Scientific Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣯⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣟⠛⣷⠀⠀⠄⠁⠀⠈⠀⠀⡀⠂⠀⠀⠀⠀⠀⠔⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣼⣻⣿⡋⠄⠀⠀⠠⢀⠠⢀⠀⠄⡁⠂⠈⠀⠀⢀⠀⠐⠊⠁⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠂⠐⠈⣉⣉⠛⠉⢁⠀⠀⠨⠕⠢⠀⠤⠔⠠⠄⠤⠆⠉⠒⠁⠀⠀⠀⣰⢶⠀⠀⠐⠀⠈⠑⠂⠤⢀⡀⣤⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢞⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢷⡻⡧⣬⣤⣧⠌⣁⠂⢄⠨⢘⣿⡔⠟⡽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⡋⣰⣤⣀⣶⣿⣿⠴⠀⠉⠀⠀⣏⣻⣧⣤⣙⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠃⠐⣰⢃⣯⣠⣼⠛⠁⠀⠀⠀⠀⠀⢰⡯⣷⡄⠍⡁⠸⠅
⠀⠀⠀⠀⣠⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣴⠛⠓⣘⠛⣿⣡⣬⡿⠋⠀⠀⠀⠀⠀⠀⣠⠀⠀⠛⡳⢷⡆⠆
⠀⠀⠀⠀⠘⡀⠀⠀⠐⣚⠃⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠿⡡⢠⣨⡁⣾⣷⣶⠏⠀⠀⠀⠠⠄⡐⠲⡌⢿⣧⠀⠀⣯⡈⡇
⠀⠀⠀⠀⠀⠈⣦⠀⠥⠏⠀⢀⡪⠁⡔⠊⠛⣛⠛⣻⢻⡓⠄⢲⣓⣾⡿⠷⠋⠉⠁⠀⠀⢀⠐⠁⠀⠀⠠⠗⢈⣾⠀⠀⠶⠁⠁
⠀⠀⠀⠀⠀⠀⠈⢔⣻⡁⠀⠰⠁⣾⠂⠀⠀⠿⢷⢶⡾⣡⣼⣾⣏⠒⡀⠀⠀⠐⠀⠀⠀⠀⠈⠐⠀⢨⠔⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠰⠀⣷⢀⡀⠀⠀⢀⠈⣿⣿⢟⠛⡉⣴⣧⣤⣀⡐⢀⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠉⠁⠀⠀⣰⣿⠁⠴⠇⢙⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⡟⠀⡁⠀⣈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠓⠛⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⣿⠤⢚⠦⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠄⠐⢶⣖⣴⣌⣷⡀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣑⢂⠠⢈⣿⡀⠀⠀⠀⠀⠀⣀⣤⣾⣸⡽⣧⡀⠀⢨⡿⡿⢿⣿⡟⠀⠆⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡎⣴⢧⣺⢿⣦⣤⣤⡴⠿⠋⠁⣡⣿⣧⢸⡇⠀⠈⠀⠀⠀⢹⣿⠶⠀⢠⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠲⠶⣤⣀⠻⣿⣶⣌⡿⣶⣿⡿⣥⢀⣀⢰⣟⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡈⣬⡟⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣦⣴⣴⣶⣧⣡⠀⣉⡛⢮⡝⠻⢿⣿⣿⣷⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⢀⣠⠠⡴⣿⣤⡔⣷⣿⣥⣤⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡼⣿⠟⠁⠀⠈⠙⠻⣿⣿⠆⠈⡓⢦⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡟⢻⣿⣿⡾⣿⠻⣿⣤⠶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⡀⠀⠀⠀⠀⠀⠈⠛⢧⣲⣍⡂⢈⠑⠦⢤⣀⣀⣀⣀⣄⣠⣤⡴⢘⣛⣤⣤⣰⢶⣋⣿⠟⠙⠷⣦⣤⣴⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⢳⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣀⣤⣤⣄⣨⠿⣿⣡⣿⢔⡠⠿⣿⢟⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⢻⡶⢤⣀⡀⠀⠀⠀⠀⣀⠉⠛⠿⠿⣷⣿⣽⣶⣷⣾⡶⠀⠀⠈⠿⣟⡁⠀⠀⠀⠆⠀⠓⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⣾⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⢿⣶⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣍⣾⢽⣿⣿⣛⠿⡿⠿⢻⣯⣡⣾⣟⣼⣭⡶⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣿⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣹⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡹⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣩⣿⣿⡟⠛⣩⠉⣹⢫⡮⢹⣿⣿⣿⣿⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣷⡝⢎⣹⣶⣿⣿⣿⣿⣟⣻⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣮⣿⣿⣿⣟⣭⡉⣶⠏⠉⣻⡿⣿⣽⣿⡶⣚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣿⣿⣿⣹⣫⣿⣸⡕⢎⣶⣿⣴⣿⣿⣿⣿⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣮⣿⣯⣾⢿⣿⣿⣿⣷⣤⣴⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣻⣿⣿⣿⣿⣿⣥⣷⣾⣿⣿⣿⣿⣿⣿⡟⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣏⣾⣿⣿⡿⠵⠁⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣴⣾⣗⣽⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⢿⢿⡿⠿⠛⠿⠿⠦⢿⢿⣿⡟⠭⠿⢿⠷⠿⠿

⠀⠀⠀⠀⢀⡀⠐⠀⠐⠀⣤⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣀⠀⠀⠘⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠛⣝⠷⢚⣳⡀
⠀⠀⠀⠖⠓⠀⠀⠀⠀⠀⠀⠃⠀⠀⠓⠡⢿⣧⡀⢀⠀⣰⠿⠿⠾⡟⠁⠀⠄⠀⠀⠀⠀⠋⠿⡿⠁
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢶⠲⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠙⠀⠀⠀⠀⢸⠍⢠⠀⠀⠄⠀⠀⠸⡟⠘⡛⣷⠖
⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠈⠐⠀⠆⠁⠰⠀⠀⠈⠁⠘⢦⣄⣿⠀⠀⠀⠶⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠐⠿⠋
⠀⠀⡀⠀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢀⢠⠆⠐⠀⠀⡀
⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⡛⡷⣦⣀⠴⠂
⠀⠈⢀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⣿⣷⣷⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣼⣥⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⣄⠀⠀⠀⡀⠀⡠⠇
⠀⠂⠀⠀⠈⠳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠾⠷⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⡄⠁⠀⠀⠀⢀⠀⠀⠐⢀⣹⣿⣿⣏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⢀⠀⡆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢬⡙⡆⠀⠀⡉⠻⠏⠁⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⢀⠀⢲⢃⠘
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠁⠀⠀⠁⠀⠀⠤⠀⠀⠀⠀⠉⣿⣿⣿⠿⢀⠈⠀⠈⠆⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⣤⠐⠀⠀⢠⡶⠂⠀⠀⠀⠀⠀⠀⢀⣐⠂⠀⠀⠀⠐⠀⢀⠁⣰⡽
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣠⠔⢚⠟⠁⠀⠀⠀⢠⣀⣤⠂⠀⠀⠃⠀⠀⠀⠀⠆⠐⠂⠀⠈⠀⢠⠞⠃
⠀⠀⠀⠀⢀⡞⠀⠀⠀⣴⣋⠤⠚⠁⠀⠀⠀⠀⠀⠘⡿⠿⠄⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⡎⢀⣠⣴⡴⠿⠓⠒⠒⠲⢤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡴⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢾⠆
⠀⠀⠀⠀⠀⠀⣂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣀⠀⠀⠙⠒⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⠙⠛⠳⢦⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣠⡾⠁⢀⡴⠞⠋⠉⠙⢻⡟⠺⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡤⢀⠀⠘⠀⠀⠀⢸⡿⠁⠀⠀⣼⠿⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⢿⣧⠤⠀⠁⠀⠀⢸⡇⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢡⣾⡇⠀⠀⠀⣿⣇⠀⢠⣿⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⣾⡏⠀⠀⠀⢀⣿⣿⠷⠾⠏⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣾⡏⠀⠀⠀⢰⣿⠣⣈⠀⢤⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢈⢷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⣿⠇⠀⠀⠀⠀⢸⡏⢰⡷⣯⠘⠀⠀⠀⠀⠀⣀⢀⡀⣼⣤⣢⣤⣠⣦⡆⣴⣿⣦⣤⣴⣶⣶⣿⡿⣿⠿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣣⣶⠀⠀⠀⣠⣴⡾⣿⣁⠀⠀⠀⠀⠀⢠⣵⠟⠛⠛⠻⢿⡇⢩⣿⣿⣿⠛⠟⠋⠉⠉⠁⠄⠀⠈⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⠀⣰⣿⡼⠂⠁⠀⠀⠀⠀⢀⣴⠿⣿⠿⠟⠛⠛⠛⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⣀⢀⣀⣨⣶⣿⣧⣾⣷
⠀⠀⠀⠀⠀⢠⠀⠀⣠⣶⣿⣿⣿⣿⣯⡻⢄⡿⢁⡸⠧⢴⠄⠀⠀⢠⣿⣿⣟⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠶⠄⢀⡀
⠀⠀⠀⠀⠀⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡾⢯⡘⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⢿⠿⠻⣿⣿⣿⡿⣟⣉⣁⡐⣶⡶⣶⡆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣭⣿⣿⡙⠛⠁⢠⣗⠫⠽⠖⠀⠀⠀⢺⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣯⠿⣯⠳⡄
⠀⠀⠤⠀⠀⣾⣿⣿⣿⣿⡟⣋⣭⠏⣡⣶⣾⠄⣩⠜⠂⠀⠀⠀⠀⠘⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⠙⠛⠻⠷⠋
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⡙⢻⣿⡆⠙⠉⢱⠎⣿⣼⡦⠄⠀⢀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣠⠦⣄⡀⠀⠀⢹⡆⠀⠀⠀⠄
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⣤⡙⠋⢷⣿⡷⣷⣿⢈⣀⢀⣼⣿⠋⠀⠄⢀⣦⠔⠂⠀⠀⠀⢀⣼⠁⢀⣤⣤⡾⠛⠀⠀⠘⣀⠀⢸⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣯⣴⠿⠛⠉⠉⠙⣿⠳⠷⠀⣴⡟⠁⠀⠀⠀⠀⢠⣾⣿⣴⣿⣿⣍⠁⠀⠀⠀⠀⠘⢿⣼⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡟⢻⣧⣼⣶⡟⠁⠀⢀⡀⠀⠀⠈⠓⠓⢾⡟⠁⠀⠀⠀⠀⠀⢳⣿⣿⣿⡟⠠⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⡄
⠀⠀⠀⠀⢹⣿⣿⣿⣍⣽⣿⡿⣿⠫⠘⣷⠀⠀⢸⠇⠀⠀⠀⠀⠀⢈⡇⠰⣀⣠⡀⠀⠀⡈⢿⣿⣿⣇⠀⢠⡅⠀⠀⠀⠐⠀⠀⣿
