡀⣇⣉⣵⣯⣷⣾⣿⣿⡁⡏⠠⢌⡂⠨⠅⠨⠅⠨⠅⠨⠅⠨
⢐⡂⢐⡂⢐⡂⢐⡂⠄⠨⠅⢑⡂⡀⠈⣟⣪⣭⣽⡟⡀⡀⢁⡿⠁⡀⡀⡀⡀⢀⣴⠟⠉⠒⠮⣽⢿⣻⢰⢏⣽⡀⠂⠨⠅⢐⡂⢐⡂⢐⡂⢐⡂⢐
⠨⠅⠨⠅⠨⠅⡈⢐⡂⢐⡂⠨⠅⣰⢹⣽⣿⢡⢱⡀⡀⡀⣿⡀⡀⡀⠋⢉⣼⠟⡀⠉⠉⡀⣰⣯⣿⣟⣿⣽⠁⠌⢂⡐⠂⠨⠅⠨⠅⠨⠅⠨⠅⠨
⢐⡂⢐⡂⢐⡂⠌⠡⠌⠡⠌⢀⠞⡀⢸⣮⢿⣿⢿⡀⡀⣸⠇⡀⡀⡀⣴⠟⡀⡀⡀⡀⡀⢀⣿⣿⣿⣽⣹⠃⠷⡀⠌⡑⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐
⠨⠅⠨⠅⡈⢐⡂⢐⡂⢀⡶⠁⡀⡔⠁⠹⣿⣾⣆⡀⡀⣿⡀⡀⣠⡿⠁⡀⡀⡀⡀⡀⡀⣾⣿⣿⣡⢃⠃⡀⡀⠘⡄⠅⠨⠅⠨⠅⠨⠅⠨⠅⠨⠅
⢐⡂⢐⡊⢁⡊⢁⠊⡴⠁⡀⡀⠞⣀⣀⡀⡀⠈⡀⡀⡀⣿⠈⣾⠋⡀⡀⡀⡀⡀⡀⡀⡀⣿⣜⠏⡏⣿⡀⡀⡀⡀⠘⣄⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐
⠨⠅⠨⠅⠨⠅⣠⠋⡀⡀⡀⣾⡋⡪⣁⢎⣝⢦⡀⡠⠒⣇⣿⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⠿⣿⣇⡀⡀⡀⡀⡀⡀⠈⢦⠡⠌⠡⠌⠡⠌⠡⠌⠡
⠰⢂⡐⢂⢀⡾⡀⡀⡀⡀⡀⡿⣿⣛⠫⡳⣳⣞⣸⣳⡀⠈⣄⡀⣀⣀⣀⡀⡀⡀⡀⡀⡀⡀⠘⡀⠢⡀⡀⡀⡀⡀⡀⡀⡀⠹⣄⢐⡂⢐⡂⢐⡂⠐
⢐⠡⠌⣰⠋⡀⡀⡀⡀⡀⢠⡀⡀⡀⠈⠉⠉⠛⢻⠱⣀⠼⣼⣼⣧⣼⢍⢯⢷⣄⡀⡀⡀⡀⡀⢀⠞⠳⡀⡀⡀⡀⡀⡀⡀⡀⠈⣦⠡⠌⠡⠌⠡⡂
⠨⡀⣴⠁⡀⠉⠒⡀⡀⢀⠏⡀⡀⡀⡀⡀⡀⡀⡀⠙⠒⠋⡀⠙⠾⣟⠷⡺⣪⣵⣟⣄⠜⡀⢀⠏⡀⢁⠙⣄⡀⡀⡀⡀⡀⡀⡀⡀⠳⡐⢂⡐⡈⢐
⢐⡀⡇⡀⡀⡀⡀⠘⡖⣹⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⠉⠳⢮⣛⣻⣿⣷⣤⠋⠌⠡⢌⠨⠄⠳⡀⡀⡀⡀⡀⡀⡀⡀⠙⡌⠢⠌⡑
⠨⠂⡇⡀⡀⡀⡀⡀⡇⡏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⠛⠿⡿⠁⢐⡂⢐⡂⢐⡂⠌⡈⠳⣄⡀⡀⡀⡀⡀⡀⠈⣆⢂⠨
⢐⠡⢻⡀⡀⡀⡀⡀⡇⡇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⠨⠅⠨⠅⠨⠅⠂⠌⠡⠌⡀⠳⡀⡀⡀⡀⡀⡀⠈⡄⠐
⠨⠨⠈⡀⡀⡀⡀⡀⣿⡇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡾⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⠂⣀⡽⠖⠒⡀⠤⡀⡀⠸⠐
⢐⢈⠄⢳⡀⡀⡀⡀⠸⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡼⠠⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡⣠⠞⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⠨⡐⠊⠈⡄⡀⡀⡀⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣸⡀⢂⡐⢂⡐⢂⡐⢂⡐⢂⠐⡴⠁⡀⡀⡀⡀⡀⡀⡀⡀⣠⠋⠠
⢐⡑⢂⠄⢷⡀⡀⡀⢰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⠌⠡⠌⠡⠌⠡⠌⠡⠌⣠⠋⡀⡀⡀⡀⡀⡀⡀⡀⣤⠋⡀⢂⡐
⠨⠅⠨⡂⣿⡀⡀⢠⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⡀⢐⡂⢐⡂⢐⠂⣤⠋⡀⡀⡀⡀⡀⡀⡀⢀⡴⠋⠄⠡⠌⠡⠌
⢐⡂⠐⠡⢳⡀⡀⠃⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢳⢈⡤⠖⠦⠴⠃⡀⡀⡀⡀⡀⡀⢀⡤⠚⠁⡐⢂⡐⢂⡐⢂⡐
⠨⢑⡂⠄⡇⡄⡞⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢰⠐⢒⠤⠚⡀⡀⡀⡀⡀⡀⡀⢀⡤⠚⠠⢂⡐⠨⠅⠨⠅⠨⠅⠨⢑
⢐⠡⡂⠨⠘⣁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⠚⡀⡀⡀⡀⡀⡀⡀⢀⠴⠋⠠⡂⢐⠢⢌⡐⢂⡐⢂⡐⢂⡐⠨⠅
⠨⠨⢕⡢⡂⡟⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢐⠊⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠣⣄⡀⡀⡀⡀⡀⡀⡀⡟⢐⡈⢐⢑⡂⢐⠨⠅⡨⢅⠨⠅⡨⡐⢂⡐
⠠⠄⠨⢅⢰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠳⡀⡀⡀⡀⡠⡏⠄⠨⠅⠨⠅⠨⠅⠠⠄⠨⠌⠨⠅⠡⠌⠡⠌
⢐⡂⠐⡀⡏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢦⣀⣌⠎⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡊
⢘⠡⢂⡀⡅⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠘⡄⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡⠌⠡⠌⡑
⠨⠠⡢⢠⣷⣄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⠐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⡐⢂⠌⠡
⢐⠐⢠⠃⡀⠉⠿⣷⣤⣈⠢⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠌⠡⠌⠡⠌