⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀⠀⠀
⠀⠀⠀⡼⣵⠔⠒⠒⠢⠊⠉⢩⠻⣷⡀⠀⠀⠀
⠀⠀⠀⢨⡧⠀⡠⠀⠀⠀⡀⠀⠉⠑⢵⠀⠀⠀
⠀⠀⡠⠊⠀⡸⠄⠀⠀⠀⢱⠠⡐⡀⠀⠡⠀⠀
⠀⣰⠁⢀⢆⣇⡀⡄⠀⡀⣤⡷⢤⣡⠀⠀⢃⠀
⠀⢿⠀⣬⠏⣵⣿⣯⠀⣿⡿⣿⣧⢹⡄⠀⡸⠀
⠀⠈⢲⡷⠀⠑⠒⢋⣀⡘⠒⠒⠁⡮⠗⠛⡀⠀
⠀⡰⠃⡷⢄⣀⣀⠀⠀⢀⣀⡠⢴⢰⠀⠸⡬⠖
⢸⡾⡀⢇⠀⡔⠘⢻⡟⠋⠁⢉⣊⢺⢀⠧⢰⡀
⠀⢩⢚⠛⣯⣿⣿⣾⣿⣿⣿⣥⣶⣞⢉⢔⠈⠓
⡴⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀
⠁⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⣠⡶⢀⣀⣀⣀⡧⡀
⠿⣻⣿⡿⢾⡿⠓⠒⠒⠒⠒⠊⢛⡿⠿⠿⠷⣞⠙⢿
⡞⠁⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠈⣷⠀
⠻⢦⣤⣤⠴⠚⠁⠀⠀⠀⠀⠀⠈⠓⠲⠶⠴⠞⠋⠀
⠀⠀⠀⠀⠀⠀⠐⠲⠒⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠙⢍⠉⠛⠒⢲⣦⣤⣤⣤⣤⣤⣤⣴⣶⡚⠋⠉⠡⠃
⠀⠀⠁⠀⢀⡻⢀⡉⠙⣲⠉⢲⡏⠁⣀⣛⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠻⢍⣺
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀
⠀⢫⠑⠄⠀⢸⣦⣀⠀⣀⡀⡠⠤⢼⣿⣄⠀⠀⠀⠀
⠀⣈⡆⠀⠀⣿⡏⠀⢀⠀⠀⠀⠀⠘⠻⢿⣆⠀⠀⠀
⠘⠛⠃⠀⢀⠜⠁⣰⡃⠀⠀⠀⢆⡠⢀⠀⠙⠄⠀⠀
⠀⠀⠀⣰⠁⢀⢄⠇⠀⠀⠀⠀⣈⣦⣁⡆⠀⠈⡄⠀
⠀⠀⠀⣏⣄⣾⢟⣽⣷⡗⠐⣿⣿⣷⡍⢺⢀⣶⡇⠀
⠀⠀⠀⠘⢻⡯⠨⠛⠚⢃⣀⠙⠂⠉⠁⠾⠿⢻⠁⠀
⠀⠀⢀⠔⠃⠣⢄⣀⡀⠀⠀⢀⣀⡠⡼⡀⣀⣆⣢⠄
⠀⠀⢺⡿⣷⣄⢀⣖⠙⣻⠛⢋⡀⢑⣽⣿⣿⠃⣂
⠀⠀⠀⢙⢈⣻⣿⣿⣿⣯⣿⣿⣯⣿⣿⡛⡡⠲⠈⠡
⠀⠀⡠⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠃⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⠀⠀⣶⣄⠤⠤⣀⠤⠦⣿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠨⣿⠁⢀⠄⠀⢀⡀⠙⠿⢿⡀⠀⠀
⠀⠀⠀⠀⠀⢀⠴⠃⢰⠇⠀⠀⠈⢷⢤⡄⠀⠲⡀⠀
⠀⠀⠀⠀⠀⡎⢀⣶⣾⣤⣦⣀⣤⣾⣷⣾⡄⠀⢡⠀
⠀⠀⠀⠀⠀⠳⣸⡟⢺⣿⡿⠀⢿⣿⣿⢯⣷⣠⠟⠀
⠀⠀⠀⠀⠀⡠⢺⣇⠀⠀⠀⠒⠂⠀⣀⡎⠉⢨⢦⡀
⠀⠀⠀⠀⢸⢷⢸⡀⡩⠷⢶⡶⠞⠙⢿⣧⢇⣏⡫⠀
⠀⠀⠀⠀⠈⡕⢛⣿⣿⣿⣮⣿⣿⣿⣿⣾⢋⢤⠚⠧