⠀⠀⠀⠀⠈⣿⡟⣿⣿⢿⢏⡝⠀⣴⠾⡏⠁⠀⢻⠀⠀⠀⠀⠀⠀⠾⠁⠀⠈⠁⠈⠉⠀⠀⠙⣗⣿⣿⡄⠘⠷⢎⢀⡀⠀⣸⣶⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣾⡏⣾⠁⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣿⢷⣦⡹⢯⣿⣻⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⡇⣿⠀⠀⠧⠀⡆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⢷⠻⠀⠀⠙⠛⠟⠛⠛⠛⠻⣿⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⡏⢰⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣶⣼⡧⡴⠞⢠⣼⣾⣷⣄⠀⠀⣤⣤⣴⣶⣦⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣹⣿⣧⡟⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠉⠉⠁⠀⡀⠚⡟⠁⠉⠛⡇⠈⠉⠉⢿⡥⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠴⠀⠹⣿⣷⣿⣿⣷⣿⣾⡙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⢠⡶⠿⠀⢠⣿⠶⢡⣄⠀⢰⣄⠀⢶⣾⠟⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣟⣻⡿⠆⠀⠀⠀⠀⠀⢀⠤⠤⣾⠇⠃⠀⠀⠀⣤⣷⡀⠀⢀⣠⡀⢸⣧⡈⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀⢀⠟⠀⠀⠀⠀⢠⡿⠏⠀⠈⠀⠙⠁⠸⣇⠉⠉⠉⣹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⡻⠁⠢⠀⠀⠀⠀⠀⠀⠈⠂⠀⢠⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣯⣿⡤⣿⣦⣀⡀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⣞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡄⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣤⣤⣤⡤⠲⡎⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣗⣻⣣⡀⠣⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⡾⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣏⣌⢀⡛⡉⠓⠀⢀⡄⠀⠀⠀⢰⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⡐⢦⠀⡄⠀⢀⣠⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣿⣿⣿⣼⣯⡟⣻⠶⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣶⣄⣀⣀⣠⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢾⣻⣿⣿⣿⣾⣾⡏⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⠀⠀⢄⠠⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⡿⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠿⣇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⡿⣿⣿⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠙⠿⣶⣼⣿⣧⡀⠈⠟⠿⣿⣿⣿⣿⠿⢃⡾⠚⠟⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠷⠶⠤⠶⠏⠁⠀⠈⠀⠠⠀⠈⠀⠀⠀⠀⠉⠀⣀⣿⣿⣿⣿⢏⣴⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣠⠀⣤⣄⣀⣤⣤⣤⣤⣴⣾⣿⣿⣿⣏⢸⣯⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣾⣿⣿⣿⣿⣏⢸⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⡙⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠰⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢨⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣺⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⣿⣿⡿⠯⠁⠀⠉⠻⣿⣿⣷⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢽⣿⣿⣿⣿⡧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣱⣿⣿⠏⠀⠀⠊⠀⠀⠀⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⡙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣵⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣀⣠⣴⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣠⣴⣾⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢔⠀⡀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⣠⢉⣠⣴⣤⣔⣷⣦⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠙⣿⣿⠟⠉⠻⣿⣽⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠀⠀⠀⠀⠴⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣴⣾⣿⣆⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⠀⠀⠀⠠⠄⠈⢻⣿⣿⣿⣷⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠖⠀⠀⠀⠐⠀⢀⣀⡀⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⢂⠀⠂⠡⠀⣰⣿⣿⣿⣶⣌⢻⣿⣿
⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⣾⡿⠋⠋⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⠀⡾⣿⣧⠄⠂⠀⡀⠄⡉⠤⠀⠈⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠶⣾⣽⡶⣆⣴⠿⠠⠀⠐⠀⠀⠀⠀⠀⠂⡄⠀⠀⠙⠻⣿⣿
⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣆⣀⡒⣚⡭⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻
⠀⠉⠺⢷⣀⠐⠂⠦⡤⢀⢀⠀⠀⣀⠀⢀⣠⣤⣾⡾⠛⠛⢛⠿⠉⠙⠁
⠀⠀⠀⠀⠉⠙⠛⠚⠅⠦⠖⠖⠀⣠⠤⠀⡀⠊⠊⠀⡠⠖⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣋⡴⢚⣭⠀⡠⠀⠠⠄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⣀⣴⣞⣯⠟⠋⠉⢠⣎⣑⡸⠁⠀⡖⠊⣧
⡀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⢀⣾⣹⣿⠂⠀⠀⠙⣯⠜⣇
⣿⣶⣬⣍⠉⠀⠀⠀⠀⠀⠀⠀⢸⣷⡼⠃⠀⠀⠀⠀⠘⠛⠿⠿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿

⠀⠀⠀⠀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⢰⡶⠀⠀⠀⠀⠀⡠⢶⡆⠀⠀⠀⣠⡶⣆
⠀⠀⠀⠀⢿⣯⣷⣄⠀⠀⠀⢁⡈⠒⠀⠴⠄⠰⣇⡈⠀⠀⠘⢧⠀⠰⣶⣶⡜⠉⡼⠃⠀⠀⡰⢀⢀⡻⠆
⠀⠀⠀⠀⢸⡛⡿⣿⣆⠀⢀⠈⠓⠂⠀⠀⠀⠀⠛⠁⠀⠀⠀⠰⣿⣴⡿⡍⠃⣩⠞⠀⡀⡘⢓⣄⣏⢻⣦
⠀⠀⠀⠀⠈⠳⠅⢈⣻⠏⣻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⣌⣛⣷⣾⣿⡿⢀⣿
⠀⠀⠀⠀⠀⠀⢠⣮⣿⠿⠛⢿⣷⣶⣦⣀⡀⠀⠀⠀⠈⢹⠋⠉⠀⠀⡒⠀⠙⣦⣴⣿⣿⣿⠻⣮⠁⠋⠁
⠀⠀⠀⠀⠀⠀⠟⠛⠁⠐⠦⢄⣩⡿⣿⣼⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠜⢿⣦⣉⣉⣭⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠦⡘⠀⠀⠀⠀⢰⡤⠤⡀⠀⠐⠒⠚⠒⠒⠀⠀⣠⢤⣤⠀⣉⡉⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠲⡶⠂⠀⢀⣴⣿⡇⠈⢿⣄⠚⠶⢄⠀⠀⠠⢀⡠⠶⠒⣸⡏⠀⣿⣿⡄⠀⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣼⣧⡀⠀⢿⣦⠁⠈⢃⢀⣶⣌⠀⢀⣼⡷⠀⠀⣿⢻⣿⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⡿⠿⠃⠀⢐⡦⠀⠀⠘⠙⡿⠀⠀⠀⢰⠆⠀⢘⡇⢻⣿⣇⠀⠀⠆⡀
⠀⠀⠀⠀⠀⠿⣦⣄⠀⢌⢉⠀⠀⠀⢂⠀⠀⢻⣴⡣⠀⠈⠀⠀⣠⣜⠋⠀⠀⣽⡇⣾⣿⡏⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠟⠃⠈⠸⣄⣀⠀⠊⠀⠀⡼⠇⠀⠀⠀⠀⠀⠐⠿⡀⠀⢀⣾⡥⠛⠉⠀⠀⠀⠙⠛⠂
⠀⠀⠀⠀⠀⢴⣷⣤⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⢠⣾⣦⣀⠀⠀⠈⠂⢀⣄⣀⠀⠀⠀⠀⠀⢀⣤⣶⡄
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣆⠀⠀⣀⣤⣶⣾⣷⠀⠀⠀⠀⣈⣋⣙⠛⢲⣄⠀⢹⡞⣷⢿⣦⡀⢀⣴⣟⣾⣿⡆
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠋⠀⠘⠶⡌⣻⣿⣿⣿⣿⣿⣷⣿⡁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⡟⣿⣿⣿⣿⠉⠀⣀⠀⠀⠈⠂⠂⠀⠐⠀⠀⠀⠀⠸⣷⣽⣿⡃⠛⠘⣿⣷⣿⠅
⠀⠀⠀⠀⠀⠀⠙⠋⠁⠈⠀⠻⣿⡿⠋⠀⠀⡿⢴⣦⣀⠀⠀⠀⢀⣀⢠⣤⠀⠈⠙⠛⠛⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣄⠀⠀⢠⣄⠀⢸⡟⣻⣷⡶⣶⣬⣿⣿⡭⠃⠀⣾⣤⣄⠈⠃⠀⠈
⠀⠀⠀⠀⠀⠀⢀⡸⣷⠛⠋⠉⠀⢰⣿⣿⣆⠀⠉⠙⠃⠹⠃⠹⠿⠿⠃⣠⣴⣿⢟⣻⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⠰⠋⠀⢀⣀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣸⡿⢛⣵⣸⡏⠀⢈⠀⠀⠐⠩⣿⡆
⠀⠀⠀⠀⠀⢀⣀⢶⣿⡽⠃⠀⠀⠠⣮⡙⣿⣿⣿⣶⠀⠀⠀⣴⣿⢛⡱⣾⢻⡯⡿⠁⠰⠁⠀⠀⠐⣀⣹⡇
⠀⠀⠀⠀⠀⠸⣿⠟⠋⠀⠀⠀⢀⣴⣿⣿⣿⣼⢿⣿⠀⠀⢸⡟⣡⣾⣷⡟⠿⠟⢃⡀⠀⠀⠀⠀⠈⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⣿⣿⡎⠝⢆⠈⠈⠁⠀⢀⠀⣉⣉⣁⠀⠐⠒⠹⣿⣅⡒⣦⢤⣄⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⢿⣿⣿⣆⠀⢀⡤⢐⣲⣤⡞⠛⠛⠉⣠⣶⣿⡉⢻⠟⠟⣛⣢⣩⣵⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣿⣽⠿⠛⢠⣾⡿⠟⠁⠈⠁⠀⠀⠀⠳⣶⣶⣶⡶⠏⠙⠛⠛⠛⠙⠛⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⣼⣷⠦⠀⠐⠃⡜⠓⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠄⢨⡀⠟⠆⠈⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠠⡀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢬⡅
⠀⠀⠀⠀⠀⠀⡃⠂⠁⠐⠟⠀⠀⠀⠐⢦⠀⠈⠂⠀⢀⠀⠀⠀⡄⠀⢄⡰⣄⠉⠲⡘⠀⣠⠁
⠀⠀⠀⠀⠀⠀⢓⣠⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣄⠀⢳⣄⠀⠰⡀⢀⢳⣮⢠⠈⠄⢀⠔
⠀⠀⠀⠀⠀⠈⠀⠀⠈⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⡁⣄⠩⠃⠀⡘⢶⢦⡽⠇⠀⠅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠃⠀⠀⠀⠐⢦⡄⠀⠀⠀⠀⠈⠀⡍⠣⠀⠠⡀⠓⢂⣐⠒⣀⣠⠶⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠀⠄⠀⠀⠀⠱⠋⠤⠀⠀⠀⠢⡂⡂⠀⠰⢀⣈⠈⡉
⠀⠀⠀⠀⠀⠀⢁⠐⠠⠄⢀⠀⠀⠠⠄⠀⢀⠀⠀⠁⠄⠀⠀⠀⠈⢠⡁⠁⠉⠀⠉⠈⠋⠙⠓⠂
⠀⠀⠀⠀⠀⠠⠀⠁⡀⢀⠀⠀⠁⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⢀⠌⠀⠀⠀⡈⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⢠⠈⠁⠈⡄⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠃⠈
⠀⠀⠀⠀⣀⠁⠈⠀⠄⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀
⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠘⢅⠁⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠀⠀⠡⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⡀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢱⡀⠀⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡋⣀⠀⠉⠛⢒⣲⣷⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠦⠤⠤⠉⣻⣅⢹⣿⣿⣿⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⡐⠂⠈⠻⠿⠟⣫⣽⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠂⣿⣿⣆⠀⠀⢀⡤⠀⡰⢊⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡅⠡⢷⣾⡟⠋⠀⠀⠳⠌⢹⣂⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⠒⠒⠚⠿⠇⢀⣴⣧⡀⠀⢹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣤⣤⢤⣄⡀⠀⠀⠙⡿⠋⣀⣴⣾⣿⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⢉⣿⣿⡿⠁⣐⣶⠋⣴⣾⣿⣿⣿⣇⣀⣠⣶⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡻⠖⠛⠁⠁⠘⠿⠿⣦⡙⢿⣿⣿⣿⣿⠿⠿⠋⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⢀⣀⠀⣀⣀⡀⢻⣿⣶⣝⡻⢿⣤⣴⢦⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣾⣿⣿⣿⣁⢿⣟⢻⣿⣿⣿⣿⣿⠃⠨⢯⣤⡅⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠋⠽⠛⠁⠈⠙⡿⢿⣿⣻⣽⣶⣿⡿⠁⡸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⣠⡼⢀⣘⣿⡿⠿⠿⣿⢧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢻⡽⠿⠇⢸⣿⡋⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⢀⣴⡾⠃⣼⣿⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠙⡿⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⣺⡁⠀⠀⢠⠏⠀⠀⠀