Robotics Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢦⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠶⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢄⣀⡈⠙⠛⠛⠛⠋⠉⣁⣀⣀⡴⠶⠛⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⠗⠀⢸⠀⠀⠉⠁⠀⠛⠚⠛⠛⠫⣤⣍⢡⡀⠀⠀⢸⡇⠀⡀⢨⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢀⡀⠶⢾⡀⢶⣿⣟⡄⢱⠄⠀⡎⣿⣶⡞⢀⠙⠀⣰⠚⠓⠐⡇⢸⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣤⠛⢛⠀⢶⣽⣿⣧⠴⠂⠀⢷⣈⣿⣣⣼⠶⠀⠙⢳⡶⠺⣷⠸⠁⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⢸⠀⠀⠁⢀⡤⠀⠠⣄⠀⠉⠀⠉⠀⡀⠀⠀⢸⡇⠀⠘⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣤⠶⣍⠀⠀⢀⣼⠂⠀⠀⣠⡾⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⣄⠀⢀⣷⠴⠛⠁⣀⣠⠾⠋⠀⡃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠉⠛⠿⣥⠤⠚⠟⠋⠉⠀⠀⣿⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠿⢧⡀⠀⠀⠀⠈⠢⣄⠀⡀⠀⢂⣴⠏⠀⠀⣠⡾⠉⠉⠀⠀⠉⣩⡟⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠋⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠙⠛⠚⠛⠁⣴⣿⠶⠛⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⡴⠷⢦⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢀⡴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣴⠶⠒⠶⢾⣧
⠀⠀⠀⠀⢰⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡞⠁⠀⠀⠀⠀⠙⣧
⠀⠀⠀⢠⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠘⠷⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠂⠛⡈⢳⠀⠀⣿⠀⠀⣿⡀⠀⠀⠀⣀⣀⣤⣴⡶⠿
⠀⠀⠀⠀⠀⠀⡏⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠦⣤⠀⣄⠀⣀⠁⢸⠀⠀⣿⠀⠀⠉⠛⠛⣿⡟⠛⠉⢹⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⠛⢿⡷⠶⠶⢦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠉⠀⠀⣿⡀⠀⠀⠀⢀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠳⠶⠶⠶⣶⣤⣤⣤⣀⣀⣽⣇⣠⡶⠞⠋⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿⠀⠀⠙⠛⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⠉⠁⢀⣠⣾⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣠⣾⣦⣤⣤⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠿⠿⠶⢶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠀⣘⣠⣴⠿⠋⠀⣿⠀⠀⠀⣾⡇
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠄⣀⣀⣀⣀⣀⣉⣉⡿⠟⠛⣿⡟⠛⠋⠀⠀⠀⢀⣿⣄⣀⣀⣽⣇
⠀⠀⠀⠘⣧⣀⣀⣀⠀⢀⣾⠀⢀⣀⣠⣤⡤⣾⡇⠀⠀⠀⠤⠀⢉⡉⠉⠉⣉⣉⣤⡴⠛⣿⣇⠀⠀⠀⠀⠀⡏⠁⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠈⣿⠋⠉⣿⠋⠁⠀⣾⢿⡄⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣤⡴⠚⣿⠋⠉⠛⣻⣶⣶⢃⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⡟⠀⠻⣦⠀⠀⠻⢶⣤⣀⣀⠉⠁⠀⠀⠙⠋⣉⣀⣴⠾⢋⣠⡶⠟⠁⠀⡟⠘⣷⠶⠶⠶⣶⠿⠃
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⣷⡀⠀⠘⢳⣄⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⣉⣡⡶⠛⠁⠀⠀⠀⣀⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡯⠀⠀⣟⠀⠀⠀⠙⣷⡄⠀⠀⠙⣷⠶⠶⠿⠟⠛⠛⠚⠛⠛⠛⢿⡏⠁⠀⠀⠀⢀⣠⣶⠟⠁⠀⣿⠀⠀⢨⣿
⠀⠀⠀⠀⣰⡷⠶⢶⣏⠀⠀⠀⠀⠈⠻⣦⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⢀⣠⣶⣿⡏⠀⠀⠀⠀⣿⠀⠀⢸⡟
⠀⠀⢀⡾⠁⠀⠀⠀⠙⡿⣆⡀⠀⠀⠀⣿⠻⣾⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣧⣾⠟⠋⠀⣿⡇⠀⠀⠀⠐⣿⣤⣤⡾⢷⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⣰⡟⠀⠀⠀⠀⠀⠀⣇⢸⣧⠀⠀⠀⣿⠀⠈⠉⢹⣟⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠀⠀⠀⠀⣿⠁⠀⠀⠀⢰⠋⠳⢦⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⣩⡿⣦
⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣻⡀⢀⣿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⢦⣀⠀⠀⠙⠛⠶⣄⣀⡰⠶⠛⠋⠀⣠⣿⣀⣀
⡿⠒⠦⢤⣤⣤⣀⣸⡀⣿⠿⠾⣿⠇⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡽⠳⣤⣀⠀⠀⣼⠋⣀⣀⣤⠞⠻⣯⣤⣩⡽
⠘⢧⡄⠀⠀⠀⠀⠉⣻⣿⣤⠾⠁⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢰⣯⡀⢠⡞⠛⠳⢾⢿⡖⠉⠉⢳⣤⣤⢾⠇⣏
⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⣀⣼⣏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢸⡇⢹⡇⠀⠀⠀⠀⠀⠙⣶⡶⢾⡏⠀⢸⠄⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠿⢷⣶⣿⣧⠀⠀⠀⠀⠀⠀⢰⡿⠿⣶⣶⣶⣶⡿⢿⣷⠀⠀⠀⠸⣧⣄⣳⠀⠀⠀⠀⠀⢰⠏⠀⢸⡧⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠿⣤⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⢷⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠿⠿⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠿⠷⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⡁
⠀⠀⠀⠀⠀⣀⣠⠶⠞⠛⠁⠀⠀⠀⠀⢀⣴⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⠉⠉⠉⠛⠶⢦⣀⡀
⠀⢀⣤⣾⣛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣤⡀⠀⠀⠀⠉⠙⠛⢦⣄⣀
⠀⣼⠋⠉⠉⠙⠛⠶⠶⠶⣤⣤⡶⠋⠁⢀⣴⡟⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣄⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠈⠉⣷⣦⡀
⠀⢿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠇⢀⣴⠟⠉⣥⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⡷⣦⡀⠀⠉⢻⡶⠶⠚⠛⠛⠛⠁⢹⡃
⠀⠀⣹⠉⠹⠛⡿⢳⡶⣤⣤⣴⡿⢻⠅⠀⢀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣶⣾⠃⠈⠻⣦⣄⣸⡇⠀⣀⣀⣀⣀⣠⣼⠇
⠀⠀⠹⣄⣼⡄⠁⣼⡀⠠⡄⠀⢀⣼⠷⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠃⣴⠏⠛⠛⠿⠙⡟⢛⠙⡏⢹
⠀⠀⠀⠀⠀⠙⠶⠜⠛⠶⠼⠷⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠹⣆⠀⢀⣸⣠⣷⣀⣶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠉⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠢⠀⠀⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠶⠀⢀⠀⠶⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠐⠂⠀⠀⠠⠀⠉⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠃⠀⠀⠀⣀⢠⠀⠀⠶⢤⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠁⠀⠂⠀⠀⠒⠐⠈⠀⠀⣠⠔⠀⠀⠀⠀⠱⣀⡧⠴⣁⠴⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⣤⣄⣀⣠⣤⡤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣖⣋⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠒⠈⡋⠈⠉⠁⠈⠓⠈⡶⠠⢄⠀⠀⠀⠀⠀⠀⢀⡕⢤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠋⢠⠃⠀⠀⠙⠲⠤⠤⠤⠴⠊⠁⠀⠀⢻⠐⢄⣀⡠⡔⢋⡠⠃
⠀⠀⠀⠀⠀⠀⡠⠚⣀⣤⠀⡎⠀⣴⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣇⡀⠴⠊⠁
⠀⠀⠀⠀⠀⣘⢁⠖⠁⠈⢳⠁⠀⠙⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠁
⠀⠀⠀⢀⠴⠣⢿⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⡠⠤⡇⠀⠀⢀⡇⠀⠀⡇⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡆
⠫⡤⠊⡽⠲⠶⢮⠙⣆⠀⠈⢑⠒⠤⠤⢀⣀⣀⠂⠀⠀⣀⣀⡀⢬⠴⠚⠁
⠀⠉⠲⠆⢨⠇⠀⠉⠁⠀⠀⢀⢒⡁⠒⢄⠀⠀⠀⢀⠔⠋⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣱⣤⠂⡀⠀⣇⣔⠁⠈⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠒⠒⢎⠀⠀⠀⠀⠀⢨⠗⠒⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣶⡶⡎⠀⠀⠀⠀⠀⢘⡶⣶⡶⡏
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠰⠴⠣⠄⠤⢱⡀⠀⠀⠀⠀⣸⡡⠤⠤⠣⠤⠤⢄
⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠐⠈⠠⠀⠀⠙⢆⠀⢀⠞⠁⠀⠀⠈⠄⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⣏⣩⣉⣹⣉⣹⣉⣩⣉⣹⣹⠀⢸⣸⣁⣋⣈⣛⣀⣙⣈⣋⣘⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⣉⣀⠀⠀⣈⣉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡟⡄⢎⢸⣉⠆⢸⠰⣉⡇⡜⡕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠵⢧⡬⠭⠭⠤⠤⠭⠭⣤⠵⠵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠋⠙⠛⠛⠛⠛⠛⠛⠉⠋⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡇⠀⡖⢲⠓⡖⢲⠒⡖⢲⡖⢲⠀⣿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡙⣌⢲⡇⠀⠓⠛⠒⠓⣚⡒⠛⠚⠓⠋⠀⣷⢊⡼⣱⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣉⣉⡉⠙⣦⣑⡬⠛⡇⠀⠀⠀⠀⠘⠧⠟⠀⠀⠀⠀⠀⡟⠫⣔⣡⡞⠋⣉⣉⣱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡆⢸⠋⠀⠀⡇⢠⡴⠧⣄⣠⠜⢤⡀⡤⠷⣤⠀⡇⠀⠈⢻⠀⡎⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡜⠀⠀⠀⡇⠀⠷⠾⠅⠸⠶⠾⠀⠹⠶⠇⠀⡇⠀⠀⠘⢤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡏⠭⢭⡏⠉⠉⣯⠭⠭⣽⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⣒⣒⡇⠀⠀⣗⣒⣒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡧⠤⠴⡇⠀⠀⡷⠤⠤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡯⠭⢭⡇⠀⠀⣯⠭⠭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣓⣒⣒⣇⡀⣀⣗⣒⣒⣻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠃⠓⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⠇⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢠⣀⢖⡁⠀⠀⠀⠀⠐⠖⡄⠀⣀⠀⠀⠀⡀⠐⠀⢀⠉⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣽⣿⣇⠀⠀⢀⠄⣄⡀⠀⡟⠅⠋⡙⢻⣃⡴⠖⠻⠓⠛⠓⠛⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠃⠘⡇⠀⢀⡘⢀⣋⢁⠀⡄⣲⣾⣇⣀⣹⡇⢹⠀⠠⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⣰⣤⣶⣛⣡⡶⢰⠇⣰⡇⢈⣽⠊⠙⣿⡇⠘⣧⠀⡆⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣴⡿⠤⣄⠙⢻⣶⣿⡶⠃⠙⠁⠸⣷⣾⣿⠃⠀⠙⢶⣿⣆⢻⣆⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⡇⢻⠒⢄⡙⣾⡿⠛⠀⠀⠀⠀⠱⠙⠛⠏⠀⠀⠀⠈⣿⣇⠈⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠁⣇⢸⡐⠲⣬⣿⣷⠀⠀⣠⡄⠀⠀⠀⡎⠀⠀⠀⠀⣰⡟⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣠⣇⠀⠁⢻⡿⣿⣿⣆⠀⣸⣧⣤⣤⣤⣅⣀⡀⠀⣠⣯⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠐⡉⠉⣿⣿⠍⢹⠂⠙⠀⠈⢩⣟⠛⠫⠍⠉⣉⢉⣽⣿⣿⣿⣿⠿⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣋⡎⠹⡏⠀⠀⠀⠀⣴⠟⠝⠋⡒⠁⠀⠂⠄⠒⠻⠿⠿⣿⡍⠳⢌⡁⢄
⠀⠀⠀⠀⠀⠀⠀⠐⣋⡼⠀⠑⠈⠀⠀⠀⡏⠙⠓⠶⠀⢠⠀⠀⠀⢰⠀⠸⠗⢺⣟⡠⠀⠙⢺⣤⢶⠄
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⡄⠂⠀⠀⢠⡇⠀⠀⠀⡄⢼⣄⠀⠀⣸⣷⡙⠀⠀⣿⡅⠀⠀⣸⢷⡿⣶
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⣀⣀⡇⠀⠀⠀⢺⣿⣿⠀⣰⣿⣿⠁⠀⠀⢸⣷⣄⣠⣿⢿⡴⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡴⢃⣤⣾⣿⣿⠃⠀⠀⠀⢸⣿⠁⠀⠹⣿⣿⠉⠀⠀⠀⢻⣷⣿⡟⢈⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢺⢀⡾⣡⣿⣿⣿⡟⢻⠄⠈⠃⠀⣻⡇⠀⠀⠀⠘⠿⢷⡀⠄⠀⠀⢻⠛⠙⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠉⣿⠉⠀⢸⣇⡀⠀⠀⣿⣧⠀⠀⠀⣠⣾⣼⣧⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣠⣼⠀⠀⠈⣏⣙⢻⣿⢻⣿⠀⠀⢴⢻⠟⢉⠹⣇⠉⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⣿⢉⣿⣿⢼⡏⠀⣶⣻⣎⣴⠃⢰⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣴⣾⡈⠋⣹⣾⣿⣶⣯⣬⣭⣇⣠⣾⣞⠛⠓⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣤⣶⣿⣿⣿⣿⣇⣰⣯⡽⣿⣿⣿⡇⠀⠈⠉⠘⢿⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⢀⣤⡖⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⠋⠀⠀⢹⡟⣿⣧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣶⣄⣀⠀⢸⣿⣿⣿⣿⣿⣯⣁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣴⣾⣿⣿⣿⣟⠋⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠕⠀⠀⡠⠤⠤⠄⠒⠐⠠⢤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢲⣶⣤⠒⣶⣢⡄⡆⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⡏⠁⠀⠈⠓⠀⠀⠀⠃⢆⡞⠚⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⡇⢰⠐⠒⠒⠒⠂⢤⢀⢸⡇⠀⠀⣿