⠀⠀⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⣄⠤⠤⣀⠤⠤⣿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⣿⠁⢀⠄⠀⢀⡀⠙⠿⢿⡀⠀⠀
⠀⠀⠀⠀⠀⢀⠴⠃⢰⠇⠀⠀⠈⢷⢤⡄⠀⠲⡀⠀
⠀⠀⠀⠀⠀⡎⠀⣶⣾⣤⣦⡀⣤⣾⣷⣾⡄⠀⢡⠀
⠀⠀⠀⠀⠀⠳⣸⡏⢸⣛⡳⠀⢿⣛⣻⢪⣷⣠⠟⠀
⠀⠀⠀⠀⠀⡠⢺⣇⠀⠀⠀⠒⠂⠀⣀⡎⠉⢨⢦⡀
⠀⠀⠀⠀⢸⢷⢸⡀⡩⠷⢶⡶⠞⠙⢿⣧⢇⣏⡫⠀
⠀⠀⠀⠀⠈⡕⢛⣿⣿⣿⣮⣿⣿⣿⣿⣾⢋⢤⠚⠧
⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⣄⠀⠀⠀⠠⡀⠀⠀⠀⠀
⠀⢠⠟⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠱⡀⠀⠀⠀
⠀⡇⢀⣤⣒⣯⡭⡤⠊⠙⠄⠀⠀⠀⠀⠀⠙⠒⠠⡀
⠀⠿⠟⠉⣠⠤⢽⣷⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀
⠀⠀⠀⠀⢯⠀⠀⡿⠞⠀⠀⠀⠀⠀⡰⠁⠀⠀⢻⠀
⠀⣄⠀⠀⠀⡉⠂⠁⢈⣶⣦⣤⣄⣴⠈⠀⡀⠀⠀⠀
⠀⢺⡂⠀⠀⠑⢄⠀⡟⠀⠀⠹⡞⣿⠀⡰⠁⠀⠀⠀
⠀⢼⢟⣦⣀⠀⠀⠀⠘⠦⣄⡰⠃⣿⠗⠁⠀⠀⠰⠀
⠀⠢⣄⠉⠉⠳⢦⡀⠀⢀⣀⠤⣴⠏⠀⠀⠀⡠⠁⠀
⠀⠀⠀⠃⠀⠀⠀⠘⠋⠁⠀
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⢤
⠀⠀⠀⢾⠈⠓⠲⠶⢤⡀⠀⠀⠀⢀⣠⠞⠉⠁⠀⡰
⠀⠀⠈⡏⠂⠀⢰⣾⣴⣿⠤⠤⠤⠾⢿⣦⣾⡆⠀⠁
⠀⠀⠀⢳⣤⣴⣶⡿⠋⡠⠄⠀⢀⡀⠀⠉⢿⣶⢾⠟
⠀⠀⠀⠈⠉⣳⡿⢁⠐⢄⡴⢠⢈⣇⠤⠀⢈⣻⠁⠀
⠀⠀⠀⠀⠐⢺⢶⣧⣔⣿⣷⣿⣾⣿⣷⣷⡦⠿⡆⠀
⠀⠀⠀⠀⠀⣸⣼⡏⢸⣛⡻⠀⢿⣛⣻⢎⣷⣠⣇⠀
⠀⠀⠀⠀⠀⠉⢿⣇⠀⠀⠀⠒⠂⠀⢀⣽⠟⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣩⠷⢶⠶⠞⠛⢮⡀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⣄⣒⣿⣿⣿⣮⣶⣿⣿⣿⣾⢉⠴⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣦⣤⣄⡀⡄⠀⠀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⠀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢀⣤⣾⡿⠛⢹⡇⠀⠀⠀⢧⢌⣍⠻⡿⣿⡄
⠀⠀⠀⠈⢻⢏⠀⣴⣯⣧⣤⣀⣤⣾⣷⣾⡄⢱⠸⣟
⠀⠀⠀⠐⠛⠚⢾⡏⢸⣛⡿⠈⢿⣛⣻⢊⣧⣾⠒⠋
⠀⠀⠀⠀⠀⠠⠸⣅⠀⠀⠀⠒⠂⠀⢀⡞⡉⢨⢦⡀
⠀⠀⠀⠀⠀⣧⠶⣼⣹⠟⢶⡶⠞⠛⢩⣧⣇⣞⠉⠁