⣠⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⡞⠀⠀⠀⣼⣿⡿⠛⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⣠⣅⠀⠀⠀⠹⣿⣿⣿⣿⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣤⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠛⠛⠛⠛⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⣶⣆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢹⣦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠸⣤⣭⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠋⠉⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠤⠾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢠⣾⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⣄⣤⣤⣤⡀⠉⠁⠀⢳⠀⠀⢀⣶⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡧⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠏⠁⠈⠛⢻⣂⡀⠀⠲⣷⠀⢼⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡆⠀⠀⢀⣀⡈⠻⣗⠀⠀⠜⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⢶⠶⠞⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣀⢀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠟⠉⠀⠑⣄⠀⢀⢀⣠⣠⣄⢤⡈⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠺⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣽⣿⠟⢻⠉⠛⠯⠟⠳⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⣴⡾⠤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⢀⠀⠀⣤⣤⣤⢀⣠⣒⣢⣼⠶⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⢳⡀⠀⠀⣴⣆⠀⠀⠀⠀⠀⢠⡴⠊⠻⠋⠛⢰⠋⠘⢀⠁⠈⠉⠉⠉⠛⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠐⠀⠀⠀⠀⣠⠆⠀⠐⢲⡟⣧⠀⠀⠈⢶⣌⡀⡀⣀⡤⠏⠁⠀⠀⠀⣀⠘⠀⠀⡈⠀⠀⢀⣠⣰⣾⡿⠋
⠀⠀⠀⠄⠀⠀⣤⣰⣶⣶⣶⣶⣿⠙⠛⢿⣷⡶⠿⠦⠞⢇⣀⡀⠴⠿⠻⠋⠀⠀⠀⠀⠉⠙⠙⠛⠀⠀⣀⣄⣠⣤⣼⣷⣷⣾⡿⠾⠿⠿⠿⠟⠉
⠀⠀⠀⣀⣿⣶⠿⠛⣫⣾⣿⣿⣀⡀⠀⠀⣿⠶⠦⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⠆⠴⠶⣦⣌⡁⠀⠀⠙⠉⠹⡏
⠀⠀⠸⣾⣿⣁⠀⢠⣿⠟⡉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠯⠽⢜⣦⣅⣀⠁⢈⣷⣄⠀⠀⠁
⠀⠀⠀⠙⠉⠛⠛⠛⠁⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣶⣿⣿⣿⣿⣤⣔⣛⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⡆⠀⠀⠈⠙⠇⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠽⠿⠿⠿⠿⠛⠁
⠀⢀⠀⣠⣤⠀⠀⢀⠀⡄⠈⠈⠁⠀⠀⠀⢀⡄⠀⠀⢠⣔⠻⣿
⠀⠀⠁⠋⠉⠁⠉⠛⢋⠀⠀⠀⠀⠠⠀⠉⠘⠁⠀⡹⠊⣿⡒⠻⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠄⠀⣠⠼⢃⡀⠀⢲⣤⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠒⠚⠋⠀⠀⠁⠀⢭⣿⣴⡆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣄⣦⡖⣷⡀⣠⠇⢀
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠆⣀⣤⢴⣦⠾⢷⠷⠾⢿⢛⡗⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⣀⠀⠘⣺⠯⣿⣽⠟⣈⡿⠿⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠐⠋⠟⠢⠜⠆⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣤⡀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⢀⣐⠂⠐⠂⢺⡌⠀⠈⢧⡀⣶⣶⡉⡞⠀⢀⡦⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠛⣷⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠘⠁⢠⣮⣷⣷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⠾⢷⣦⣤⣀⡀⠀⠀⠐⠖⠂⢀⡄⠐⣮⣽⣿⣿⢿⡉⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡘⠂⠞⠛⠾⠛⠀⠀⣀⣀⡀⠀⠉⠋⠛⢾⣭⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠈⠀⢠⣤⠈⢷⡕⣦⡀⠀⢀⠀⣠⠚⣿⠃⣶⣄⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠘⠷⠄⠈⣆⣴⡎⠈⢼⠇⢀⣿⣿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡿⠟⠛⠁⠀⠹⣄⡤⠈⠟⠠⡐⡼⠀⢸⡏⣿⡷⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠆⠳⣆⡀⠰⠀⢀⡟⠁⠀⠀⠈⠻⡀⠀⣾⡿⠟⠁⠀⠰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣀⠀⠀⠁⠀⣀⡀⠀⠀⠸⣷⣄⡀⠈⠀⣤⣄⡀⠀⠀⣀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧⣤⣶⣿⣿⠃⠀⠀⠀⠒⠢⠉⠇⠀⢯⠻⣿⣦⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⢿⣿⣿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠟⠋⠀⠘⣽⣷⣄⣀⢀⣤⢴⠆⢀⠉⠉⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠶⠛⠀⣼⣿⡄⠛⠻⠹⠟⢿⡿⠇⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⢀⣄⠀⠀⢻⣿⣿⣄⠀⠀⠀⢀⣀⡸⢟⣽⣽⠁⠈⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠉⠀⠀⣸⣮⣿⣿⣷⠀⢠⡿⢫⣼⣿⣿⡇⠀⠁⠀⠠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣤⣄⣤⣾⣿⠻⡍⠙⠋⠀⢈⣙⣉⠉⠀⢳⣿⣢⣤⣄⣀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠿⠿⣿⣿⣿⣧⠀⣴⣬⠶⠞⠉⠉⡴⠾⠏⣟⣛⣭⣮⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠘⠋⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡉⠀⠀⠀⠀⢀⣀⢂⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⢀⣔⣱⢿⣷⣮⣥⡀⠀⠀⢸⣷⣄⣶⣿⡞⡇⠀⠀⠀⠀⠋⠑⢠⡿⣻⠅⠀⠀⠀⠀⠀⢠⣿⣷⣤⣾⣿⣷⡀⠀⠀⠀⠀⠣
⠀⠀⠀⠸⠋⢁⣽⣿⣭⣄⣹⠆⠀⢸⣿⣿⣧⣻⣿⣇⠀⠀⠀⠀⡀⠀⢈⣆⡨⣰⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣶⣏⠆
⠀⠀⠀⣴⡖⢿⣿⣿⣯⡋⢿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠢⡿⣺⠇⡂⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿
⠀⠀⠀⠟⣠⡾⡿⣿⠇⢉⡷⡗⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⡀⠀⠀⠀⣿⣿⠇⠈⠉⠀⠀⠀⠸⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠠⣿
⠀⠀⠀⣇⣴⠟⢹⣿⠷⢎⣁⠀⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢌⢺⠗⠂⠄⠉⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⡏⠀⠀⠀⠈⢣⡄
⠀⠀⠀⠟⠀⣒⣿⢟⡂⠀⠉⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠋⠄⠈⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢼⡇
⠀⠀⠀⢀⠜⠋⣿⣗⠉⠿⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⠁⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⢠⢿⣿⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠃⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣂⣤⣄⣾⡿⠛⠃⠀⠀⠀⠀⢸⣿⢿⣷⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣣⣿⣈⣿⣿⠇⠀⠀⠰⠄⠀⠀⢸⣿⣿⣿⠀⠀⠀⢀⣾⣿⣷⡄⠀⠀⠀⠀⠀⢿⠎
⠀⠂⠀⠈⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣫⣿⣯⡀⠀⠠⠐⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢠⡘⡿⠂⢀⡤
⠀⠀⠀⢀⡰⣿⣿⣧⣽⠖⠀⠄⠀⠀⠀⢿⡟⠁⣞⠣⡄⡄⠦⠌⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠸⣿⣿⡿⠁⠀⠀⠀⢦⣟⣇⣠⣾⠃
⠀⡂⠀⠀⠀⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠙⠘⢻⣤⠙⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠁⠈⠻⠉⠁
⠀⡀
⠀⠆

⠀⠀⠀⠀⠉⢉⠛⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠠⠖⠟⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⢦⡀⠀⣬⣠⣶⣾⣿⣷⣶⣄⣀⠇⢀⡀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣦⣦⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣽⣿⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣿⣿⣿⣿⣿⡿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠒⠠⡀⠀⠀⠀⠀⢀⡤⠒⠠⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢀⣀⠄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⢰⡆⢀⠀⠀⠀⠀⠀⡀⠠⠀⠈⢀⠀⠈⠆⠀⠠⠀⡞⠠⠀⠈⠀⠀⢉⡉⣠⣅⢠⡄⠀⠀⡔⢎⠀⢸⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠅⣾⠀⠀⠀⠀⠀⠀⠍⢠⡌⢡⡄⠀⠀⠀⠻⣬⠑⡯⠃
⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠅⠀⢠⠀⠀⠡⡈⠀⠘⠀⠄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢁⠉⠀⠀⠀⠈⠀⠀⠀⠒⠊⠀⠀⠀⠀⢀⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠚⡆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⢀⡈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠐⠀⠀⠀⠁⢸⣏⠀⠀⠀⡀⢀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠆⠐⠤⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⡀⢰⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠀⠐⢄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⢀⡁⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠈⠃⠀⡂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠠⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠱⣀⢀⣀⣤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⠂⠉⣩⠉⠑⠠⡀⠀⠀⠀⠰⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⢄⢀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉⣐⣀⠔⠁⠀⠀⠠⢄⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠔⠉⡑⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣃⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⠀⠑⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠃⠂⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠊⡀⠀⣀⠈⠳⣄⠀⠰⠌⡤⠂⡐⡄⠀⠀⠛⠀⢠⡷⢾⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠉⠁⠢⠀⡇⠈⠋⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠇⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠁