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠈⠢⢄⣀⣀⡠⠏⢸⠀⠳⠤⡞⠁
⠀⡴⢢⢫⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠟⠛⠒⠒⠲⠶⣶⠾⠤⢶⠒⠃
⡴⢜⢦⣱⡵⠛⢣⠤⣤⡠⡤⠤⠤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⢳⣀⣀⡀
⠈⢪⡗⠁⠀⠀⢸⠊⠁⡇⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡇⣏⠀⠀⠀⢸⠛
⠀⠀⠓⢄⡀⠀⣸⠀⠀⠇⡏⠉⢹⠀⠀⠀⠠⠀⠀⠁⢸⢘⠀⠀⢿⠈⠉⢹⠉⢹⢸
⠀⠀⠀⠀⠈⠉⠡⡳⡀⠀⠇⠀⡿⠀⠀⠀⠀⠀⠀⠓⠃⠊⠀⠀⣼⠀⠀⢸⠀⡼⢸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢾⢳⡀⠀⡇⠀⠀⠀⢀⠀⠤⠀⠨⣈⡄⠀⡇⠀⠀⢸⠀⡇⢸⠀⠀⠀⠀⢩⢱⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⡗⣾⠤⠤⠤⡔⠊⠁⠀⣿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⠉⠉⠉⠉⠉⠙⠢⣄⣀⣿⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣱⡖⠒⠤⠤⠤⣤⣄⣀⣀⣀⣸⣃⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠏⡝⠉⠓⠚⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠦⣀⠀⠀⠀⠀⠀⡜⠀⢦⡤⠤⠤⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⡆⠀⠀⠀⠈⠉⠒⠒⠒⠛⠂⠉⠁⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⣧
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠺⣀⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡏
⠀⠀⠀⠀⠀⠀⢸⠉⠁⠒⠤⡤⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣇⡀
⠀⠀⠀⠀⠀⢴⡋⠑⠠⢄⡀⡇⡠⠔⠊⢉⠦⠀⠀⠀⠀⠀⢰⠚⠭⢄⣀⠲⠃⣈⠥⠶
⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣈⣻⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠈⢙⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣄⡉⠒⠢⢼⡤⠒⠊⣁⡼⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣲⣤⣧⣖⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠊⠔⢈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡁⠢⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡡⡄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⢱⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⡀⠀⠀⠀⠀⠀⠀⣜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡵⡀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠉⠉⠀⠐⠒⠚⠛⠀⠒⠒⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣄⡄⠀⠠⠐⠒⠒⠤⡀⠀⠀⠀⠄⠀⢉⡐⢄⠀⠁⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠇⠀⢂⠀⠿⠆⠀⡁⠀⠀⢘⠒⢢⣴⡖⠊⠇⠀⠠⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠑⠂⠐⠊⠀⠀⠀⠈⠢⢄⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠒⡄
⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣧⣐⣠⠂
⠀⠀⠀⡄⠨⢊⣦⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⡀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣪⠞⠁⣜⡇
⠀⠀⠀⠀⠹⣟⢅⠉⠑⠒⠭⢖⡠⢄⡀⠀⠀⠀⠀⠀⠑⠢⠤⠄⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⠜⠀⠀⠀⠀⢀⠔⣠⠞⠁⠀⡔⡻⠁
⠀⠀⠀⠀⠀⠈⢧⡱⡀⠀⠀⠀⠈⠛⠮⢵⣦⣄⣠⠄⠀⠠⠀⠠⠤⡠⡿⢿⠟⠿⣯⠤⠤⠤⣤⡄⢀⡀⠀⡠⣎⠴⠊⠀⠀⠀⠐⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢌⠢⡀⠀⠀⠀⠀⠀⠈⡿⠁⡖⣤⠀⢰⠒⠒⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠹⢙⡟⠁⠀⠀⠀⢀⠈⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢠⡀⠀⠀⠀⠀⡇⠀⣨⡁⠀⢸⠈⠉⠀⠀⠀⠀⠀⠀⠂⠀⠲⠞⣛⠚⠃⠀⠙⠀⠀⠀⡠⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢆⠀⠀⠀⡅⠀⠓⠋⠀⢸⠀⠀⠀⠀⣠⠀⠪⡄⠃⠀⣙⠓⠒⢚⡁⠀⢠⣤⡴⢮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⣤⢄⡀⠀⢨⠬⠀⢸⠀⠀⢒⠒⠓⡲⠕⠂⡆⠀⢉⡩⠤⢍⡁⠀⣸⠀⢱⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥⢎⡗⠀⠴⢢⠀⠀⠉⢉⣉⣉⣉⠀⠀⠈⠁⠀⢨⣑⡚⣉⡀⠀⣿⠀⣠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⢧⠀⠈⠉⠀⠀⠘⠻⠹⣿⠉⡟⠁⠀⠀⠀⢠⡤⠒⢪⡄⠀⠉⠴⣫⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣥⢹⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠛⠢⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⢾⣘⡂⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣶⠿⠚⠵⣩⣩⣉⣉⣌⣽⠛⣭⡟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠉⠀⢀⠉⠳⡀⠀⠀⠀⠀⠀⡠⠂⠉⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢀⠀⢤⢠⡎⠀⠀⠤⠱⠸⠀⣃⡗⠀⠐⡀⠀⣰⡀⠲⠢⠠⠀⡀⡀⠉⢶⡠⠀⡀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉⠐⠈⠐⠂⠙⠒⠺⠓⠷⠛⠍⠃⠅⠂⠥⠂⠅⢂⠍⠋⠖⢲⠤⣥⢤⠴⠪⠐⠍⢂⠔⡩⠢⠓⠡⠢
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠶⠛⠤⠐⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⢀⠀⠀⢙⠀⠀⡀⠀⠀⢢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⢂⠀⠀⠛⠁⠀⡬⠀⠙⠁⠀⠀⠆⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠑⠄⠀⠄⠊⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠑⣍⡓⠒⠂⡆⠀⠀⡤⠀⠀⢰⠒⠈⡏⠠⠂⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣇⣀⡀⣇⣀⣀⡸⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠥⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⡋⠘⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⡄⠀⠀⠀⠀⠀⡇⢘⠒⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⡤⠄⠳⣀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⡇⡰⠢⢤⡜⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠠⠉⠑⡔⠋⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⡇⠀⠀⠀⠀⣸⠉⠀⠀⠀⠈⠲⡔⠉⠡
⠀⠀⠀⠀⠀⠰⠧⣀⡞⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⠐⠐⠂⠐⠂⠐⠀⠐⠒⠀⠀⠀⠀⠂⠂⠀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠘⣄⡠⠧
⠀⠀⠀⣀⣠⣅⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⣧⣀
⠀⠀⢰⣁⡄⠠⠌⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡉⡠⠀⣈⣱
⠀⠐⠉⠀⡀⢀⡀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣆⣀⣰⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⣀⠀⡀⠈⠠
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂
⡇⢀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⢹⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⢀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⢺⠀⠀⠀⠀⠀⠀⢸⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣒⡒⢺⠀⠀⠀⠀⠀⠀⣚⠒⣒⣺⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠀⠀⠀⠉⠑⡄⠀⠀⠀⡔⠉⠁⠀⠀⠀⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣰⠀⠀⠀⠀⡎⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣢⡞⠀⠀⠀⠀⠀⠘⣦⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣥⣼⣤⣤⣤⣤⣤⣼⠥⠭⠤⠤⠤⠤⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⣀⡤⠖⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠤⠤⠤⢤⡶⠛⠉⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠒⣿⢀⣴⣶⣿⡤⣄⠀⠀⢀⣤⣤⣶⣦⡀⢸⡇⠀⠀⣰⠋⢉⡟⢹⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢪⠀⣿⠀⢸⢿⣿⣷⣏⠀⠀⢸⢸⣿⣧⣼⠛⢸⡇⠀⠀⣿⠀⢸⡁⢇⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢤⣿⠀⠀⣉⣉⠁⠁⠀⠀⠘⠈⠉⠉⠛⠀⠘⡇⠀⠀⠘⢦⣬⠷⣼⠒⠁
⠀⣤⠴⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣧⣄⣀⣀⣀⡀⢈⣙⣟⠁⠀⠀⡇⠀⠀⠀⠀⣠⡴⠛
⢀⡈⠙⢳⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣦⢤⣤⣭⣭⣉⣉⣉⣉⡉⠀⠀⠀⣷⢀⣤⠶⠋⠳⢤⡀
⢾⠙⠲⢛⣷⠓⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⡀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠋⢳⡀⠀⠀⠀⠻⣄
⠈⠙⠒⠋⠙⠲⡏⣰⠳⣤⣀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⣤⣽⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠻⠿⣄⠈⠙⠛⠒⠒⠖⠛⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⡏⠀⠀⠀⠀⠈⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⢤⣤⠶⠶⣾⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠷⠾⠿⠿⣶⣶⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠂⠀⢀⡈⡇⠀⠀⠀⠐⠂⠀⠐⢲⠈⡇⠀⠀⠀⣀⡤⣷⠈⣷⡀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠀⠒⠒⠒⠒⠶⠶⠤⠤⢤⣭⣭⣄⣉⣈⣀⣚⣚⣀⣧⡠⠔⢊⡡⠖⣿⠀⣸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠀⠒⠒⠒⠒⠢⠤⠤⠤⠤⠤⣤⣤⣄⣀⣀⣈⣉⣉⣯⠤⠚⠉⠀⠀⢸⢻⣉⠉⢉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠀⠀⠀⢸⣰⡋⣻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⣤⢏⡽⠛⢯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠾⠋⢹⠸⡇⠀⣸⠃⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠠⣿⠉⠉⠉⠉⠉⠛⠛⣿⠛⠛⢻⡿⠾⠟⠋⠁⠀⠀⠈⠛⠁⠀⢻⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠐⣿⡄⠀⠀⠀⠀⠀⠀⣧⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠈⠙⢛⡽⢻⡀⠀⠀⠀⠀⣠⠿⣤⣒⣺⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣛⣁⣀⣀⣀⡴⠋⠀⢘⡇⠀⣠⠴⠋⠁⠀⠀⠉⡽⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⣬⣭⣭⣽⡤⠖⠛⠉⢰⠻⠷⠦⣤⣤⣀⣀⡾⠁⣠⠟
⡀⠀⢀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⡒⠲⠶⣤⣭⣷⢞⡁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⣸⣿⠯⠤⠄⣼⣆⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣥⢠⠀⠀⡠⡖⠲⣤⣤⢲⠲⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠞⠉⠑⡀⠀⢧⣳⣴⢻⢿⣘⣶⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣡⢀⣤⠃⠀⠈⠉⠁⠈⠀⡉⡁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣻⠀⠀⢸⢿⠽⠾⢾⠶⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠅⢧⣤⣤⣈⣩⣭⣭⣭⠭⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡲⠶⣶⠀⠠⡘⡿⠿⠿⠿⠿⠶⠎⠈⠒⠒⢒⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠤⡀⠀⠈⢃⠀⡇⠀⢐⡐⠄⠀⠀⠀⠀⠀⠀⠧⠃⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠘⠤⠆⢀⣀⡜⠀⡇⠀⢀⣤⣤⣴⣶⣶⡶⠶⠿⢯⠆⠀⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⢷⣤⣴⣿⣿⢇⡏⡇⠀⣿⠀⡴⠚⢏⠉⠉⠉⠳⢸⠀⠀⡆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⢀⣿⣿⣿⣿⣸⡇⡇⠀⣿⠀⠑⠔⠈⠁⠈⠀⡁⣸⠆⠀⡄⠈⣄
⠀⠀⠀⠀⠀⠀⠀⡰⢋⣈⠳⣀⣾⢿⣿⣿⣏⣿⠇⠁⠀⣿⢸⠠⡁⡀⠤⠤⠀⢓⢻⡃⠀⣿⡤⠈⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⡸⠀⡟⠛⣿⣿⣿⢿⡿⠀⡇⠀⣿⠀⠆⠒⠐⢀⣁⣁⣬⡼⠂⠀⣿⣧⣤⣄⡀⣀⠬⢿⠒⠒⢐⠢
⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⣾⠁⠈⣾⣿⣿⣿⡇⣾⠃⠀⠙⠒⠚⡿⠛⠛⠛⠹⠀⠀⠀⠀⡟⠫⠍⣁⡀⡏⢀⠄⣷⣶⠤⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠀⠀⠀⢻⣿⣿⣿⢱⡇⡆⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠙⢶⠚⠛⠉⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣦⠀⠀⢸⣿⣿⣯⣾⠃⣇⠀⠀⠀⠀⠆⣤⠀⣠⣞⣠⠠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⠲⣤⡤⢍⡉⢹⣿⣶⣯⣦⣤⣶⣶⣾⣿⡿⠟⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠆⣌⠑⠀⢱⠈⣿⣿⡏⠉⠀⠀⠀⣿⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠏⢹⠀⣇⡼⠀⡟⣿⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⠋⠉⠁⠀⢁⣿⣀⠀⠀⠀⠀⢿⠲⡦⠖⠒⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⣈⠹⡆⠒⠒⠙⠂⣷⣶⠾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢂⢈⠆⣳⣶⠾⢿⡶⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⣁⣠⡏⠀⠀⢘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⢰⡏⡏⠀⠀⠀⢸⡇⠀⠀⠈
⢀⣠⣤⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣿⣼⢸⠃⠀⠀⠀⢸⣇⣀⣤⡾⠒⠠⠄⣀
⠈⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠌⠀⠀⠀⠀⢘⣿⣯⣤⡀⣀⣤⠴⢾⡇
⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣐⣛⠷⠶⠚⠋⠉⠉⠙⠻⠯⣒⡈⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⣿⣿⣻⡿⣿⣿⣿⣷⣦⣤⠶⠒⡋⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢾⣯⣟⣻⣇⠨⠅⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠉⠙⠛⠓⠒⠶⠶⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⠋⠉⠉⠛⠒⠒⠦⠤⢀⣀⣀⡈⠉⠙⠳⢤⡀
⣠⢤⠞⢻⢹⣧⠶⣆⠀⠀⠀⠀⠀⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⡄⠈⠟⠳⣄
⠙⢦⠱⡴⢾⢃⡼⠃⠀⠀⠀⠀⢸⠃⢰⠁⠀⠀⠀⣴⡆⠀⠀⢀⡄⠀⠀⠀⠀⠀⡇⢰⠀⠀⠈⠳⡄
⠀⠈⣗⣋⡉⢽⡄⠀⠀⠀⠀⠀⡟⠀⡎⠀⠀⠀⠰⠤⠤⣄⣀⣈⡁⠀⠀⠀⠀⢠⠁⠃⠀⠀⠀⢠⡇
⠀⠀⡏⠀⠀⢸⡁⠀⠀⠀⠀⢰⠃⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡎⢸⠀⠀⠀⠀⣸
⠀⠀⣧⠤⠀⠀⢧⠀⠀⠀⠀⣾⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡎⠀⠀⠀⠀⡏
⠀⠀⣇⠀⢀⡀⠘⡆⠀⠀⠀⣏⠀⠳⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠁⠀⠀⠀⢸⠃
⠀⠀⠸⡏⠉⠀⠀⠹⣄⠀⠀⠙⠲⢤⣀⣀⡈⠉⠉⠓⠒⠲⠤⢤⣀⣀⣀⡰⠃⡼⠀⠀⠀⣠⠏
⠀⠀⠀⢳⡠⠖⠁⠀⠈⠲⣄⡀⣠⡞⠁⠀⠉⠙⠓⠒⠶⠤⢤⣀⣀⡀⠀⢀⣠⠥⣶⠚⠉⠁
⠀⠀⠀⠀⠱⣄⢀⡔⠀⠀⡀⠉⣳⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡀⠀⢸⣆⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠻⢤⣀⡴⠀⢀⠏⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠟⢺⠉⠉⢹⠁⠈⢩⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⢀⣀⣈⡀⠀⠋⠀⠀⣠⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠿⠋⠉⡏⠉⠙⠓⠦⣄⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠴⠶⠶⠶⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠶⠀⠀⠀⠀⠀⠀⠈⢉⠓⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡇⠀⠀⡠⠀⠀⢠⡇⠀⠀⠀⠀⣀⣟⣒⡒⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠰⣞⣋⣭⡾⣥⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣼⠀⠀⠀⠉⠁⡼⢁⢀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡗
⢶⠶⢄⣀⣠⣠⠞⠻⡁⠀⢣⠈⠙⠓⠒⣶⠦⠤⠤⠤⠤⠤⢤⡤⠾⠶⠖⠒⢶⠚⠁
⠈⢧⠀⠙⢆⠘⣄⠀⠑⠀⠀⢀⠀⣠⠴⠏⠀⠀⠀⠀⠀⠀⣼⠀⠀⣀⠀⠀⡈⠋⠛⠛⣆⡀
⠀⠈⢧⠀⢈⡆⠈⢀⡴⠶⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠀⠀⡰⠁⢀⠆⡰⠋⣷
⠀⠀⠈⠷⠞⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⣰⡀⣀⣌⣰⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⣿⣠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣀⡤⠚⠃⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠚⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠑⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠲⠆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢀⡀⠄⣀⡀⠀⠀⠀⢀⡠⠄⣀⡀⠀⠀⠀⠀⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠀⢀⠋⢠⣤⠉⢿⡆⠀⠰⠋⣠⣄⠙⣿⡄⠀⢠⡶⠙⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠰⠄⠈⢦⡈⠋⣠⣾⠇⠀⠸⣆⡙⠋⣠⡿⠁⠀⠉⡇⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣤⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠙⣧⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣯⢸⣿⡅⣿⣧⣸⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠉⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠟⠛⠻⣿⠛⠛⠛⠛⠻⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⢢⣤⡐⠒⢺⣇⠀⣘⣿⠗⢺⣆⠀⣘⣿⠒⠒⠒⠒⠲⡶⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢠⣶⡟⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠙⡿⠀⣰⣶⡄⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣀⠘⠿⡇⢸⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⠂⣷⡀⠛⠟⠃⣠⡿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡌⢶⠉⢶⠶⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⠁⢶⢶⡖⠉⣤⢡⡄
⠀⠀⠀⠀⠀⠀⠀⢇⡸⠀⢠⡎⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣯⠀⠸⠀⢱⡄⠀⠆⠱
⠀⠀⠀⠀⠀⢀⠻⡜⠃⢀⠏⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣏⠀⢰⠀⠀⠱⠀⠘⢃⠾⡀
⠀⠀⠀⠀⢠⡌⣶⠁⢠⠟⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⡆⣿⠀⢸⠀⠀⠀⠻⡀⠈⣤⢃⡄
⠀⠀⠀⠠⣆⡸⠀⢠⡎⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⠀⢸⠀⠀⠀⠀⢡⡄⠈⢎⣱⡀
⠀⢀⡰⠛⠉⠓⢲⡆⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⢱⡖⠊⠉⠛⢦⡀
⠀⠘⠁⣴⣿⣦⠀⠃⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠈⠀⣶⣿⡆⠈⠃
⠀⠘⣆⡈⠛⠋⡠⠇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠰⣄⠙⠛⢁⣴⠃
⠀⠀⢹⠉⠀⢻⠁⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠀⠙⠏⠀⠉⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣧⠘⠓⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠀⣏⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⡿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣸⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣇
⠀⢘⣋⣉⣉⣉⣉⣱⠀⠀⠀⠀⠀⠀⢀⡴⢛⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⣎⣉⣉⣉⣉⣹⠇
⢀⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⠁⢠⣿⣆⡀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⣷⠀⢈⡆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧
⣾⣿⠿⠋⠉⠉⠙⠻⣿⣧⠀⠀⠀⣰⠿⣆⡈⠛⠛⠉⠶⠆⠀⠀⠰⠾⢿⡀⠙⠛⠋⢀⣼⢷⡄⠀⠀⠀⣾⣿⠟⠋⠉⠉⠙⠻⣿
⣿⣿⡄⠀⠀⠀⠀⠀⢻⡿⠀⠀⣠⡿⠟⠛⣻⣶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠃⢶⣶⣟⠛⠻⣿⡀⠀⠀⢿⡏⠀⠀⠀⠀⠀⢠⣿
⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⡶⢋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠻⣦⣈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢉⡴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣌⡙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⠾⢋⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠻⢦⣜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⠛⠛⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⣴⣶⡄⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⣤⣶⣆⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠘⠿⠿⠃⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⠻⠿⠟⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣤⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢯⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣭⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠉⣡⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡍⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠋⣸⡇
⠀⠀⠀⠀⠀⠀⣴⠚⠛⠛⠛⠚⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠚⠛⠛⠛⠻⠂
⠀⠀⠀⠀⠀⣴⣿⣶⣶⣶⣶⣶⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣶⣾⣶⣶⣿⣷⡆
⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠀⣀⣽⣤⣭⣤⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣭⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣄⣽⣧⣈⠃⣿⣗⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣿⣿⣿⣿⣿⣛⡿⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣶⣾⣿⣿⣿⣿⣿⣷⡶⣦⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢸⣿⣷⣿⠀⣨⣟⠛⠛⠛⠋⡀⢸⣼⡟⢹⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⣿⠛⣿⣄⣧⣿⡀⢰⣿⡆⠀⣼⢻⣇⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⢿⣿⣿⣿⣃⣀⣉⣀⣠⡟⠀⢻⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⠆⠀⠸⣿⣯⣴⣶⡶⣾⣭⣽⠇⠀⢺⣿⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⣀⠛⣛⡷⣷⡛⢛⡀⠀⠀⠀⠹⣟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⢸⣿⡿⠿⠷⠾⠿⣿⣽⡄⠀⠀⢀⣜⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠛⠆⠀⣿⡿⣿⠀⠀⠀⢸⣏⠉⠁⠀⠠⠟⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠁⠀⢿⣿⣿⡀⠀⠀⢸⣿⣷⠏⠀⠈⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢿⡿⠟⠀⠀⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⡏⣸⠖⠀⠀⠻⣿⣩⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡏⣠⡝⣿⣿⣿⠟⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⡿⢿⣶⡆⠀⣿⡟⢿⣿⣿⣿⣿⣽⣡⣿⣿⣧⣿⣻⣿⠀⠀⠀⣀⡀⠰⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣷⣤⣿⡇⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢾⣿⣁⡀⡈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣈⡛⠛⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣛⣿⣿⠀⠀⢢⣽⣭⣾⣥⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⣿⠿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠸⡿⠀⣿⡇⣤⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⣷⡐⡘⣿⣿⣿⣷⣿⡟⢿⣽⣿⡿⠛⠻⣾⣗⡄⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣶⣶⣦⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠀⣿⣿⣇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣶⣦⣤⣭⣿⣿⣿⢻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣼⣏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣷⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣾⡟⢿⣿⠟⣡⣶⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣉⣙⠛⠉⠀⠈⠻⢸⣿⣿⣇⣽⣿⣇⠀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⣿⠿⣿⡇⠀⡈⢺⣟⣲⣍⢹⣿⡏⠃⢸⣷⣮⠉⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣾⠿⣶⣿⡇⠈⡏⠀⣿⣯⣾⣾⣿⡷⠃⢸⣿⣵⣷⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣈⠉⠀⠀⣍⠀⣿⣿⣿⣿⣿⢧⠀⢸⣿⣿⣿⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠋⠉⠉⠻⣷⡀⠀⠶⠀⣿⣿⣿⣿⣿⣿⡗⣾⣿⣿⣿⣿⣿⣟⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