⠀⠀⠀⠀⠀⣀⣐⣾⣿⣿⣾⣾⣿⣿⣿⣿⢋⢠⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⡾⣡⣿⣀⡤⠤⢤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⡶⠟⠀⡤⠀⠀⠈⠙⢄⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡿⡟⠁⠀⡜⡡⡻⢦⠀⠀⠘⡆⠀⠀
⠀⠀⠀⠀⠀⡾⢉⠙⢶⡾⢿⣧⣧⣶⣷⡇⠀⢧⠀⠀
⠀⠀⠀⢘⠾⣋⣥⡖⢿⣖⡿⠁⢿⣛⣿⡇⠀⣿⠀⠀
⠀⠀⠀⠸⣾⣹⣿⣅⠀⠀⠐⠒⠂⢀⢔⠀⣼⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠈⣩⠿⢶⡶⢾⣟⣿⣿⣟⣀⡀⠀
⠀⠀⠀⠀⠀⣴⣂⣿⣿⣿⣾⣿⣿⣿⣿⣿⢋⢴⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⠿⣿⣿⣶⣦⣄⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⣿⠟⢻⣇⠀⢸⡟⠛⡿⣿⣷⡄⠀
⠀⠀⠀⠀⠀⣿⣿⠻⣻⢟⠌⠉⠁⠙⠻⣏⢉⣿⣿⡄
⠀⠀⠀⠀⠀⢿⠟⠏⢰⠇⠀⠀⠈⢇⠀⠄⠙⠶⣿⡇
⠀⠀⠀⠀⠀⡎⠀⣴⣾⣤⣤⡀⣤⠾⣶⢞⡄⠀⢹⠁
⠀⣴⣾⡆⣬⠧⣸⡏⢸⣴⡷⣀⢿⣶⡿⢊⣷⣠⠞⠀
⠀⠈⠈⠀⠀⡠⠺⣅⠀⠀⣬⣤⡳⠀⣀⡆⠉⢨⢦⡀
⠀⠀⠀⠀⢸⢇⢘⠀⡩⠹⣿⣿⠟⠙⢿⣧⢂⣎⠫⠀
⠀⠀⠀⠀⠀⡑⢙⣿⡿⠟⢿⣿⠟⠿⣷⣾⢊⢤⠚⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠲⡆⠀⠐⠖⣠⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣿⣿⡷⢿⣾⡿⠿⠿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠣⢀⠄⠀⢀⡀⠀⠘⢇⡀⠀⠀
⠀⠀⠀⠀⠀⠀⡴⠃⢰⠇⠀⠀⠈⢷⢤⣄⠀⠳⡀⠀
⠀⠀⠀⠀⠀⣾⠀⣶⣾⣤⣦⡀⣤⣾⣷⣾⣄⣤⣱⠀
⠀⠀⠀⠀⠀⢿⣿⡏⢸⣛⡻⠀⢿⣛⣻⢾⣿⣿⡟⠀
⠀⠀⠀⠀⣠⣿⣿⣇⠀⠀⠀⠒⠂⠀⢀⡮⣿⣿⣧⡀
⠀⠀⠀⠉⢹⣿⣿⡈⣩⠷⢶⡶⠞⠛⢿⣧⣽⣿⡻⠃
⠀⠀⠀⠀⠀⣄⣉⣿⣿⣿⣮⣷⣿⣿⣿⣾⢋⢴⠘⠣
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣦⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀
⠀⠀⣹⡿⠟⠁⠀⣶⣄⡤⠤⣀⠤⠦⣿⣧⣀⣀⠀⠀
⠀⠀⠀⠀⠀⡰⠺⣿⠁⠀⠀⠀⠀⠀⠙⠿⢿⡌⢳⠀
⠀⠀⠀⠀⠀⡇⡴⠃⢰⡇⣰⣂⡴⢲⢤⠀⠀⢣⢸⡇
⠀⠀⠀⠀⢰⡟⠀⣶⡮⣯⣯⠁⣄⠀⢣⣀⠀⢸⡀⢆
⠀⠀⠀⠀⡎⣧⣸⡏⢸⣛⡻⠑⢾⣷⣾⣟⢛⣲⢗⠈
⠀⠀⠀⠀⢧⣡⢿⣇⠀⠀⠐⠒⠂⠈⣀⣿⠾⣿⢰⣢
⠀⠀⠀⠀⠈⠿⢠⠉⣨⠷⢶⡶⠞⠙⢧⡀⢀⣿⡟⠁
⠀⠀⠀⠀⠀⡔⢓⣿⣿⣿⣮⣿⣿⣿⣿⣞⢁⢴⢺⡆