⠀⠀⠀⢠⡀⠢⡈⠀⠀⠰⠂⠀⠀⠀⠀⠐⢁⡄⠀⠑⡈⠀⡠⠁⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠈⠒⠴⣦⣿⣔⡾⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡷⠈⠀⡌⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⢀⣤⠖⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡆⠀⠀⣤
⠀⠀⠀⠀⢠⣿⡇⠐⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⢀⢠⡀⡄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠶⠞⠃
⠀⠀⠀⠀⣾⣿⠓⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⠀⠀⠀⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣸⢀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠅
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣧⣤⣤⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢍⠙⡶⠊⣀⡤⠬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣶⣿⣷⡟⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠉⠘⢶⣟⣺⣿⢦⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⢉⣿⠞⣹⠮⠿⠟⠂⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢽⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⣷⠞⢉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠖⠻⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠌⣿⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠺⠻⠿⣯⣟⢻⣿⣾⣿⣤⣊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠘⠛⠽⣿⢿⣽⣗⣖⣠⢄⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣄⣀⣀⣀⣀⣀⣰⣧⣤⣿⣥⣤⣭⣭⣋⣉⣀⣀⣰⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣝⣛⣩⣛⣻⣟⣽⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠰⡀⠀⠀⡀⢀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠆⠀⣂⠔⢢⢀⠀⠀⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠉⠀⠹⠀⠀⠀⠀⠀⠀⠀⢀⣩⠂⠤⡽⡓⠉⠁⠀⢴⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠫⠞⠀⠀⠀⠀⠀⠀⢼⡠⠇⠀⠀⢠⠛⠀⠀⠂⠂⠀⠀⡜⡙⠀⠀⢸⠀⠀⠀⠀⢉⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢭⠀⢁⡀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠒⠀⣾⡄⠀⠀⠃⠀⠀⢀⠄⠀⠀⠀⢸⣀⠠⠀⠀⡌⡤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣶⣀⣖⣤⢀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⢹⠉⣃⠀⠀⢰⠀⠀⠀⢀⡠⠖⢻⠿⠀⠀⠀⢘⠥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⡏⠀⠁⢄⢠⠂⡤⢠⠀⠀⠤⠀⣤⣤⠄⠘⠀⠀⠀⡾⠟⠀⠀⠐⠉⠀⠀⢸⠀⠀⠀⡛⡿
⠀⠀⠀⠀⠀⠀⠀⣞⠿⠑⠀⡠⠀⢈⠉⠀⠀⠡⠛⠓⣆⠀⠀⠀⠀⢨⢄⠐⠀⠀⠀⡀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢣⠄⠁⠈⢤⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠠⢀⠀⠈⠀⡆⢠⠜⣤⣤⡄⢰⠀⠀⠘⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⠁⠀⠀⢀⠰⣶⠄⠀⠶⠾⠶⢾⡣⠄
⠀⠀⠀⠀⣀⣀⠄⠀⢀⡀⠀⠆⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢬⠀⠀⠉⠉⠀⠛⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⣩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⠀⠊⠀⠀⠀⠨⣳
⠀⠀⠀⢀⣀⣀⣾⣆⠀⣀⠀⠀⠤⡦⣷⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⠈⠀⠉
⠀⠀⠀⠈⠀⠀⣄⣀⣠⣶⣦⣿⠶⢦⣧⣤⠤⣤⣤⡤⠤⡤⡤⠄⠀⠀⢠⣼⡍⣁⣀⡀⣤⣀⡀⠀⣠⡤⠸⣦⣤⣤⣄⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠾⠿⠿⠲⠾⠗⠒⠒⠛⠀⠈⠓⠚⠛⠛⠉⠉⠃⠚⠛⠃⠈⠉⠙⠛⠉⠉⠉⠉⠉⠛⠉⠁⠁

⣿⢿⣿⠿⡿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿

⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠿⠿⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉


⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣯⣽⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠉


⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⣿⣷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣶⡷⢿⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⡾⠿⠿⠶⡿⠷⣶⡿⠷⢾⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⣄⡄⠀⠀⣤⢠⣤⠀⠀⠀⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠔⠎⡛⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠂⠘⠀⠃⠇⠘⠂⠉⠈⠀⠀⠀⠀⠀⠁⠈⠁⠀⢀⡀⢸⣳⡠⠔⠁⠀⠀⢀⡜⠓⢤⡀⢰⠋⠀⠀⠠⠀⠠⠀⡇⠀⣰⣦⡁
⠀⠀⠸⢇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⣼⣠⠏⠀⠀⠀⠐⠀⠈⠀⠀⠈⠀⠸⡆⢄⠀⢅⠀⣐⠼⠁⠀⡇⡜⠃⠀⠀⠀⣀
⠀⠀⠀⠘⡆⡜⠀⠀⠀⠀⣤⠀⡰⠂⠀⠀⠼⢾⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠒⠟⣶⠛⠛⠉⠁⠀⠀⠘⡇⣇⠀⢀⡰⢶⣝
⠀⠀⠛⢄⢻⡇⠀⠀⣠⡞⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⢉⠦⠤⠤⠴⢠⡤⣧⡄⢼⠆⠀⠀⢰⠉⠂⠌⣐⠀⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢳⣈⠉⢉⣀⠜⠋
⠀⠀⠀⠈⢢⡇⠀⠀⢈⣧⡀⠀⣸⡄⠀⠀⡠⡄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠘⣆⠌⠐⠀⢁⠂⠈⠂⡼⠀⣠⣤⣄⠀⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢳⠀⠀⠁⠘⠛⠙⡍⠀⠀⠀⠉⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⣴⡽⠀⣀⡠⢤⠤⡬⠷⣤⠤⠤⠤⠖⠋⢀⢮⠞⠁⠀⡴⢹⢀⣤
⠀⠀⠀⠀⠀⢹⢠⠶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⡿⠋⠀⢸⠁⠠⠀⠀⠀⠄⠈⢦⠀⠀⠀⠀⢸⠘⠒⣦⡸⠁⠓⠊⡼⠀⣾⣿⡆
⠀⠀⠀⠰⢆⢸⡏⠀⠀⡠⠤⠤⣀⣀⠴⠊⠳⡀⠀⠀⠀⠀⣀⡠⣤⠄⣀⣀⣀⠘⣦⠈⡀⠀⠀⠄⠀⣘⠇⠀⠀⠀⠈⠓⠊⠡⡷⠒⡆⣸⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠈⢾⡇⠀⠘⣅⠀⠀⡼⠉⠓⢦⣸⠁⠰⠀⠖⠉⠃⠀⠀⢀⠠⠐⠉⠉⠉⢷⠚⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⠖⢲
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⡞⠁⠺⠇⢠⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⣤⣤⠀⢠⣤⡄⠀⣠⣤⡀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠠⠂⢼⠙⠲⢄⣠⠋⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣠⡇⠀⢸⢹⠀⠀⠀⡿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⡴⠞⠁⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣾⠀⢸⣿⡇⠀⢸⢸⠀⠀⠀⣙⠇⢸
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡀⠠⠍⡇⠀⠀⢀⢏⣌⢧⠀⠀⢸⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⠀⣧⠄⢾
⠀⠀⠀⠀⠠⠀⡷⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠛⠀⡇⠀⠀⢸⢸⣸⢸⠀⠀⠘⠋⠀⠈⠛⠁⠀⠘⠛⠀⠀⠀⠿⠤⠼⠰⠆
⠀⠀⠀⠀⠀⠀⡧⡇⠀⠁⠀⠀⠀⠀⠀⠀⠐⡿⠷⢶⠂⠀⠀⢸⢰⡏⠙⢆⡇⠀⡆⠘⣆⣡⠞⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⠀⠀⠀⠀⠀⠀⢀⠇⠂⠘⡆⠀⠀⠀⠶⠁⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⢠⣾⡁⢀⣀⣠⠔⠛⠓⢤⣠⠎⠀⠈⠲⣤⡀
⠀⠀⠀⠀⠀⠀⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⢹⡀⠀⠀⠀⢀⠀⢀⠀⠀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠈⠛⠿⡀⠀⠀⠀⠈⠋⠀⠤⠆⠀⠈⠁
⠀⠀⠀⠀⢀⡞⠤⣈⣆⠀⠀⠀⠀⠀⠀⣸⠃⠠⣕⠀⠀⢧⠀⠀⠀⠉⠀⣿⠀⠀⠀⢰⡆⠀⢇⣤⣤⣀⣀⣀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡞⠈⠘⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣧⠀⣤⡄⠀⢶⠀⠀⠀⠣⠤⠄⣀⣀⣀⣀⣤⠀⠀⢠⣤
⠀⠀⠀⠀⢣⣀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⠐⣿⠀⠀⠀⢸⢿⠀⣿⡇⠀⣿⠀⠀⡤⡄⠀⠀⠀⣶⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⡀⠙⠿⢿⡿⢿⡿⠿⠿⠿⠿⠛⠀⠀⠀⢿⠀⠀⠀⢸⢸⠀⡇⡇⠀⣿⠀⠀⡇⡇⠀⠀⠀⢸⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢖⣢⣀⣀⣹⣷⣤⡤⠼⢷⣦⠤⠤⠄⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⢸⢸⠀⡇⡇⠀⡿⡆⠀⡇⠇⠀⠀⢸⢸⠀⠀⣷⡇⠀⠐⢶
⠀⠀⠀⢀⣤⣤⠔⠊⠉⡿⠃⠀⠐⠖⠁⠀⠺⠊⠀⠀⠀⠀⠀⢤⡄⠤⠤⢾⠤⠶⠶⠾⠾⠶⠷⠷⠶⠻⠗⠦⠗⡖⠒⠒⣼⠛⠒⠲⠟⠓⠿⠆⠙
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠘⠈⠀⠈⠉⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠐⢒⠺⠓⠢⠒⠘⠏⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⣀⡀⠀⠀⡰⣴⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⡤⠤⠀⠤⡴⠀⠀⢠⠂⠁⠀⢀⠔⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡛⠚⠒⠐⠢⠐⠚⠁⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠠⠇⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛⠀⠀⠷⠀⠀⠀⢀⣠⠖⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠂⢠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢳⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠠⡴⠿⠁⠙⠉⠁⠀⠀⠀⠩⠆⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠙⠉⠃
⠀⠀⠀⠀⠀⠀⢐⠀⢓⠀⠀⠀⠀⠀⠘⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠜⡁⡐⠲⠂⠀⠀⠀⠈⠇⢀⣄⠀⠀⠀⠀⠀⠀⢰⡶⣶
⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⡀⣈⠙⠀⠀⢐⣖⣶⡞⠆⠀⠀⠀⠀⢤⠚⣁⡚⣠⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠌⣄⡀⠀⠈⠉⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠯⣣⠅⠀⠀⠀⠀⠀⠀⠀⣩⠃
⠀⠀⠀⠀⠀⠈⠛⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⢺⠠⠄⠀⠀⠀⠁⢀⣦⢤⣤⡤⣤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⠀⠀⣠⠰⠿⠒⠛⠋⡉⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢤⡘⡛⡀⠜⠁