⠀⠀⣼⡇⠀⡷⠘⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠘⠛⠀⠟⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠟⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⢦⡏⠉⠉⠳⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣾⢿⣇⣒⢐⠂⣿⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢺⠓⠛⠛⠛⠋⠉⣉⢉⡉⠉⠙⢛⣛⣙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢰⣇⡰⠀⠀⠀⠋⠘⠉⢷⣦⣶⢡⠎⠹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠚⠋⠉⠑⣠⠆⠀⣦⡙⣖⡽⠋⠻⣄⣓⣺⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠃⢀⠀⣀⠟⠀⠀⠈⠛⠋⠀⠘⠁⠉⠉⠁⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⢟⠆⠀⠀⢠⡶⢶⠒⣶⣒⣖⢒⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢋⡜⠀⠀⠀⢸⣏⣻⣉⣻⣉⣯⣽⡏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠧⠤⢧⣤⣤⣦⣤⣥⣤⣤⣤⣤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⣦⣴⡶⠶⠶⠖⠺⣿⣿⣿⣿⣿⣿⣭⣤⣞⣉⣉⣁⠐⠶⠶⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠙⠉⠉⠑⢆⠀⠙⡇⠉⠁⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠐⠙⣦⠈⡀⠀⠈⠀⠀⡇⠀⠀⠷⠀⠃⠀⠀⠀⡀⠀⠀⢀⣀⣉⡋⠀⠀⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣆⠸⠤⠂⢀⣁⣤⣼⠀⠀⡇⠀⠀⡰⣤⣤⣷⣞⣻⣿⡶⠶⠾⠛⠻⣜⠀⠀⡏⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠻⣦⣄⣤⣾⣿⣿⡇⣸⠇⡇⠀⠀⣿⠀⣠⢦⠟⡙⠁⠉⠘⠛⢷⠄⣿⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⣿⣿⣿⣿⣿⢃⣿⢀⡇⠀⠀⡏⠀⢣⣀⡠⠞⠀⠒⠀⠤⠛⠀⣿⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢦⡀⠀⠀⣼⣿⣻⣿⣿⣿⣸⣯⠸⡇⠀⠀⡟⢀⡀⠁⠀⠀⠀⠀⠀⠐⢞⠀⣿⠀⠀⣧⡀⠠⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⡤⣄⠙⣦⣼⣿⣳⣿⣿⣿⡇⣿⡿⠀⡇⠀⢴⡇⠧⡀⠤⠠⠀⠘⠶⠒⠐⢊⡁⣿⠀⠀⣿⣷⠖⠀⠉⠒⠂⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡀⣀⠀⡟⠛⠛⣿⣿⣿⣿⢻⣿⡇⢀⡁⠀⠀⡿⠀⠤⠰⠆⠰⠀⠋⠈⢁⣈⣀⡻⠀⠀⣿⣿⣀⣀⣀⡀⠐⠀⣤⣽⡗⠒⠲⠀⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣠⠧⠀⢺⣹⣿⣿⡟⣿⣿⢠⡜⠄⠀⠐⣧⣠⣴⢶⣶⣶⣿⠿⠿⠏⠉⠉⠀⠀⠀⣿⣽⡿⠉⠉⠁⢀⡛⡠⢄⠙⣤⣀⡀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠿⠛⠃⠀⠘⣿⣿⣿⣿⣿⠏⣸⠇⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⠀⡇⠀⠈⠉⠐⠒⢠⣤⡑⠊⣠⣿⠿⣅⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣆⠀⠀⠀⠀⢻⣿⣿⣿⡿⢦⣿⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣉⠉⠁⠀⠀⣌⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡽⣇⠀⠀⠀⢸⣿⣿⣿⣇⣼⡏⠀⡇⠀⠀⠀⠀⠀⣇⣀⣀⡀⠠⠴⠎⣀⣀⠠⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⣆⣄⠀⣘⡛⠛⠻⢿⣿⣇⣠⠛⣄⢀⣀⣠⣤⣤⣶⣶⣶⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢢⠘⡿⣍⠉⠲⡀⢸⣿⣿⣿⣿⡿⠟⠛⠛⠉⣿⣿⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢈⠛⣠⡇⠘⠀⠀⠃⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡏⠈⣷⠀⠀⣠⡄⠀⠟⢻⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢠⡤⠿⠖⠚⠋⠁⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠶⢀⣇⣠⣤⠤⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠓⠲⢤⣀⠀⠀⣀⡠⣦⠈⡏⢀⣀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠴⢄⠈⢿⠋⠁⠀⠀⢨⠀⣾⠾⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢈⠆⠀⣶⣦⡽⠿⢷⡶⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡈⠈⠀⣴⠉⠀⠀⠀⢸⡁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢻⡷⣿⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠀⠀⣘⠀⣾⠁⡿⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇
⢀⣀⣤⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⢠⡟⢸⠇⠀⠀⠀⠀⠀⠘⢀⣂⣠⣤⠿⠐⠒⠤⠤⢄⡀
⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⡏⠀⠀⠀⠀⠀⠀⢸⣿⣯⣉⠀⠀⠀⠀⣀⣠⣤⣗
⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣙⠳⢨⣍⢦⣄⣀⣀⣤⣴⠾⠿⠿⢿⣿⣦⠞⠛⣭⠵⠚⡛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠉⠁⠀⠀⠀⠀⣀⣠⣸⣋⠡⠔⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⢿⣿⣿⣷⣯⣟⡻⠿⣿⣿⣿⣿⣿⣷⣄⡴⠖⠛⣉⠠⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⢿⣷⣾⣭⣛⠻⢿⡿⠒⢈⣁⠴⠖⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣵⣷⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠙⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠃⠀⠐⠀⠠⠀⠂⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠍⠀⠀⠀⠒⠀⢸⠀⠡⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡀
⠀⠀⠀⠀⠀⠀⠔⠂⢉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠂⠀⠀⠀⡆⢈⠀⠒⢄
⠀⠀⠀⠀⠀⠁⠔⠉⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⡀⠀⠀⢀⠋⠁⠈⠑⠄⠁
⠀⠀⠀⡀⠑⠎⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠈⠖⠁
⠀⢠⠩⠩⠈⡆⠀⠀⠀⠀⠀⠘⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⠊⠀⠀⠀⠀⠀⠀⡞⠈⠉⢢
⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠐⠀⠀⠀⠀⢸⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⡃⠀⠀⠀⢘⠂⢺⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⣉⡇⠀⠀⠀⢨⢉⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠈⠑⠀⠀⠠⠊⠀⠈⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⣀⣀⣀⣀⡂⠀⣔⣀⣀⣀⡀⡀⣃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣼⣄⢀⡀⡀⡀⢀⡀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢠⠒⠉⡉⠐⢄⠀⠀⠀⠀⡠⠂⢉⠉⠒⡄⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⢰⠡⠌⠣⠀⡆⠀⠀⢰⠀⠜⢡⠌⡆⢸⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹⠀⠀⠀⠀⠣⡈⠑⠒⢁⡴⠁⠀⠀⠈⢦⡈⠒⠊⢁⠌⠀⠀⠀⠀⡏⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢀⡀⣀⡀⢀⣀⡀⠀⣀⡀⣀⣀⣀⡀⠠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢤⠤⢠⡄⠤⠤⠤⠤⠤⠤⠀⠇⠀⠀⠸⠀⠤⠤⠤⠤⠤⠤⢤⡤⠤⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⡀⡀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⡆⠀⠀⢸⠦⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠴⠇⠀⠄⢰⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠛⠐⠃⠘⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠃⠘⠀⠛⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠒⠒⠒⠀⢴⡃⠀⠀⢘⡦⠀⠐⠒⠒⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢱⠀⠀⡎⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⣦⢄⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⣿⠀⠋⢰⡟⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠏⠈⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⡟⠀⠀⢸⠁⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠘⠻⠦⠤⣿⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠖⠛⠛⢶⣀⡇⠀⠀⣼⠀⠀⣀⣀⣀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢿⡀⠀⠀⣸⢿⡇⠀⠀⡿⢠⡟⠁⠀⠈⢷⠀⢿⠀⠀⠀⠀⠀⠀⠘⢳⠦⣤⣄⣀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⡈⠛⠲⠚⠉⢸⠀⠀⠀⡇⠈⢧⣄⣀⣠⠟⠀⢸⡇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢩⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠷⠶⠦⢬⣭⣥⣤⣄⣸⡇⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠶⠴⠤⠤⠄⠀⣀⣤⣀⣀⡀⠀⠀⣀⠀⠀⠀⠈⡅⠀⠀⠀⠀⢠⡏⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⡀⢀⣀⣀⣀⣧⣠⣤⣤⣤⣤⣄⣄⣠⣄⣠⣄⣉⣉⣉⣽⣇⣈⣁⣀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⢸⣧⡅⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⢸⠤⢴⠇⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⡏⠀⡆⢸⣿⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠓⠒⠶⣤⡀⠀⠀⠀⠀⠀⣸⡇⢸⠀⡾⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣸⠓⠒⠃⠈⣿⡄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣿⠃⢸⣺⡃⠀⣀⡴⠋
⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⡏⠀⠀⠇⠀⢹⣷⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣼⡏⠀⢸⠈⠉⠉⠁
⠀⠀⠀⠀⣾⠀⠀⠀⠀⣾⠀⠀⠀⡀⠀⠀⠹⣷⡀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢀⣼⠟⠀⠀⢸
⠀⠀⠀⢰⡇⠀⠀⠀⢰⠇⠀⠀⠀⡇⠀⠀⠀⠙⢿⣦⡀⠈⠳⣄⣀⠀⠀⠀⣀⣤⠞⢁⣠⡿⠋⠀⠀⠀⢸
⠀⢀⣤⣾⣁⡀⠀⠀⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⣉⣛⣛⣋⣉⣤⡶⠟⠉⠀⠀⠀⠀⠀⢸
⡴⠋⠀⠀⠈⠉⠙⠛⢳⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⡇⠀⣿⠙⠒⣶⠄⢰⠏⠀⠀⠀⠓⠂⡄⠐⢶⡶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⢶⡶⠢⠞
⠀⢻⣀⣻⡄⣰⠋⢠⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢦⡀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠋
⠀⠀⠉⠉⠉⠛⠲⠟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣦⣀⣀⣿⢦⣄⣠⣤⣿⣀⣀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⠤⣤⡤⣬⡉⠙⡏⠀⠀⠀⠀⡏⠉⣽⠷⠶⠶⢦⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠾⠃⠀⠀⠀⠈⠷⢶⡇⠀⠀⠀⢀⣷⠞⠃⠀⠀⠀⠈⠓⢶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠖⠛⠉⠉⠙⠛⠶⣄⣿⠀⠀⠀⢸⣠⠶⠛⠋⠉⠙⠛⠶⣤⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣉⡉⠉⠉⢉⣉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡚⡅⢜⢱⡛⡇⢰⠡⡏⣳⢠⢗⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣣⣇⣈⣓⣋⣁⣀⣑⣚⣁⣘⣜⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠚⠓⠒⠒⠒⠒⠒⠒⠚⠓⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡇⠀⡴⢶⠶⡶⠶⡶⢶⠶⡶⠶⡄⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢮⡑⣌⡇⠀⠧⠼⠤⠷⠴⠧⠼⠤⠷⠴⠂⢸⣥⠎⡵⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠲⢷⡌⢦⣱⠼⡇⠀⠀⠀⠀⠀⣎⣱⠀⠀⠀⠀⠀⠈⠧⣎⡴⢃⡾⠖⠒⠒⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⢢⡀⢻⠞⠁⠀⡇⠀⢀⣄⠀⠀⢠⡅⠀⠀⣠⡄⠀⢠⡀⠈⠳⡟⠀⡔⠉⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡼⠀⠀⠀⠁⠘⣏⣨⡏⠙⣅⣨⠋⢹⣅⣩⠃⢸⠃⠀⠀⢧⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠈⠁⠀⠁⠈⠀⠈⠁⠈⠀⢸⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡤⠤⠤⡤⠤⠤⢤⠤⠤⠤⡤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⡇⠀⠀⢸⣉⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⡇⠀⠀⢸⠒⠒⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠭⠭⡇⠀⠀⢸⠭⠭⢭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣒⣒⡇⠀⠀⢸⣒⣒⣚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠧⠤⠤⠷⣄⣠⠾⠤⠤⠼⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⡟⣹⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠦⠀⠀⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡔⠓⢦⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⢧⣤⡞⠀⠐⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣧⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⣀⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣎⡆⢾⡆⠀⠀⠀⠀⠀⠀⠀⢸⡁⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⣧⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⢿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢸⡇⣀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣸⡆⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⣼⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣛⣛⣛⣻⣏⣉⣻⣉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢒⡾⠁⠀⠀⠀⡤⢤⡀⠀⠉⠉⣷⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡹⠊⢩⡇⠀⠀⠀⠀⡹⢯⠀⠀⠀⠀⢸⠓⢞⠙⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠯⣈⡿⠁⠀⠘⡇⠀⠀⠀⠀⢙⣚⠀⠀⠀⠀⣸⠀⠀⢳⣏⣈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠄⢀⠈⡇⠀⠀⠀⢻⣄⣀⣀⣀⣙⣴⣁⣀⣀⣠⠇⠀⠀⠀⡟⠀⡠⣄⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢾⣠⡇⠀⠀⠀⠀⣼⣅⣽⠈⠉⠉⠉⢹⣅⣽⡄⠀⠀⠀⣄⣸⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⣄⣼⡀⠀⠀⠀⣸⣄⡤⣇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠺⠧⣤⡼⠧⡄⢀⠴⠿⣤⡤⠿⠒⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠒⠋⠉⠉⠉⠉⠉⠙⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠐⠀⠀⠀⠘⢢⠐⠀⠀⠀⠂⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡀⠀⠀⠀⠉⠁⠀⠴⡀⠙⠃⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠉⠢⣄⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⣀⠴⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⠉⠒⢢⠤⠤⠤⠤⡄⠒⠘⠁⠀⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠔⠁⠀⠀⢸⠁⠀⠀⠀⠀⢠⡄⠒⡄⠀⢰⡏⠉⢲⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⠁⠐⠒⠒⠒⠒⠃⠉⠁⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⢷⡀⣹⡤⢾⣀⣠⠎⠈⣳⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠈⣧⠴⠚⠁⣳⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢄⡤⠛⡿⠿⠛⠛⢿⡟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⢀⡟⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⠏⠀⠀⢸⡁⠀⠀⠀⠀⠀⠈⠁⠀⡝⠉⠓⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣑⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⡜⠀⠀⠀⠀⠙⠦⢄⣀⣀⣄⡠⠴⠚⠁⠀⠀⠀⠹⡋⠛⢤⠀⠀⣀⡤⠚⠅⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠉⢸⠁⠀⢠⠃⠀⣠⣴⣤⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣯⠉⠀⢁⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⢀⡷⠚⢧⢀⡏⠀⠀⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⣽⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠋⠀⠀⠀⢹⠁⠀⠀⠘⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⠃
⠀⠀⠀⠀⠀⣀⡤⠯⣼⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡸⠁⠀⠀⠈⢳⠀⠀⠀⢠⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢀⠴⠚⣉⣧⡀⠀⠀⠀⣼⣄⠀⠀⠸⢇⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢸⡇
⠹⣤⠞⠁⢠⠛⢲⠶⠻⣄⠘⢦⡀⠀⠀⠘⡋⠲⠦⢤⣄⣀⣀⣀⠘⠂⠀⠀⠀⣀⣀⣀⣠⣤⡴⠖⠊⠁
⠀⠈⠳⢴⡇⠀⢸⠀⠀⠈⠚⠋⠀⠀⠀⠀⣱⠖⠒⠶⢄⠈⠉⠉⠉⠉⠉⢉⡽⠿⠿⢤⡀⢀⠃
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⡶⠒⠠⡀⠳⡀⠀⠀⠀⣴⠃⡠⠄⠲⣾⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⣿⠴⠁⠀⠀⠀⢹⣴⣇⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠓⠛⠓⢾⡁⠀⠀⠀⠀⠀⠀⠀⣹⠶⠒⠛⠛⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣀⣀⣠⠗⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠛⠋⢽⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠛⠩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠚⠛⠒⠒⠤⢄⣧⠀⠀⠀⠀⠀⠀⢠⣇⠤⠄⠒⠚⢓⠶⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢠⠈⠁⡠⠀⠀⠈⠳⣄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⣁⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⢤⠤⠤⡤⠤⠤⡶⠴⠤⠤⠤⠤⢾⠀⠀⣾⢠⡤⠤⡤⠤⢤⡤⠤⢤⡤⠤⣤⠄⢾
⣀⣀⣀⣀⣀⣀⣀⣀⣽⣶⣾⣶⣶⣷⣴⣴⣷⣦⣶⣶⣴⣶⣾⣄⣀⣿⣴⣦⣤⣷⣤⣴⣦⣤⣴⣦⣤⣶⣤⣾⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⠤⠤⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠀⢸⠛⠓⠒⠒⠒⠒⠒⣶⠋⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⡇⡜⠉⡧⠀⡠⠒⢦⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠓⣾⠀⠀⣞⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠉⠚⠁⠀⠑⠠⠊⢸⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠹⣤⠜⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠖⡤⣀⣀⣠⡤⡄⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⡛⢦⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠓⠧⠿⣼⠤⠦⠊⢸⡖⣃⣀⡷⠀⠀⠀⠀⠀⡰⢧⣈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠲⠶⣶⠶⢦⠤⠤⠼⠷⠛⠁⠀⠀⠀⠀⢀⣼⡙⢲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⢉⣽⣤⣤⣄⣀⣀⡀⠀⠀⠀⣠⠞⢤⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⢋⣉⣀⣀⣈⣓⣉⠀⠀⠀⣀⣩⡭⢿⣧⠾⡅⣱⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠁⢰⡏⢫⣘⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢦⣸⠀⠀⠋⡉⡉⠉⠙⠛⢲⠀⢻⠀⢸⣙⣺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣀⣸⡆⠀⡟⢤⠞⠀⠀⠀⢸⣿⢸⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⡟⡇⠀⣇⡠⢤⡀⠀⠀⢸⣧⢸⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢻⠁⣧⠀⢸⡓⢚⣀⣀⣀⣸⠟⢸⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠒⣾⠀⣿⠀⠀⠉⠉⠉⠉⠉⠉⠀⢸⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⡿⠀⢸⡆⠤⠤⠤⠤⠤⠤⠤⠤⢼⠖⣋⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧⣠⡟⢦⠘⠓⡖⠲⡞⠒⠒⠒⠒⠲⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡎⠀⢃⠈⡆⢠⡉⢙⡇⠀⠀⠀⠀⠀⣧⡤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠇⠀⠸⠿⠇⢸⣉⣹⠀⠀⠀⠀⠀⠀⢿⠤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⣼⠀⠀⠀⠀⠀⠀⢸⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⣾⠀⠀⠀⠀⠀⠀⢸⡓⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠦⣯⡀⠀⠀⠀⠀⢠⠾⡋⢹⠆⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠙⠶⠃⣹⠀⠀⠀⠀⢸⣄⠉⠉⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⣤⠤⠴⢒⡽⠀⠀⠀⠀⠘⠮⣍⣓⡒⠒⣊⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⡄⠠⠤⠀⠄⠠⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠀⠉⠀⠁⠀⠀⠐⠒⠚⠛⠁⠉⠉⠙⠒⡠⠤⢄⣤⡭⠖⠦⠀⠀⠀⠀⠀⠀⠀⠠⠈⢁⠞
⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠀⠀⡀⠁⠀⡀⠀⠀⠀⠀⠀⠛⠠⡀⠀⠐⠀⠀⠀⠈⠂⠀⢀⣈⠀⠀⠒⠤⠤⡀⡄⠂⠀⠀⡠⠃
⠀⠀⠀⠀⠤⢀⣀⣈⣡⣴⣢⠀⠂⠄⠀⠁⠀⠀⠄⠒⠐⠒⣀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠴⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠈⠃⠒⠀⠨⠄⠤⡄⠠⠀⠀⠐⠖⢈⡀⠀⠠⠐⠤⣄⣂⡱⠖⠃⠀⠘⠻⣋⣀⠀⠀⠀⠀⠉⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⡿⡿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣧⢠⢱⢷⢦⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣷⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠒⠒⠓⠒⠒⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡖⢲⡇⠀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⢻⠒⢦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠸⠀⠀⡄⢤⠀⠀⠀⠀⢀⠄⢄⠀⠘⠀⢸⠀⢸⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠼⡇⠘⡀⠀⠀⠀⠒⠤⠤⠄⠂⠀⠀⠀⡰⠀⣼⠤⠞⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠤⠚⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⠤⠤⠤⠤⠤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠓⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠂⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠢⠀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠒⢚⠒⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡀⠀⢉⡉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠐⠛⠉⠀⠀⠘⠛⠶⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⡀⠀⠀⠸⠾⠇⠀⠸⠾⠇⠀⢠⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣦⣄⣀⡀⠀⠀⢀⣀⣠⣴⣿⡿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠘⠿⣿⡿⠛⠛⠛⠛⠻⣿⣿⡿⠋⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠉⠛⠲⠶⠤⢤⣤⣀⣀⡀⠠⠤⠄⠐⠋⠀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡂⠀⠉⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠁⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡴⠂⠀⠀⠐⠁⠀⠀⠀⠀⢸⠀⠀⢸⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣏⠘⣧⠞⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⢈⡆⢰⡿⠁⢈⠀⠀⠀⠐⠆⢸⠀⢀⡞⢦⣼⠉⣷
⠀⠀⠀⠀⠀⠀⢠⡇⢨⡟⠁⠀⠈⠙⢶⠀⠀⠠⠄⠀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠙⣞⠁⣇
⠀⠀⠀⠀⢀⡠⠼⢬⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠊⠀⠠⠀⠀⠄⠀⠠⠀⠲⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⢸⣆⣹⣀
⠀⠀⠀⣀⡎⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⡞⠁⠀⠈⢳⡄
⣠⠖⢋⡩⢧⡀⠀⠀⣰⢧⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡼⣇⠀⠀⠀⣰⡗⠲⢄
⠙⢦⡏⠀⡜⠉⢻⠉⠳⡄⣙⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⢰⡋⢀⡜⠓⡖⠚⣇⠙⢦⣀
⠀⠀⠉⠺⣧⣀⣼⠀⠀⠉⠁⠀⠀⠀⠘⠢⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠁⠀⠀⠀⠈⠉⠀⠀⣇⠀⣸⡤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠈⡟⠋⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⣅⡐⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡙⠻⠾⠿⠯⠒⠉⠐⢄⠀⡤⠒⡛⣶⠭⡤⠭⠒⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠉⠀⠀⠘⢦⠀⠀⠀⠀⠀⢹⡔⠉⠀⠀⠳⡄⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⡀⠀⠀⠱⣀⣀⡀⠠⢤⠂⠀⠀⠀⠀⠈⢆⣀⣀⣀⡀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡇⠈⠀⠀⠀⠁⠀⠀⠀⢸⠀⣰⠁⠑⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣇⡀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠹⡀⡀⠀⠀⢀⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢀⡆⠀⠀⠈⠀⠀⠀⡜⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡀⢀⣀⠜⠁⠀⠀⠐⠁⠈⢦⡀⠀⢀⣠⠎⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠁⠀⡠⠂⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠒⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡋⠒⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡘⠁⠀⠠⠌⠣⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠘⠁⠢⠀⠠⢄⠠⢌⠊⠉⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠑⠀⠀⠄⢀⠈⠀⣀⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠨⠀⠐⢠⣧⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅⠀⠀⡃⠀⠀⠀⠠⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⣀⣠⠤⠐⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠐⢠
⠀⠀⠀⢀⠀⢀⠄⡀⠀⠀⠀⠀⠀⢂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠀⠀⠀⠀⢀⡀⠀⠀⢐⠂⠂⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠛⢉⡁⠉
⡔⠈⠀⠂⠈⡡⠈⠁⠀⠀⢨⠀⠀⠈⠁⠢⠁⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠈⠂⠀⣧⠒⢀⠀⠀⠀⠀⡀⠉⠉⢰⠚⠒⢀⡀⠠⠜
⠁⠄⠤⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠀⠄⠀⠀⠀⠀⠀⠀⢌⡡⠀⠀⠀⠀⢸⢾⡉⣇⠄⠈⠉⠈⠀⠀⠐⠁⠘⠒⠒⠋⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠙⢶⠀⠐⠀⠀⠘⠁⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣄⡔⠃⠀⠛⠒⠀⠀⠰⣿⠆⡖⠀⠀⠀⠀⢀⣶⣦⣤⣾⠽
⠀⠀⠀⠀⢀⠀⠀⠑⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⣴⣧⣤⣴⣶⣾⣿⣟⡿⢱⣾⠟
⠀⠀⠀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡏⡏⢉⡍⢰⠻⠊⠉⠀⠙⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡄⠠⢄⢱⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠉⢘⡄⠉⠀⠧⠄⠀⢺⠆⠀⠁⡗⠂⠀⢰⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠄⠐⠒⠲⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢠⠃⠀⠀⡸⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠁⠀⠀⣏⠐⠀⡕⠀⠀⢈⡄⠀⠀⡆⠀⠀⠠⡅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⢄⣀⡜⡁⠠⢀⠞⠀⡀⢠⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠲⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠘⢄⡠⠇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠤⠤⠤⠄⠀⠐⠀⠀⢀⡠⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠉⠰⠂⠀⠂⢜⡤⠁⠀⠉⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣾⣭⣛⡋⠂⠐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠉⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⠿⣿⣿⠀⣴⡾⣶⣄⣸⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣠⣿⣿⠈⣿⣤⣼⡿⣿⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠆⠈⠉⠉⢠⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣻⢿⠿⣀⡀⠠⠤⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣾⡧⠠⣤⣖⣲⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢰⣾⣿⣷⣿⣿⣿⣷⣦⣿⣿⣿⣾⡟⠑⠆⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠊⠀⢰⣠⣤⣿⡎⠇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⠇⠉⠉⠙⠛⠏⠉⠀⠀⠀⠀⢠⣼⣿⣿⣿⣷⢸⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⡶⣖⣶⣶⣶⣲⣖⢦⠀⠀⠀⠙⣿⣿⣿⣿⢸⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡿⡘⢰⣲⠀⠀⣿⣿⣿⡟⢸⡇⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠉⠀⢡⣿⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡿⣿⣿⠏⣰⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠐⠁⠀⠀⢂⣾⣿⣄⠹⣿⣿⢏⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠂⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢷⡀⢀⣾⣿⣿⣏⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠉⠻⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡄⠀⠢⠠⠂⡱⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢠⣶⣶⣶⡾⠇⠉⠁⠀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡊⣯⢉⠝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⣤⡐⠄⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⢸⡀⣅⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠘⡀⢾⣯⠇⡀⠀⠀⠀⢸⡼⠟⠀⠂⠀⠀⢸⣷⡏⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣷⠀⠀⠈⠒⠐⠊⠀⠠⠤⠄⠀⠀⠈⠀⠀⠀⠀⢸⡟⣯⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠰⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⢄⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠠⠀⢸⣇⠌⡋
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠑⠠⢄⣀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⢸⡕⢩⡏
⠀⠀⠀⠀⠀⠀⠀⣀⡆⡀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠤⠀⠀⠀⣀⣉⣉⣉⣉⣁⠀⠠⠤⠤⠼⠷⠒⠁
⠀⠀⠀⠀⠀⠀⢩⠀⠤⣧⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣙⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠤⠤⠾⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠒⠚⠒⠒⠛⠛⠓⡶⢤⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⢶⡾⠧⣮⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠁⣄⣓⡶⠒⠂⠢⠶⠦⠶⢿⣶⠗⣦⣤⠜⠒⠒⠂⠠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⣆⠀⠀⠀⠀⣀⠔⠈⡀⢠⠙⠂⣿⠘⠀⠀⠀⡐⡑⠡⢀⢺⣿⠒⢫⢷⣄⡀⠀⠀⠠⠀⠀⠀⠁⠁⠂⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠐⠈⣆⠀⡠⠊⠀⠄⣈⠖⢻⠀⠀⣿⠀⠀⠀⠀⡜⡔⠀⢢⢻⣿⠀⢸⡢⠉⢽⠑⠓⠳⠦⠦⣤⣁⣈⣶⣧⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡼⢏⢀⢀⡼⠊⠁⠀⢸⠠⠄⣿⡀⠀⣀⣚⣀⣈⢀⡡⣸⣿⣀⢸⡪⠂⣽⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡤⠖⠋⠀⠀⠀⠀⠈⡀⠀⠓⠒⢀⡛⠛⠛⠛⠛⠻⠻⠏⠀⣸⡈⣂⡍⠀⠀⠀⠀⠀⠀⣰⠃⢀⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠘⠃⠀⠀⠀⣿⡿⣿⠇⠀⠀⠀⠀⠀⢰⡟⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣂⢁⠆⠀⠀⠀⠀⠀⢀⡟⢠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⣂⠤⠄⠐⠛⢚⠛⡋⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠞⠁⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢾⣶⣶⠀⠀⢸⣶⣷⣷⣶⠀⠀⠀⠀⠀⢀⣠⣴⣄⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⡯⠀⠀⠈⠀⠈⡉⡇⠀⠀⠀⠀⢠⠋⡠⣄⠙⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢁⣿⠀⠀⠈⠀⠨⢪⡇⠀⠀⠀⠀⠀⠉⠀⢀⢠⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡃⣿⠀⠀⢠⠀⠨⢪⡇⠀⠀⠀⠀⠀⠀⡠⢊⡼⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣴⣽⠀⠀⢸⡀⠸⡘⡇⠀⠀⠀⠀⠀⠀⠑⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠀⠈⠉⡆⢀⡎⠉⠉⠓⠗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠃⠈⠓⠶⠒⠒⣧⡜⠓⠠⠤⠤⡴⡾⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠠⠐⠠⠐⠦⠂⠔⠈⠐⠉⠐⠡⠛⠖⠶⢶⠧⠶⢶⠏⡧⢤⣼⣬⣤⣥⣽⡫⠐⠬⠊⠅⡊⠑⠪⠐⠁⠊⠕⠊⠒⠘⠂⠑⠂⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠋⡉⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡧⢧⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡞⠉⣉⣉⠉⣉⣉⣀⣀⣉⣉⣉⠉⠉⣉⣓⢢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠤⠀⠈⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠤⣤⠀⠀⠀⠀⠀⡀⠤⣄⠀⠀⠀⠀⠀⠀⡤⠂⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠁⢰⡢⠀⠀⠀⠀⠀⠘⠠⡤⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠠⠴⠊⠀⠀⠀⠐⠀⠠⠎⠎⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠨⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢲⠀⠠⠀⠠⡄⠀⡖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡼⠿⠧⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⢀⢠⡀⣸⠀⢀⡇⢀⣇⣀⣀⠀⠀⠀⠀⢀⡀⠠⠐⠈⠈⡆⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⣀⠴⠋⠀⠑⠂
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⢀⣀⠠⠴⠚⠁
⠀⢠⠃⠀⠀⠀⢀⣠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⣜⠀⠀⠀⡰⠊⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣠⠌⠫⠼⢿⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢧⣤⠊⣦⣀⠇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠋⠤⠤⠤⠄⠀⢀⣀⣀⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⠂⠀⠀⠀⠂⡶⠶⠶⠤⠤⠤⢤⡄⠠⠤⠞⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡀⣸⠀⠀⠀⠀⠀⢀⡎⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠀⠐⠚⠑⡄⠀⠀⡠⠚⠓⠠⠼⢻⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⢀⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠖⠚⠛⠛⠛⠓⠛⠚⠛⠛⠻⠷⠶⠾⠿⠿⠿⠶⠶⠶⠶⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⠟⣩⣤⣌⠻⣆⠀⠀⠀⠀⠀⣴⠟⢩⣭⣍⠙⣦⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⠃⠰⣿⣿⣿⠀⣿⠀⠀⠀⠀⢰⡏⠀⣿⣿⣿⠀⠈⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡀⠀⠘⠛⠁⠀⣿⠀⠀⠀⠀⢸⡇⠀⠈⠛⠋⠀⣠⠏⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⣄⣀⣀⣠⡼⠃⠀⠀⠀⠀⠀⢿⣄⣀⣀⣠⡾⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢛⣛⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⣀⡀⠀⢀⣶⠖⢿⡀⠈⠛⠉⠉⠉⠉⠁⠀⠀⠀⣠⡶⠶⣦⣤⣤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠶⠶⠶⠶⠿⠿⠟⢻⣿⠀⢸⣿⣛⣻⣿⣿⣿⣿⣛⣛⠛⠛⣿⡇⠀⣿⠤⠤⠴⠶⠶⠶⠶⠶⣶⡆
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠦⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⡿⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⡏⠉⠁⠀⠀⢀⣠⣿⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣧⣿⣍⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⢀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣀⣀⡀⣹⡆⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢻⡏⢉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡟⣿⠋⠉⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡇⠀⠀⠀⠀⠀⠀⢿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠈⣛⡿⢿⡿⣷⣶⠶⣦⣼⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠀⣀⣀⠀⠀⢈
⣠⡾⠋⢰⣿⣅⠈⠙⢶⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢳⣶⠾⣿⠟⠻⣿⡉
⢿⡀⢼⠛⠁⠈⢻⡦⠀⣿⠀⠀⢿⡤⠤⠶⠶⠶⠶⠶⠒⠂⣿⡇⢸⣟⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⣹⡇⢐⣿⣛⣛⠛⠒⠲⠶⠶⢄⣸⡇⢰⡟⢁⣸⡿⢶⣄⡈⠛
⢸⡇⠸⡇⠀⠀⢸⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠛⢿⣆⣸⡟⠛⠛⢻⣦⠀⠀⠐⣿⠉⠉⢹⣧⡾⠋⠉⠉⠛⢻⡆⠀⠀⠀⠉⠃⠘⣇⠘⣏⠀⠀⢩⡇⢰
⠈⣷⢀⣿⠀⠀⣸⡃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣼⠁⢸
⠀⠸⠟⠉⠀⠀⠘⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⣆⡿⠀⠀⢿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⠳⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⢀⣀⣤⣤⣤⣤⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠖⣾⣿⣿⣿⣿⣿⣿⣿⡛⠿⠟⠀⠀⠈⠛⢻⡿⠿⠿⠿⠿⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠉⠉⠉⠉⠉⠉⢷⡀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣀⣠⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⠀⣾⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⣦