⠀⠀⠀⠀⠤⠴⠦⣐⡀⠁⣠⠦⠤⢀⣀⡸⠂⠘⠀⠙⠤⠖⠀⠀⠀⠛⠋⠙⠁⠀⠀⠀⢀⡀⠀⣴⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⡀⠀⠀⠆⣄⠈⠀⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡀⠀⠀⠀⠀⠙⣃⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠑⡐⠋⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠄⠀⠀⠀⠀⣤⢘⠃⠀⡀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄⠀⠀⠀⠀⠠⣶⢈⠀⣠⢫⠄⠀⠀⠀⠀⠒⠤⢄⣀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡌⠰⠀⠀⠀⠀⠀⠲⢿⡆⣀⡌⠀⠀⠀⠀⠀⠀⠐⠘⠛⡀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⣁⢴⡂⠀⠀⠀⠀⠀⢭⣿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠤⣤⠤⡀⠀⠀⠀⠀⠀⠀⠠⢴⣶⠄⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣘⠉⠀⣚⠀⠛⣄⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡾⡧⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡷⣥⡀
⠀⠙⠋⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣽⣯⡧⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠠⡷⠷⢚⠆⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣟⠐⠀⠀⠀⣀⠀⠀⠀⣴⣖⣉⡁
⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⡿⠉⠀⠠⠤⠴⠦⠄⠀⠗⡆⣖⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠤⠰⠀⠀⠀⢛⣻⣿⠒⠒⠒⠒⠶⠒⠂⠈⢷⡥⢶⠛
⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡤⠄⠀⠀⢀⠀⠀⠀⡼⠓⢘⡆⠀⠀⠀⣶⣾⠄⠼⢾⡗⢀⣸⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠨⠇⠀⠀⠈⢉⠀⠀⠰⠛⠃⡠⠷⠀⠀⠀⣟⠻⠀⡈⢿⡅⠸⠁⣇
⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠘⢶⡀⠀⠀⢀⡤⢾⠭⣧⢀⠀⣂⣀⡀⡰⠛⢠⣤⣼⣉⢛⣿⢻⠄⠀⢀⡇⠀⣧⠁⡞⣇⠐⡟⣿⠒
⠀⠀⠀⡇⠀⣼⣠⣸⣧⣷⣶⣶⣿⢶⠶⠿⠿⢷⣛⣛⣛⡙⠯⠭⢿⣷⢰⣾⠿⠻⣿⡿⣿⡟⣷⣾⣿⣴⣦⣻⣶⣯⣿⣅⣿⣿⣷⡆
⠀⠀⣠⣧⣸⡭⣟⣹⣿⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠛⠓⠦⠬⢭⣍⣀⣚⠛⠾⠿⢿⣷⣿⣿⣿⣿⠍⣿⣿⣿⣷⡽⠿⣷⠃
⠀⢠⠤⣗⣨⠶⣫⠽⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⢠⡀⠀⠀⠀⠀⠉⠉⠙⠓⠒⢶⣤⣤⣥⣉⡛⠺⠿⠿⣿⣿⣷⣶⣾
⠀⠀⢘⣩⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢯⣷⣦⣤⣄⡉⠁
⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣠⢞⡥⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⡖⢋⣩⡼⠷⡄⠀⠀⠀⠀⠀⠀⢠⢞⡭⠂⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⡞⢡⠘⣿⡆
⠀⠀⠀⠀⣏⢸⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣼⠛⣉⣥⠴⠾⡇⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⡇
⠀⠀⠀⠀⠹⣌⠆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢼⣋⠉⣤⠶⡟⠁⠀⠀⠀⠀⠀⠀⣧⢣⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡧⢸⠀⣿⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣤⣿⣤⣧⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⣯⣼⣤⣿⡇
⠀⠀⠀⠀⠀⠈⣳⣶⣶⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿

⠀⠀⠀⠀⠀⣀⢀⣤⢠⣄⢀⡀⠀⠀⠀⠀⠀⠀⢠⠖⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣤⣶⣤⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⣰⣞⠛⣶⡀
⠀⠀⠀⢀⣘⠋⢾⡏⠉⡽⠎⢛⣀⠀⠀⠀⠀⠀⠙⠦⣀⣬⣬⡃⣤⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⡿⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡙⠿⠾⠏⡁
⠀⠀⠀⠾⠿⠸⡿⠀⠀⢛⡿⠸⠿⠆⠀⠀⠀⠀⠀⢠⣿⣿⡸⢞⣵⢟⣀⠀⠀⠀⠀⠀⣧⣿⣿⡇⠀⠘⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡸⠁
⠀⠀⠀⢶⣶⠰⣿⡶⢠⣾⡷⢰⣶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣧⣌⠡⠿⡋⠀⠀⠀⠀⠀⠹⣿⣿⣷⡗⣰⣿⣿⠇⠀⠀⠀⠀⠀⣠⠀⣾⣮⣩⣶⡆⢠⡀
⠀⠀⠀⠈⢩⣄⢶⣷⢻⣶⢆⣬⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢻⡂⢯⡀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⠀⠿⠿⠿⠿⠇⢸⣿
⠀⠀⠀⠀⠀⠈⠀⠛⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠑⠻⢦⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⣿⣿⣷⣿⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⢸⠟⢉⣉⠛⣿⠀⢠⢀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠳⣄
⠀⢀⡄⣿⣿⣿⣿⢰⣀⣠⣶⢾⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣴⣴⠀⠀⠀⠀⠀⣿⣿⡈⠀⢁⣿⣿⠀⠀⠀⠀⠀⡞⠀⢠⡀⢙⣶⣄⠀⠀⠸⡆
⠀⠘⠇⣿⣿⣿⣿⢸⣿⠶⠶⢸⣿⠀⠀⠀⠀⠀⠀⣿⣶⣷⣾⣷⣿⠀⢿⢿⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿⠀⠀⢀⡇
⠀⠀⠀⣿⣿⣿⣿⠸⣿⠛⢻⢸⣿⠀⠀⠀⠀⠀⠀⠙⠿⣿⢿⠿⠟⠀⢸⢸⠄⠀⠀⠀⠀⣿⣿⣈⣠⣀⣿⣿⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠉⡇⢀⡼⠁
⠀⠀⠀⠛⠋⠩⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣄⣀⣠⣎⡞⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠼⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀⠀⠀⢼⠄
⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⢫⣻⠇⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⢀⠰⠚⠋⠁⠸⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠀⠀⠀⣾⣭⣶⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣤⡤⢸⠩⣭⣭⡭⢻⠠⣤⡀
⠀⠀⠀⠉⠛⠗⣶⣶⣤⣀⡀⡶⠒⢦⠀⠀⠀⠀⠀⠀⢨⡿⢿⡅⠀⣴⡟⠉⢻⣆⠀⠀⠀⣶⡆⠀⢬⡥⠀⢠⣥⠀⠀⠀⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡆
⠀⠀⢠⣶⣶⣴⣬⣿⣿⣿⣿⣿⣾⣿⣷⣦⣄⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⣾⣧⠀⢸⣷⠀⠀⠀⠿⠟⣵⡎⠿⠿⠿⠿⠏⣶⠹⠿⠃
⠀⠀⠘⠿⣟⢙⡿⠿⠿⠿⠿⠿⢿⡟⢙⡿⠿⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⡟⠀⠀⠀⣿⡇⠀⣿⣿⠀⢸⣿⠀⠀⠀⢸⣿⣮⣴⣿⣿⣿⣿⣷⣭⣾⣿
⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠉⠀⠀⠉⠀⠉⠀⠀⠀⠃⠀⠀⠀⠙⠁⠀⠙⠋⠀⠈⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣂⠉⠩⠍⢁⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠊⠁⠀⠀⠀⠀⠈⢂⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⢀⡀⢀⠀⠀⢀⠀⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠡⡀⠀⠀⠀⠀⡨⢀⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡱⢌⡒⠶⠄⣊⠥⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠤⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⠃⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢘⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠚⠂⠀⠈⠐⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠢⣀⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠠⡂⢰⠀⢀⢄⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⡀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠐⢄⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡋⠈⡐⡊⠉⠁⠀⠈⠀⠴⠄⠙⠊⠁⢙⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠰⣁⡹⠀⠏⠀⠂⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢡⠀⠈⠀⠀⠀⡤⠀⠀⠀⠀⡤⢄⠀⠌⡌⠐⠀⠀⠀⠀⠀⠀⢀⠎⠀⠑⠤⡤⠊⠀⠒⠠⢄⡀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡱⡀⠀⠀⠀⠀⡠⠀⠀⠀⠑⢀⠌⠜⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠱⡀
⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⡄⠀⠈⠪⢕⠠⠀⡀⠦⠌⠀⠄⡊⠔⠁⠀⠀⠀⠀⠀⠀⠀⢰⢧⡀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠱
⠀⠀⠀⠀⠀⠘⠂⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠻⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡰⢀⣀⣆⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⢩⡍⣭⢩⣭⡍⡍⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀
⠀⠀⠀⠀⠠⠠⠉⠁⣀⠈⡜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠇⠄⠰⣰⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀⠀⠀⡠⠁⢀⠌
⠀⠀⠀⠠⠡⠁⢀⠀⠈⠀⠘⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠔⠁⠑⠤⡀⢠⠎⠁⠀⠀⠀⠀⠈⠢⠊⠀⡠⠊
⠀⠀⠠⠡⠁⠀⠉⠀⠀⠀⠀⠈⠜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⡇⠀⠀⢠⠊⠐⡀⠀⠀⣷⠊
⠀⠠⠡⠁⠀⠀⠀⠀⢞⡱⠀⠀⠐⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⢀⠀⠀⠙⠃⠀⠀⠈⠂⠊⠀⠀⠀⡅
⢀⢀⠁⠀⠛⠂⠀⠀⠀⠀⠀⡈⠂⠑⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⣧⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣅⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠐⠂⠐⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣀⠀⠀⡥⠀⠀⠀⠀⠤⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢠⡎⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢃⠀⠀⠊
⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠐⠂⠄
⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⡃⠀⠀⠀⡤⣖⡧⠀⣂⣀⠔⢒⠄⢀⣠⠀⠀⠀⢠⠀⢀⢢⣄⣐⠄⠀⠀⡅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠁
⠀⠀⡀⠀⠠⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠨⢰⡌⢇⠀⢀⣼⠀⢠⠔⠀⢠⡜⢸⢀⠇⢀⡠⠮⠂⠀⠀⡇⠀⠀⠙⠦⠀⠙⠁
⠀⠀⠃⠃⠉⠁⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠋⠁⠚⠁⠐⠚⠀⠙⠀⠋⠀⠀⠊⠁⠛⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⠆⠀⠀⠁⠶⠦⠠⠶⠦⠼⠿⠧⠷⠄⠴⠶⠴⠄⠠⠶⠶⠦⠿⠇⠀⠘⠀⠀⣖⠀⠤⠀⢐⡀⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⣀⠀⠀⠈⢠⡄⠀⠀⠈
⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠇⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠣⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠉⢀⣀⣀⡀⠊⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠂⠴⣀⠠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢄⠀⠁⡀⠀⣤⠒⠆⠈⠉⠉⠐⡁⠈⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣨⡑⠚⠃⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠖⠁⠀⢠⣴⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣬⣻⣿⡄⠀⠀⠁⠰⠂⠀⡚⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⠀⠖⠀⠀⠀⠀⢰⡀
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣧⣤⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⢸⣤⢿⠇⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣿⢿⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣦⣿⣿⡟⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⢀⠀⠈⠐⠺⠿⠿⠿⠀⡼⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡗⠀⠀⠀⠀⢤⠄⠀⠀⠀⠠⠶⣈⠁⠀⡀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢡⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠛⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠮⢻⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⡹⣿⣷⣤⡧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠽⣻⠟⣻⣷⣐⠀⣀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣯⣾⣷⣹⣿⣿⣀⠆⢀
⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠈⣻⡄⠀⠀⠀⢳⠟⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⡙⣧⣀⠈⠄⠀⠀⠀⠀⠀⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠁⠈⢻⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⣀⣉⠿⣿⣿⡯⠘⣯⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⠛⣷⣦⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡴⠒⢉⠄⠠⠟⠋⢿⣿⣾⠈⢿⣅⡂⠀⠀⠀⣠⣾⠀⠀⠀⡖⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⢠⡤⠁⠀⠀⠀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠙⠛⠄⢂⠙⣷⠀⠀⠐⠛⠉⠫⠀⠀⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠉⠈⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣀⠀⠈⠉⠀⠆⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡶⠄⠿⠂⠀⠀⠁⠀⠀⠀⠀⠐⠀⠛
⠀⠀⠀⠀⠀⠈⢧⢀⣤⠴⠚⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⠶⣀
⠀⠀⠀⠀⢠⠼⣆⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢒⡔⠄⠀⠀⠀⠀⠁⠀⠀⢀⡰⠋⠁⠀⠉⡤⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⠂⠀⠀⠀⠀⠀⢣⣛⠃⢰⠆⢶⡀⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡀⠀⠀⠀⠀⠸⠛⢿⠀⢶⠈⠃⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⡷⡄⠀⠀⠀⠀⠸⡇⢠⠀⠀⡃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⢿⠀⠀⠀⠀⠀⠀⠙⠈⡀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⢫⣧⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⣠⡇⠐⠙⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣴⣾⠋⠀⠰⠷⠈⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣋⣭⣵⣾⣯⡐⠷⠀⠀⡀⠀⣿⣿⣿⣿⣦⡀⠀⠘⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⠛⠉⣿⣦⣄⠈⠁⠀⠀⠉⠛⠿⣿⣿⣶⣶⢟⣿⠇⠀⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠅⠈⠀⠃⡸⠋⡣⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣏⣀⣠⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣫⣿⠃⢀⠀⠐⠜⠂⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣽⣿⡿⢛⡛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠠⠀⠤⠜⠀⢀⡠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣌⢻⣿⣿⣿⠿⠿⢿⣦⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⡀⠀⠀⠐⠀⠀⠠⠄⠅⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣾⣿⡟⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠵⡀⢄⣴⣶⣿⣿⠥⢀⠀⠄⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⡿⣏⣿⡇⠀⠀⣀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢬⣿⣿⣝⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⢰⣿⣿⠀⠻⣾⣿⣦⡀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠋⠈⢿⣝⡻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⣟⢇⠀⠀⠉⠉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⠿⠟⢻⣮⡓⠦⡤⣶⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣴⡿⠟⠿⣶⡀⠙⠻⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣾⣿⠃⣴⢿⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠹⠦⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⢠⣾⡿⠙⣷⠀⣀⣤⣤⡴⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⣴⣿⠟⠀⢀⣿⣿⣿⠟⠁⢀⣤⣾⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣝⡲⠶⢶⣶⣶⠿⠟⠋⠀⢀⣠⣾⡿⠋⠀⣠⣾⣿⠟⠁⣠⣶⣿⣿⡿⠛⠁⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠳⣝⡶⣤⣤⣤⣤⣤⣴⣶⡿⠟⠋⣠⣴⣿⠿⠋⢁⣴⣾⣿⣿⠟⠋⠀⢀⣴⠶⠶⢤⡈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣛⠶⣯⣭⣍⣉⣩⣥⣤⡶⠿⠛⠉⢁⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⣾⡇⢰⣆⣼⡇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣍⣉⣉⣁⣀⣤⣤⣶⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣉⣉⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠓⣤⠤⠤⠤⠤⠶⢍⡀⠀⠀⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠃⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠓⢄⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⡤⠃⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢚⠦⣀⢀⠓⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠀⠀⠁⠀⢱⠀⠑⠂⠔⠂⠤⠤⠤⠴⢂⠀⡖⠊⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣂⣀⡀⢀⡤⠐⠒⢷⡦
⠀⠀⠀⠀⠀⠀⠘⠴⡀⢠⢧⡄⢆⠰⠤⣀⠀⡷⠶⡏⠁⢠⠀⣹⠹⣄⠀⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠳⡳⠈⠉⠀⠀⠘⠦⠤⠔⠣⢀⠌⠁⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠂⠽⣝⠉⣝⢉⡎⡃⠀⢤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠛⢆⠈⣷⡱⣤⠜⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⢄⠀⠀⠀⠀⠉⠀⠀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⡦⠤⣀⠀⠀⣀⣰⠖⠉⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠤⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⡑
⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠜⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⢸⠀⠀⣀⣀⠤⠄⠃⠀⠰⡤⠤⡴
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⡩⢷⠈⠉⠉⣹⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠀⠀⢀⠔⠊⢆⡀⠑⠒⢶⡁⠉⣉⠽⣄⠀⠀⠀⢀⠄⠀⢇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠡⠀⠈⠀⠀⠀⢋⠉⠉⣷⠀⠙⠤⠤⠋⠳⡀⠐⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠑⠊⠁⢇⠀⠀⠀⠀⡰⠁⠃⠀⠀⠀⠀⢀⠇⠐
⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠤⠊⠀⠑⢄⡀⠀⠀⠀⡠⠊⠒⠒⠒⠉⠀⠀⠈⠢⠄⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢦⠀⢸⡉⡿⠀⣠⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⠀⠀⠙⠀⠀⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠃⠀⠀⠀⠈⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡴⠦⣄⣀⣀⡤⠖⠒⠒⠲⢤⣄⣀⣀⣀⡤⠖⠚⠳⣄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣙⠲⢤⣀⣀⠀⠀⠀⣀⣀⣤⠴⢚⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠬⣭⣭⣭⡭⠤⠴⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⠀⡀⠀⠒⠒⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠉⠁⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⣄⡀⠘⠛⠒⠢⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠸⠧⠀⠀⠛⠁⠅⠀⠀⠀⠀⠀⠀⠐⡞⠯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠂⠃⠈⠀⠀⡀⠈⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⡀⠒⠚⠀⠀⠀⠀⠀⠀⡑⠀⠈⢁⣒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢍⠉⣀⣀⣤
⠀⠀⠀⠀⠠⠀⠀⠀⣀⠄⠀⠂⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⢰⡏⡐⠀⢀⡁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠹⣭⠤⢤⣤⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠹⢦⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠘⣇⢀
⠀⠀⠀⡠⡿⢀⠋⠘⠓⠒⠛⠛⠛⠚⢛⠳⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠀⠀⠀⠀⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠈⠉⠉⠉⢾
⠀⠀⠀⠃⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢
⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠀⠐⠀⠀⠀⠀⠚⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠸⠇⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⣧⣀
⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀⢸⣶⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⠗⠀⠀⠉⠉⠀⠀⠀⠀⠑⠄⣀