⠀⠀⠀⠀⠀⠀⠀⣀⣲⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢤⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣠⠖⠉⠄⠀⠀⠌⠉⠲⣄⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⣠⣒⣉⣥⠤⢤⣽⣶⣶⡀⡀
⠀⠀⠀⢰⡗⠋⠉⠉⠉⠉⠉⠉⠛⢮⡆⠀⠀⠀⢠⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢢⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢰⣻⡇⢪⣿⡆⠀⠀⣼⣿⠂⢸⣷⠄⠀⠀⢸⣸⣿⠀⢿⡽⠀⠀⠀⠸⣯⠇⢸⣿⢸⠀⠀⠀⡎⡇⢰⣿⣳⡄⠀⠀⣾⣟⣲⢸⠉⡂
⠀⠀⠀⠹⣧⣀⣀⣀⣀⣀⣀⣀⣠⣾⠋⠀⠀⠀⠀⠙⠛⣦⣀⡀⠠⢤⠤⠀⣀⣠⡾⠛⠁⠀⠀⠀⢿⣧⠈⠛⠛⠁⠈⢀⠙⠛⠋⢸⣶⠇
⠀⠀⠀⠀⠈⠢⡤⠤⠴⠶⠶⢦⠐⠁⠀⠀⠀⠀⠀⠀⠀⡹⣶⠬⠭⠭⠭⠭⢴⡾⡁⠀⠀⠀⠀⠀⠀⠈⠦⣀⡀⠀⠀⠀⢀⣀⡤⠋
⠀⠀⠀⢀⣴⣿⠄⠀⣶⣦⠀⠨⣷⢦⡀⠀⠀⠀⠀⢀⠞⣾⣿⢠⡖⠒⠒⣦⢸⣷⡞⢆⠀⠀⠀⠀⠀⢀⣴⣶⠛⠛⠛⠋⠉⢳⣶⢄
⠀⠀⠀⡮⣤⠟⡀⠀⠉⠉⠀⢸⠫⣤⢧⠀⠀⠀⠀⢜⣴⡟⢇⠀⣛⠛⠛⠃⢀⡟⣷⡜⡄⠀⠀⠀⠀⢯⣀⢿⠀⠀⠀⠀⠀⢸⢧⣤⡧⡀
⠀⠀⠸⣀⠾⠀⢹⣶⠦⢴⣶⠋⠀⠧⣠⠇⠀⠀⠀⠘⠟⠃⢸⡛⠛⡶⣖⠛⣻⠀⠛⠟⠀⠀⠀⠀⢻⣿⠏⢀⣿⣄⡀⣀⣤⢏⠀⢻⣿⠃
⠀⠀⠀⠀⠀⠀⣸⠛⡇⢼⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣛⡇⣟⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⣤⠏⢣⣬⣨⡄
⠀⠀⠀⠀⠀⠮⠤⠵⠇⠲⠏⠬⠧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠤⠽⠟⠿⠥⠤⠵⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠥⠼⠀⠸⠷⠥⠬⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⠙⣧⠀⠀⠀⠀⢹⠋⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣧⠀⠀⠀⠀⢺⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡎⠙⡾⠃⠀⠀⠀⠀⠙⣷⠀⢶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⠀⠀⠀⠀⠀⡿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠾⠷⠶⠷⠶⠶⠶⠶⠶⠶⠿⠶⠾⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⡇⠀⠀⡟⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠙⡗⠀⠀⢸⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⡏⠀⠀⠀⢸⡇⠀⢀⣤⣤⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠛⠶⠖⠲⠚⠃⠀⢸⣤⣬⠀⠀⠘⠳⠖⠶⠖⠃⠀⠀⢸⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠏⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣧⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢼⠁⠀⠀⠀⠀⠀⠀⣻⠀⠀⢠⡄⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⣤⠤⡤⣤⡀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠈⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢀⠀⡀⠀⡀⠀⠀⢀⡀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢻⠁⠉⠉⢻⠀⠀⢸⠋⠉⠉⢹⡇⠀⢸⠉⠉⠉⢹⠁⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⣇
⡶⠛⠓⠒⠒⠒⠒⠒⠒⢿⠀⠀⢸⠀⠀⠺⠤⠤⠤⠾⠀⠀⠸⠧⠤⠤⠼⠃⠀⠸⠤⢤⠄⠼⠀⠀⢸⡇⠀⠀⡿⠉⠉⠉⠉⠉⠉⠉⠉
⣷⢤⡤⢤⡤⠤⢤⣤⠤⣿⠀⠀⢸⡀⢀⡀⠀⢀⣀⣀⡀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⡀⢀⡀⠀⠀⣸⡇⠀⠀⣿⠠⠦⠤⠤⠤⠤⠴⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡆⠀⠀⣷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢉⠀⢀⡀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⢀⠀⠀⢀⡀⠀⡀⠀⢸⡇⠀⠀⡿
⠿⠀⠶⠠⠶⠐⠲⠖⠶⣿⠀⠀⠘⠀⢸⡏⠀⠉⠀⠀⡏⠁⠉⢻⠀⠀⡏⠈⢸⡇⠀⢸⠁⠈⠙⠀⢸⡇⠀⠀⣿⠲⠒⠶⠶⠶⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠘⠗⠒⠚⠂⠀⠛⠒⠒⠛⠀⠀⠛⠒⠚⠃⠀⠚⠒⠒⠛⠀⢸⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣏⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠒⠒⠒⠒⠒⠺⡟⠀⠀⢸⡗⠒⠒⠒⠒⠒⠒⠒⠒⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠹⡇⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠒⠒⠒⠒⠒⠚⡇⠀⠀⢸⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣩⠆⠀⠀⢀⣀⣤⣤⡤⠤⠤⠤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡁⣤⣄⡀⢀⢠⣤⣄⡀⠈⡆⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⢌⠁⠛⠛⣺⠋⠈⠿⠷⢿⡄⢼⠀⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢶⠁⠀⡏⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⡄⣼⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⡇⢠⡖⠒⠲⠲⠦⠤⠤⢤⡄⠀⡇⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⡇⠈⢧⡀⠀⠀⠀⠀⠀⣰⠇⢸⠃⢿⣀⣀⣠⡾⠁
⠀⠀⠀⠀⣠⠴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣉⡛⠲⠶⠶⠚⠋⠀⢸⠀⠈⠉⠉⡏
⠀⢠⠚⢣⡘⣄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢋⠉⠉⠙⠛⠛⠛⢶⡶⠿⠖⠲⣟⠛⠁
⣠⢦⠳⣄⠱⣘⡦⠗⢳⣀⣠⡄⢠⣄⣀⣀⣀⣀⣴⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠈⢧
⠱⣄⠳⣬⠖⠉⠀⠀⢸⡧⠤⠃⡟⢸⠀⠀⠀⣸⠃⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢠⡟⠉⠉⠋⠉⢳⡤⡄
⠀⠈⢻⠃⠀⠀⠀⠀⢸⡇⠀⠀⡇⢸⣦⣤⣤⡟⠀⠀⠀⠀⠈⠀⠀⠠⠐⠦⢦⡀⠀⠀⢿⠘⣧⣤⣤⣠⣀⣼⠀⡇
⠀⠀⠀⠙⠦⣀⡀⠀⣸⡀⠀⠀⡇⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⡇⠀⠀⢸⠀⠀⠀⢸⡇⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠙⢧⡑⢄⠀⡇⡿⠀⠀⣸⠀⠀⠀⠀⠀⠒⠀⠀⠘⠶⠧⠼⠁⠀⠀⢸⠀⠀⠀⠈⡇⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⢳⣇⡇⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠂⢐⠲⠰⢠⠀⠀⣾⠀⠀⠀⠀⡇⠀⡏⢠⡇⠀⠀⠀⠀⠀⡖⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠗⠀⠀⡟⠀⠀⠀⠀⠀⠄⠈⠉⠑⠒⠛⠒⠘⠀⠀⣿⠀⠀⠀⠀⡇⠀⡇⢸⠇⠀⠀⠀⠀⠀⣹⡬⠗⠚⣷⠒⢂⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⠀⠄⢠⠀⠀⠀⠀⡀⡏⠀⠀⠀⢸⡇⢰⡏⢻⡒⠒⠒⢒⣲⠋⠁⠀⠀⠀⣿⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇⠀⠀⠀⢸⡇⠀⠙⠉⠉⠉⠉⠉⠉⠳⢤⣀⠀⠀⣿⣉⣙⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠗⠂⠠⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡰⠛⠒⣏⠀⠈⠉⠉⠉⠛⠛⠓⠲⠶⠶⢶⠤⠼⠧⠤⠴⢶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⣤⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠋⠉⠉⠉⠉⣷⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠸⣤⣀⣀⣀⣀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⣿⠀⠀⠀⠀⠈⠙⠲⠤⠤⣤⣤⣤⠴⠥⠴⠖⠚⠉⠀⠀⠀⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣇⢸⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠳⠤⣀⣉⠉⢀⣠⠴⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠈⠙⡏⠀⠀⠀⣸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠲⡇⣿⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠠⢮⣁⠀⠉⠒⠤⣄⣀⣇⣠⠔⠋⠀⣀⡽⠃⠀⠀⠀⠀⠀⠀⠀⡾⠉⠒⠦⣤⣀⡓⢋⣀⣤⠤⠞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡀⠉⢯⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⢙⡏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠉⠙⠒⠤⣄⣀⠀⡇⢀⣀⠤⠒⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣄⣀⠈⠙⣿⠉⠀⣀⣤⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣤⣴⡶⢦⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣤⣶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠈⢁⠞⠀⢀⡟⣤⠋⣠⢶⣀⣤⢳⡾⢃⣤⡶⢰⡟⠀⠀⠉⡴⠁⠀⣸⢀⣴⡄⣤⣤⣤⣄⣄⣤⣴⡟⣠⣴⣄⣤⣶⢀⣤⣴⠏
⠀⠀⠀⠀⠀⠀⢿⠤⠖⠋⠘⠧⠺⢷⡿⠻⠷⢾⠖⠻⠾⠷⠿⠔⠀⠀⢸⡧⠶⠚⠁⠻⠾⠻⠷⠿⠛⠻⠿⠷⠿⠔⠧⠟⠻⠶⠷⠺⠗⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠠⠴⠂⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣠⠈⠀⠀⠀⠀⠀⠀⣴⠂⣤⣠⡞
⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⣇⣼⢿⢇⡖⣻⡆⠀⠀⣼⢃⡿⢣⠟⣠⡾⠃
⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠟⣵⠛⠋⠉⣩⠟⠁⠀⢰⣻⠏⠛⠉⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⢶⡤⣍⠀⠀⠀⠀⠈⠁⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠸⠇⠈⠷⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⡾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢦⣈⣃⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⠀⠸⣇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠐⢆⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠈⠱⣆⠀⢀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⠃⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢀⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠛⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠦⡀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⣔⢃⠀⠀⡈⠄⣅⠀⡐⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣆⠀⣤⡀⠈⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣤⣄⠀⢁⠐⠦⣼⠿⢯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠘⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣨⣅⠈⠉⠀⠀⢂⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣾⡋⠀⠀⠐⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⢤⣀⡀⠀⠀⡰⢶⣴⠛⠛⠲⠂⣠⣴⣟⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⡩⠛⢛⡶⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⡀⢀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⣤⣶⠾⠿⠛⠋⠛⠻⠟⠋⠙⠛⠿⠷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠈⣿⡄⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⢨⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠘⣿⡀⠀⠀⠀⣼⡟⠹⣷⣀⡀⠀⠀⢿⣧⣼⡟⠀⠀⢀⣠⣾⠏⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠹⣷⡀⠀⣰⡿⠀⢠⣿⠻⣿⠀⠀⠀⠈⠁⠀⠀⢀⣿⠛⣿⡀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣹⣧⣴⡿⠿⣶⣿⠃⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠹⣷⣤⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠉⠁⣀⣠⣿⠃⠀⠀⣿⡷⣶⣶⣶⣶⣶⣶⢿⣿⠀⠀⢹⣟⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣶⣾⡟⠛⢻⣿⠀⠀⢰⣿⣤⡀⠀⠀⠀⠀⢀⣴⣿⡄⠀⠸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⣼⡇⠀⠀⣼⡏⠙⢿⣦⣀⣀⣴⠿⠋⢻⣇⠀⠀⣿⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⣿⠃⠀⠀⣹⡟⢿⡇⠀⠀⠸⣿⠀⠀⢹⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣸⡟⠀⠀⢀⣿⠃⠸⣿⠀⠀⠀⢿⡇⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⠃⠀⠀⣸⡟⠀⠀⢿⡇⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣿⣀⡀⢀⣿⠃⠀⠀⠸⣿⡀⢀⣠⣿⡆⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⢸⣿⠛⠛⢻⣿⠀⠀⠀⠀⣿⡟⠛⠛⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣼⣿⠀⠀⢸⡟⠀⠀⠀⠀⣿⡇⠀⠀⣿⣦⣶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⢸⡿⠶⠶⠶⠶⣿⡇⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇⠀⠘⢿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣶⣶⣶⣿⠇⠀⠀⠀⠀⢸⣷⣶⣶⣶⡿⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⡴⠶⢦⡄⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠙⢿⠀⠀⠀⣿⠛⠉⠉⠉⠉⠉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⢹⠀⠀⠀⣿⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣤⣤⣤⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⢀⣀⣤⠤⣦⠀⠀⠀⣴⢤⣤⣀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢀⡴⠞⠋⠁⠀⠀⣿⠀⠀⠀⣿⠀⠀⠉⠙⠳⣄⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣼⣁⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣸⣆⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠒⠛⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⠷⠶⠶⠦⣄