⠀⠀⠀⠀⢀⠻⡶⠄⠀⠀⠙⡿⠉⠀⠀⣀⣀⣉⣣⡀⠀⠀⠀⠀⠀⢀⠎⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⠖⢲⡶⣲⣦⣄⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠡⠌⠡⠈⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠘⢠⣦⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⢀⠿⠀⠀⠀⠀⠀⠈⠫⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣄⢀⡀⠀⠀⠀⠀⠀⠀⡎⠨⡆⠀⢀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⢙⡋⠉⠙⣯⠀⠀⠀⠀⠀⠀⠀⠓⠰⡛⣀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠇⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⢀⠔⢺⣼⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣀⠀⠒⠘⠀⢄⡀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠐⠿⠶⠶⠶⠶⠶⠶⠿⠖⠀⠀⠀⠀⠈⠀⠐⠂⢤⣄⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠉⣭⠙⠒⠒⠒⠒⢉⠙⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⠉⠉⠙⢢⣄⣀⣤⠬⣁⣀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢃⡼⠁⡏⠀⠀⡀⠈⢻⢶⣧⠀⠀⢀⣠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠋⠩⡀⠀⣸⣤⣀⣉⡰⠃⠸⣄⡤⠖⣉⡽⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠑⠦⣝⡋⠀⠀⠀⠀⠀⠀⢀⣀⣤⢚⡡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⣞⠣⣄⠀⠀⠀⠀⢀⡎⠉⣿⣒⢒⣺⠋⡹⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡆⠗⠀⠏⠑⠠⡔⠉⡇⢀⠂⠀⢀⠃⣞⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠳⠞⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⡘⢠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠒⠤⢀⡀⢴⢰⠃⠀⠀⠀⡇⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡠⠴⠋⠀⠀⠀⠀⡆⡃⠀⠀⠀⠀⢠⠔⠋⠂⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡕⠀⠀⠀⣀⠴⠥⡀⠀⠀⠀⡠⠃⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡶⢄⣈⡷⠀⠀⠈⣢⠤⠒⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⠀⠈⢳⠧⠶⢊⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣰⠃⠀⠀⠀⣴⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⡟⠀⢦⣀⣀⠀⠀⠀⣀⣀⠠⠜⢄⠀⠐⡠⠀⠀⠀⢢⠉⠉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⢧⣀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠈⠉⠒⠒⢲⠁⠀⠀⠀⠠⠀⢀⠀⠀⡇⠀⠀⢸⠀⠈⡇⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡞⠒⠦⢄⣀⠀⠀⠀⠀⠀⢱⠀⡠⠊⠀⠀⠑⢄⠀⠀⠌⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⠀⢀⠂⠀⠐⠒⠩⡉⠉⠉⠉⢣⡀⠀⠀⠀⠈⠉⠉⠙⣳⠃⠰⡀⠀⠀⠀⠀⠀⡆⢠⠂⠀⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠸⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠊⠉⠁⠀⠈⢆⠀⠀⠀⠀⡰⢁⠆⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⢨⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡠⠶⠒⠛⠉⠉⠉⠉⠛⠒⠶⢤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠋
⠀⠀⠀⠀⣰⠋⡠⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠟⠀⢴⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠆
⠀⠀⠀⣰⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡄⠀⠔⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣠⠉⢠⡀⠀⠀⠠⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⢂⡀⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⢠⡀⡀⠀⠀⡰⡛⠁⠀⠀⠀⠀⠀⠀⢘⡄⣀⣡
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢆⠀⢁⠜⡝⠁⠀⠀⠀⠀⠀⢀⠤⠚⠛⠛⠋⠀⠀⠀⠀⡀⠀⠀⠱
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⢠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠐⠀⠀⠂⠁⠀⠀⠀⡀⠠⠀⠀⠒⠂⠀⠀⠀⡔
⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⡇⡞⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢀⣤⣴⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⣜⠣⢄⡀⣼⣸⠁⠀⠁⣀⡖⠋⠁⠀⠀⠀⡴⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠤⠂⠈⠁⠀⠁
⠀⠀⠀⠀⠀⣍⠳⠄⢀⠀⠈⠉⠉⠉⢑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⡡⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸
⠀⠀⠀⠀⠈⠆⠉⠒⠢⠄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⡄⢪⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠑⠢⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢢⣄⣀⣀⣀⠀⢀⠔⠒⠀⠀⠀⠀⠀⢐⣉⣶⠆⠀⣀⢬⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⣠⠴⠛⠉⢀⡤⣚⡭⠟⠀⠀⠀⣰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⡠⢚⡥⠋⠁⠀⠀⠀⠀⠐⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢢⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠛⣓⡶⠀⠀⠈⠑⣣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠐⢁⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣸⠞⠁⠀⠀⢀⠔⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡰⠂⠀⠰⠤⠀⠀⠠⠂⠀⠀⠀⣠⠛⡀
⠀⠀⠀⠀⠚⠢⠀⠈⠁⠀⢀⡴⠊⠁⠀⠀⡠⠚⢁⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⣤⡄⠀⠀⢯⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠲⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡴⠋⠀⠀⠀⣀⠬⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡠⠔⠊⠁⢰⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣀⠀⠀⡀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⢀⠞⠁⡠⠔⠉⠀⢀⡴⠒⠁⠀⠀⠀⠀⠀⠀⢰⠀⠈⠂⠐⠋⢹⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⣰⣫⠖⠉⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⣀⣀⠀⢨⠀⠀⠠⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢀⡾⠋⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠉⡄⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢲⡀⠀⠂⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠴⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⢀⠀⣀⡤⠶⠖⠛⠛⠉⠉⠉⡁⠒⠀⠄⡀⠀⠀⠄⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣀⠴⣯⢀⠀⠀⠀⠀⠀⠈⠐⠠⣀⠈⠑⠠⣀⠉⠒⢄⣀⣀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠠⠁⠀⠠⠊⢁⠈⠁⠀⠈⢦⡈⠐⠂⠄⠀⠀⠀⠀⠀⠙⠂⠄⡀⠁⠂⠤⢈⠐⠈⡂⠀⠀⠂
⠀⠀⠀⠀⠀⡄⠀⠀⡄⢠⠂⠀⢀⠄⠀⢀⡽⢦⣀⠀⠀⠉⠐⠠⠄⣀⠀⢀⠀⠉⠐⣂⣠⠼⠛⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡷⠁⠀⠠⠊⠀⠠⠈⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀⠀⠀⠐⠘⠛⣉⠴⠶⣭⣾
⠀⠀⠀⠀⠀⠁⠐⠢⡤⢄⠅⠠⠐⠋⠀⠀⠀⠀⢴⠋⡉⣒⡉⠉⠗⠚⠛⠓⠊⠉⠁⠠⠀⠠⠄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀
⠀⠀⠀⠀⡀⠀⠀⡜⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠈⡄
⢀⠀⠠⠘⠀⠀⠔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⠄⠀⠘⠄⣀
⠣⢀⣀⡀⠤⠊⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠈⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠠⡁⣰⠂⠀⠤⣄⠺⠆⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠠⡱⠁⠈⠂⠄⣀⠀⠈⠙⠪⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢡⠛⠃⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⣞⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⢂⢅⢀⠐⢢⠀⢰⡈⠵⣶⠒⢄⠀⡰⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⡞⠉⠀⠀⠀⠀⡄⠱⠞⠹⠀⠀⠈⠳⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⠀⠀⠀⠀⣉⣉⢏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⣀⣀⣀⠡⣀⡀⠀⠀⢤⠄⠏⣥⠀⠀⠀⣀⣜⡀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢍⡀⠀⠀⠀⠉⠐⠒⠀⠀⠒⢒⠾⠯⡍⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡈⠑⠒⠤⣀⠀⠀⠀⠀⢀⠪⠁⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣤⡀⡿⠀⢔⠒⣽⠲⣤⣀⣲⠅⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢹⡇⠀⠀⠀⢸⠀⡆⠀⡁⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣸⠇⠀⠀⠀⢸⠀⡇⠀⡇⠀⠀⠀⠀⠀⢀⡆⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣶⣾⡽⠄⡀⠈⡀⠏⠀⡇⠀⡟⠀⠀⠀⣀⣀⣤⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠄⠠⠤⠴⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠡⠤⠤⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣇⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣽⣳⣒⣛⣯⠁⡏⢨⣭⣷⠶⠾⢽⡋⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡄⠀⠀⠀⣄⡘⠯⣂⠄⠀⣀⠀⢀⡰⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄⠠⠀⠀⠀⠀⡠⠐⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⣀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠊⠀⠀⠀⠒⠲⣄⠀⠀⠀⠀⠀⠀⡀⠀⠓⠠⠀⠨⠄⠂
⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠀⡠⠒⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⡀⠤⠀⠀⠈⠐⠀⠀⠈⠉⠉⠀⣀⡀