⠀⠀⠀⢠⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⣼⠃⠀⠀⣠⠴⠶⣄⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⠶⠦⣄⠀⠀⠘⣧⠀⠀⠀⠀⡿
⠀⠀⠀⠈⠳⢦⣤⣤⡏⠀⠀⢸⡃⠀⠀⠈⡇⠀⠀⢸⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⢹⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⠳⣤⣤⠞⠁⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠳⣤⣤⠞⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠛⣿⠀⠟⢨⡷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⠏⠸⡏⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⡿⠀⠀⢸⡇⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⣧⣀⣀⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⡤⠶⢶⣄⢠⡇⠀⠀⢸⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠠⡏⠀⠀⠀⢹⣿⡇⠀⠀⣿⠀⣴⠛⠛⠛⢦⠀⢻⡄⠀⠀⠀⠀⠀⠀⢿⣄⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠻⢦⣤⡤⠟⣹⠁⠀⠀⡿⠘⣇⠀⠀⠀⣸⠇⠈⣷⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⠛⢳⡶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠒⠶⠶⠤⠤⠤⣤⣿⣤⣤⣤⣇⣀⣈⠓⠒⠚⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠓⠿⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠉⠉⠁⠀⠛⠛⠓⠒⠒⠀⠤⠶⠦⠤⡤⠀⠾⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⣶⠠⠀⣶⡶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠴⢶⣶⠄⡄⠀⢸⠇⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢰⡟⢲⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⡏⢉⡿⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣾⠀⣰⠀⢿⣧⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⠉⠙⠳⢦⡀⠀⠀⠀⠀⢸⣿⠀⣇⣸⠃⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⠏⠉⠩⠀⠸⣿⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⣾⠇⠀⡏⢿⣤⣤⠴⠋
⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⡟⠀⠀⡇
⠀⠀⠀⠀⣾⠀⠀⠀⠀⣸⠃⠀⠀⢠⠀⠀⠀⠻⣷⡄⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢀⣼⠟⠀⠀⠀⡇
⠀⠀⠀⢰⡇⠀⠀⠀⢠⡟⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⣦⣀⠀⠛⢦⣄⣀⣀⣀⣠⡴⠛⢀⣴⠟⠁⠀⠀⠀⠀⡇
⠀⣠⠶⠾⣤⣀⣀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣀⣉⣉⣉⣤⡴⠾⠛⠁⠀⠀⠀⠀⠀⠀⡇
⣾⠁⠀⠀⠀⠀⠉⠉⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⡀⠀⣀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠈⣧⠀⣿⠉⠛⢳⡆⢀⡾⠀⠀⠀⠘⠒⢰⠆⠒⢶⡒⠒⠒⠒⠒⠒⣶⠒⠒⠒⠒⣶⠖⠒⠒⠒⠒⠒⣶⠒⠴⠃
⠀⢻⣀⣹⡆⣠⠏⠀⡾⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠻⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠉⠉⠉⠛⠲⠾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠳⣄⣀⢀⣿⢦⣄⣀⣤⣾⡀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢀⣤⣤⣤⣤⣌⠉⠙⡏⠀⠀⠀⠀⣾⠉⣹⠧⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠾⠁⠀⠀⠀⠘⠧⣴⡃⠀⠀⠀⠀⣽⡴⠋⠀⠀⠀⠀⠻⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⣤⠴⠖⠲⠶⢤⣀⠀⣿⠀⠀⠀⢸⡇⣀⣤⠴⠖⠶⠦⢤⣀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠉⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄

⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⡏⡄⢠⢱⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄⠄
⠀⠀⠀⢶⣵⡤⣤⣿⡶⠀⠀⠀⠀⢾⣏⣿⡇⠀⠀⠀⠀⠀⢿⣿⡊⠀⠁⠁⣾⡿⠀⠀⠀⠀⢰⣿⣦⠀⢀⣤
⠀⠀⠀⣾⣿⣗⣾⣿⣷⠀⠀⠀⢺⣿⣿⠿⡿⣿⢿⡟⠀⠀⠰⣿⢟⣛⣛⡻⣿⡆⠀⠀⠀⠀⠘⠛⠋⢁⣾⠇
⠀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠩⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⢤⢄⣀⠀⠀⠀⠀⣠⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⣰⣏⢨⣷⣾⡱⣹⣆⠀⠀⣠⣲⣎⠿⢘⣣⣷⣿⠀⠀⠀⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⢆⣀⣀⠀⣿⣿⡷
⠀⠀⣿⣿⠇⠈⠁⠸⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⢸⣿⣶⡦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⣼⠿⡿⠋⠛⠀⠀⠀⠀⠀⠸⠉⠉⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠦⠀⠀⠀⢀⠔⠀⠀⠀⠀⣷⣾⠿⣿⡁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡉⢛⢳
⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠹⣿⣴⡿⣿⠀⠀⠀⠀⢠⢨⠛⢻⠠⢠⢠⠀⡀⠀⠀⠀⡖⢀⣠⠘⡆
⠀⠀⠰⠦⣤⣄⣠⣤⠼⠀⠀⠀⠀⠘⠛⠉⠘⣆⠀⠀⠀⠰⢾⢿⣿⢏⢺⢿⣾⣷⠇⠀⠀⠈⢁⣿⣿⣇⠁
⠀⠀⠀⠸⠁⠇⠘⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⣜⣹⣿⣷⠀⢀⣀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⣽⣿⣆⣀⣀
⠀⠀⠀⠀⢐⣦⣄⠀⡼⠁⠀⠀⠹⣿⣿⡿⢰⣥⣿⣷⠀⠀⠀⢀⣰⣾⣿⣦⡀⠀⠀⠀⠀⣠⣿⣿⣿⠏
⠀⠀⠀⠀⠈⠛⠋⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠀⠀⢶⣿⣿⣿⣭⣿⣿⡷⠀⠀⠀⠙⠛⠛⠿⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⡤⠴⠶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠙⣷⠖⠛⠉⠉⡴⠋⠀⠉⠉⠙⠻⢦⣀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠎⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢠⠏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠸⣿⣂⣠⣤⣀⣀⣾⡷⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠⠚⢹⠋⠉⠉⣱⠈⠉⠲⡄⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⠁⠀⠀⠉⠋⠉⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠸⡄⣀⠀⠐⣄⢀⢀⣠⠆⠀⡼⠀⠀⠀⢀⡴⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠳⣬⣲⣭⠭⠤⠤⠤⠤⠖⢚⣁⣠⠴⠚⠉⠀⠀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠉⠉⠉⢉⡟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢰⡟⠓⣤⠶⣄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢠⡇⠀⠀⠀⠈⢷⡄⣡⠞⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⣤⣄⡀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⣠⡿⠉⠀⠀⠀⠀⠈⠙⠷⣦⡾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡴⠖⠛⠛⠛⠛⠿⣤⡀
⠀⠀⠀⠀⢠⡟⠀⢀⣤⣤⣄⡀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⣀⣀⡀⠀⠈⠻⣆
⠀⠀⠀⠀⢸⠁⢠⡏⠀⠀⠈⠙⢷⣄⠀⠀⠀⠈⢷⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣠⠞⠋⠉⠉⠙⠻⣦⡀⠀⢹⡆
⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠸⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⡜⠁⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⡇
⠀⠀⠀⠀⠘⣇⢹⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠹⣜⣧⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⡾⠁⣀⡀⠀⠀⠈⠳⡄⠀⠀⢀⣘⣷⣸⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠘⢮⣷⣦⣄⣀⣠⠾⠃⢀⣠⣾⠵⠚⠁⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠙⢿⣿⡶⣤⣤⣤⡴⠾⣋⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣫⣭⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣭⣽⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿⡿⠋⢀⠀⣀⠀⠉⢻⣿⣿⣿⣿⣿⡿⠋⠀⠀⣤⡀⠈⢻⣿⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⡇⣿⣿⡇⠀⣧⣴⣿⣿⡆⠀⣿⣿⣿⣿⣿⡇⠀⣾⣤⣾⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⡇⣿⣿⣇⠀⠻⢿⣿⠿⠃⢠⣿⣿⣿⣿⣿⣇⠀⠙⢿⣿⠿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⡇⣿⣿⣿⣦⣄⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣼⡇⢸⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣤⣾⣿⣿⡻⣦
⠀⠀⠀⠀⢸⣿⣿⣁⣽⣿⣿⡇⣾⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣯⣨⣷⣼⡇
⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⢿⡇⣿⣿⡇⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⢸⣿⣿⣿⠙⢿⣿⣿⣿⣟
⠀⠀⠀⠀⢰⣟⣿⣿⡟⠀⢸⡇⣿⣿⡇⠀⢀⡴⣤⡀⠀⣤⣤⠀⢠⠶⣦⡀⣴⢶⣄⢠⡶⢦⡀⢸⣿⣿⣿⠀⠀⢻⣿⣿⣿⡄
⠀⠀⠀⠀⡾⣼⣿⡿⠀⠀⢸⡇⣿⣿⡇⠀⠀⠻⠟⠁⠀⠛⠛⠀⠘⠿⠟⠁⠻⠿⠋⠘⠿⠟⠁⢸⣿⣿⣿⠀⠀⠀⢿⣿⣿⣷
⠀⠀⠀⢸⣷⣿⣿⠃⠀⠀⢸⡇⢻⣿⣿⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣇
⠀⠀⢀⡿⢿⣿⡏⠀⠀⠀⢸⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⠿⢿⡄
⢀⣴⣿⡷⢶⣿⣦⡀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⢀⣴⣿⡶⢾⣷⣦
⣾⣿⣿⣤⣤⢿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣤⣴⢿⣿
⠻⣿⡇⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢸⣿
⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣤⣤⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣴⡾⣻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣾⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠗⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡟⠀⢢⠀⠀⡀⠒⢉⠄⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣨⠁⠀⠚⠋⡁⠤⠤⣈⡹⠛⠀⠈⣅⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡎⠀⠀⢸⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⡇⠀⠀⢸⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠉⠓⠒⠒⠚⠉⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⢤⣤⣀⢀⡤⣤⣤⣤⣤⣤⣀⡀⣤⣤⠖⢁⠔⠁⠀⠀⡀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠑⠢⠤⡌⢹⡇⠀⢀⣀⠀⠀⣿⢩⠤⠄⠂⠁⠀⠀⠀⠀⢁⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠉⠁⠠⠤⠔⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⣀⣀⣀⣀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠤⠤⠀⠉
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠃⠠⠋⠉⡆⠀⠒⠚⠒⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠤⠤⠶⠶⠤⠤⠤⠤⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂
⠀⠀⠀⠀⠀⢀⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠑⢤⡀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⡀
⠀⠀⠀⠀⡄⠉⠀⢀⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠴⠦⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠂⠜⠀⠀⠀⠀⠱⣌⠄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣀⣬⡁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⢧⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠉⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⠞⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠸⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠠⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⣿⣶⣶⣶⣶⣾⣶⣾⣶⣶⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