⠀⠀⠀⠀⠂⠀⠁⠉⠉⠀⡀⠠⠔⣈⡀⠀⡀⠀⠠⠄⢂⢠⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠨⡠⠤⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⢾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠨⠤⢄⣤⣬⣥⣤⠄⠀⠀⠀⠀⢀⡀⠀⠀⠠⢔⣽⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠄⣀⠀⠉⠐⠒⠀⠄⠠⠤⠀⠀⠀⠀⠤⠄⠐⠷⢤⣤⣀⣀⣀⣀⣐⣐⣨⡧⢀⠠⣊⠔⠒⠉⠉⠉⠙⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⠒⠠⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⠀⡀⠀⡴⠃⢀⠠⠀⠀⠄⠠⢌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⢧⡔⡥⠚⠉⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⠀⠀⠀⠀⠠⠀⠐⡀⠔⡯⠥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣟⠒⠤⠤⣤⠭⢤⣴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⡀⠉⠉⠙⠛⠛⠛⠛⠛⢑⣂⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠶⠖⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠄⠠⠈⠠⠀⠀⠠⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣫⠄⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⢛⡀⠀⠀⠀⢀⠀⣑⠠⠵⠕⠃⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠁⠁⠀⠀⠀⠀⠘⠘⢀⡀⠈⠁⠀⡄⠀⠈⠈⠀⠀⢸⠀⠀⠀⢠⢫
⠀⠀⠀⠀⠀⠀⠀⣰⣻⠀⡀⠀⡀⠀⠂⠀⠀⠀⠀⠈⠿⠢⠀⠀⡀⠀⠀⠀⣀⢼⣆⠉⠁⢸⡑
⠀⠀⠀⠀⠀⠀⣰⠿⢹⠉⣃⡁⠅⢀⡀⠈⠠⢠⣤⠄⠈⠈⠀⡴⠇⠀⠰⠊⠀⢸⠀⠀⢒⡞
⠀⠀⠀⠀⠀⣰⡝⠃⠀⠀⠀⠁⠀⠀⠉⢣⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡴⠿⣶⣷⣴⣤⣤⡄⡆
⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠂⣖⠀⠐⠞⠁⠆⠀⠀⠀⠰⠀⠈⠃⠣⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠈⠁⠉⠀⠀⠘⠁⠉⠉⠉⢻⠆
⠀⠀⠠⠤⠜⠗⢠⣄⢠⣐⣛⠻⠅⠀⠀⢠⠀⠀⠀⠀⠠⠷⠆
⠀⠀⠀⠀⠈⠉⠛⠙⠻⠉⣹⣿⣯⢭⣿⠩⢥⡦⠄⢦⠽⠿⠶⠶⠮⠷⠖⠒⠺⠥⠟⠿⠷⠮⠥⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠺⡶⠿⠿⡷⠀⢠⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⠄⠤⣀⡤⠔⠢⡀⠀⠀⠘⡷⠤⠒⠉⠀⡀
⠀⠀⠀⠈⠁⡀⠀⡿⠀⠀⡇⢀⡀⠀⠀⠀⢀⡎⠉⠑⡍⠀⠀⠀⢀⣧⢠⡼⠵⢤⣀⣱⠀⠄⠊⠀⠀⢘⠉⢵⠈
⠀⠀⠀⠀⠀⠁⡰⠥⠀⠀⢣⠀⠁⡠⢤⣴⠟⠻⠀⢀⣼⠀⠀⠐⣅⠈⢲⡀⠀⣤⠑⣾⠉⠛⢆⠀⢠⢬⠉⢁⣤⡀
⠀⠀⠀⠀⠀⢠⠃⣠⣀⣠⣌⣆⠀⠣⡴⡅⠀⠀⠙⡿⠿⠀⠀⠀⢈⡉⢶⠬⠦⣄⣠⡏⣦⠤⠚⠀⡈⢊⡴⣋⠜⠁
⠀⠀⠀⠘⢁⣿⣿⣿⣿⣿⣿⣿⣆⠀⣷⠹⡄⠀⣐⣒⣒⡄⠀⠀⢀⣸⠈⢆⣀⡤⠛⠒⠊⠀⠀⠀⡤⣋⠜⢁⣀⡀
⠀⠀⠀⠀⢎⢻⣿⣿⣿⣿⣿⡿⢈⠀⢸⠖⠚⠚⠒⠒⠒⠚⣆⠀⠀⠙⠀⠀⠀⠀⣠⣴⠶⢒⡚⠿⣿⠁⠀⠀⢸⣏
⠀⠀⠀⠀⣈⠑⠒⠂⡒⠒⠒⠈⠁⠉⠘⠒⠦⠤⠤⠦⠆⠒⠃⠀⠀⣤⡆⠀⠀⡾⢋⠖⡒⠒⡌⢢⠙⡄⠀⠀⢸⣍⠁
⠀⠀⠀⠈⠚⠁⠀⠀⠻⠯⠀⠀⠀⠀⠀⠄⠀⠀⠀⠔⠒⠄⠴⠀⠀⠈⠁⠀⠀⡇⠸⣀⡛⠘⡜⡸⠀⡇⠀⡆⢸⠮
⠀⠀⠀⠀⢴⢀⡶⠚⢲⡀⠀⠓⠺⠰⠀⠀⠀⠀⠀⠊⠒⠤⠴⠂⠀⢠⣤⠀⣄⠹⣤⠈⢉⠉⠐⣡⠞⠀⠀⠧⠿⠁
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠀⠀⢠⠴⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⣠⠞⠛⠳⡄⠀⢰⡆⠉⠂⣴⠶⠶⠄⠈⢀⡀⠀⢀⡄⠀⣠⠤⢤⡒⠀⢸⣂⣀⣀
⠀⠀⠀⠀⠐⣆⠀⠀⢀⡇⢰⡇⠀⠀⠀⠉⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⣾⢧⠀⢸⡇⢰⡇⠀⠈⠁⠀⢸⠉
⠀⠀⠀⠀⠀⡌⠛⠒⠋⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣟⠛⠛⠂⠀⡟⠈⣇⢹⠃⢺⢁⠀⠀⢀⡀⠸⠶⠖⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢧⣀⣀⣠⠄⠀⣸⡇⠈⠁⣿⣤⣤⡄⠸⠃⠀⠘⠟⠀⠈⠦⠤⠖⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⡉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⢒⣤⣤⡄⢀⡴⣊⠥⢄⠉⢆⠲
⠀⠀⠀⠀⢠⣄⠈⠉⠀⠀⠠⡆⠀⠀⠘⠀⠈⢫⡂⢠⠛⠒⠠⢼⡀⠛⠑⠙⠀⠀⣀⠁⡀⡄⢠⣾⡔⠁⠀⢀⠃⣼⢠⣤
⠀⠀⠀⠀⠀⠁⢰⠭⡆⢰⠯⡆⠀⡟⡇⠀⠀⠀⡸⠡⠀⠀⠠⠀⠈⠟⢠⣄⣤⠀⠳⣄⢀⡗⠋⠀⠀⠀⢴⣧⡴⠃⢸⠏
⠀⠀⠀⠀⢶⣾⣯⡿⡽⠽⠯⡿⠿⠿⣿⠟⠀⠘⢇⠀⠀⠀⠀⠀⠀⡆⠈⠻⠃⠀⢂⡬⠛⠬⡀⠀⠀⠀⠔⠈⠀⢻⣮⡄
⠀⠀⠀⠀⢸⣿⠀⣶⡇⠀⣿⡇⢠⣿⣿⠀⠀⢀⡠⠣⡀⠀⠐⣂⣀⡇⠀⠀⠀⡰⠉⠀⠀⠀⠉⢦⠀⠀⠀⠀⣦⣠⠟⠁
⠀⠀⠀⠀⢸⣿⠀⣿⡇⠘⠿⠇⠀⠿⣿⡆⠀⡉⣀⢀⠙⠉⠀⠀⠀⠀⠐⠀⠙⠁⠀⠀⠀⠀⠀⠸⠟⠄⠀⠀⠸⠛⠋
⠀⠀⠀⠰⠿⠿⠿⠯⠿⠿⠯⠿⠽⠽⠽⠿⠃⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠰⠀⠀⢠⠄⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢰⣿⣷⡄⠀⠀⠀⠡⠀⠀⠂⡀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠀⠀⠀⠀⠀⠜⠛⠋⠀⠀⠈⠐⠐⠀⠁⠟⠀⠐⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣛⢢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⡖⡟⢦⠀⠀⠀⠀⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠨⡈⠀⢀⠀⠐⣀⢀
⠀⠀⠀⠀⠀⠀⢀⡠⢂⣤⣤⡐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡈⢳⡀⠀⠀⠸⣿⣿⠇⢠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠃
⠀⠀⠀⠀⠀⠀⣈⢠⡸⣿⣿⠟⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡇⠀⢧⠀⠙⣄⠀⠀⠈⠁⢀⠎⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠙⠀⢅⠀⠅⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⢚⣏⣻⠾⢧⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀
⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠋⠉⢹⡄⠀⠀⠹⣄⠼⣶⣦⣄⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠫
⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⢈⠀⢀⠁⠠⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠃⠀⠀⠀⠈⠂⠀⠀⠉⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⡃⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠻⢶⣤⡀⠀⠀⢀⣀⠙⠀⠀⠀⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⢀⣤⣤⣄⠀⠀⢀⣠⣄⠀⣠⣤⡄⣀⣀⣀⠀⣀⡀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠙⠃⠀⠀⣨⠈⠀⠀⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⡙⠛⠃⣴⡟⠙⠋⠀⢹⣿⠁⣿⣋⣉⢸⣿⣿⣿⡇⣴⡟⠛⠃⢰⣿⠿⠷⠀⠀⠀⠀⠀⠀⠔⠀⡆⠘⠄
⠀⠀⢀⠀⠀⠴⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢈⡙⠻⣷⡄⣿⣇⡀⢀⡀⢸⣿⠀⣿⣋⣉⢸⣿⢿⣿⡇⣿⣇⡀⠀⢸⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠐⠂⠀⢠⠂⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠟⠁⠈⠻⠿⠟⠋⠻⠿⠃⠛⠛⠛⠈⠛⠀⠛⠃⠈⠛⠟⠃⠺⠿⢿⠆⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⢀
⠀⠰⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⡀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠃⠼⡀
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⢁⠁⠠⡀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢂⢰⢬⠀⠂⠐⢄⠀⠀⠀⠂⠀⠄⢄⢠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⢠⣇⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢇⠀⠀⣀⡀⢄⠄⠘⢀⠀⠀⠑⠐⠒⠒⠈⠄⢢⣤⡦⢰⠀⠰⡀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠀⠀⠀⠀⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠐⡁⢀⣰⠈⠡⠀⠀⠀⠀⠘⠩⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠔⠈⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣰⡖⠆⠀⢀⡀⢄⢠⠂⠑⠢⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⡤⠊⠀⠀⢨⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠀⢀⡄⠀⠐⠇⠈⠂⠁⠀⢀⠀⡀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠁⢀⡈⠁⠀⠀⠀⠀⠀⠳⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⣀⣀⠀⠀⠀⢀⠀⠐⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⡀⠀⣠⣤⣤⣄⡀⠙⠏⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⢀⣸⣧⡀⠙⠛⠛⠛⠁⠈⠋⠀⣀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠈⢻⡟⠉⠀⠀⠀⠰⠶⠀⠀⠀⠙⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠇⠀⠃⠀⠈⠁⢀⣤⣶⣷⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⡀⠀⠀⠉⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⡀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠁⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠉⠁⠉⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣤⠀⠈⠋⠀⢰⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠰⣿⣿⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡀⣀⣤⣤⣄⣤⠤⠀⠀⠀⣀⠄⠘⠛⠉⠹⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠈⠛⠟⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠬⠀⠀⠀⣀⡀
⠀⠀⢠⣄⣾⣦⡀⣠⠤⡹⠻⣆
⠀⢀⣠⣼⣿⢿⠄⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠖⠓⠘⠛⣿⢰⡄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣧⣿⣞⣋⠉⠈⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠾⢻⡙⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⡃⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸
⠁⠀⠸⢳⣿⢳⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢙⢹⣧⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠒⢰⣾⣖
⠀⣀⣴⣶⣿⠻⠇⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠯⠅⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢈⣽⡟⠙⠢
⠛⠁⢘⠹⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠰⢸⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⠉⠨⣿⣿⣤⡀
⠀⠀⡝⢂⣿⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⣾⣟⠇⠀⠙⠆⠀⠀⡠⠖⡀⣠⣤⠀⠀⠀⠀⢀⣤⢤⣾⡶⠀⠈
⠀⠀⡄⠘⣿⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⢹⡏⠃⠀⠀⠀⠀⠀⠀⣀⡀⣹⡿⠲⢄⡀⠀⠁⠀⢘⣽⡿⠖⡤
⠀⠰⠈⢤⣿⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡇⠃⠀⠀⠀⠀⠀⠘⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⢀⢸⡇⠂
⠀⠐⠀⢸⣿⡂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡇⠤⠀⠀⠀⠀⠀⠀⡠⠀⢺⡏⠀⠈⠀⠀⠀⠀⡀⢼⡇
⠀⠁⠈⣺⢿⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⡇⢈⡀⠀⠀⠀⠀⠀⠀⠀⢾⡟⡉⠂⠀⠀⠀⠀⠁⣸⡇⠰
⢸⣳⣄⢼⣾⡧⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⣭⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠠⠁⣼⡇⢀⡄
⣻⣀⣈⣻⣻⣃⣉⣹⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣏⣈⣿⣗⣉⣵⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣸⣉⣻⣟⣉⣇
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤⡀⠋⠶⠴⠴⣄⡄⠀⠀⠧⢀⠀⡀⠑⢖⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠒⠂⢠⢀⣤⠀⠀⣰⠀⠘⣧⡄⠐⠛⠁⠛⠄⠀⣅⠂⠬⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠠⡔⡖⢻⢀⠠⠒⣄⢼⠝⠏⠋⠀⠀⠶⠋⠑⠒⠚⠷⠂⢀⣀⠀⠂⠰⣌⣆⠀⡀⠈⢹⣄⡄
⠀⠀⠀⠀⠀⠀⢠⠹⣦⣼⣧⣶⡿⠟⠉⠀⢓⡳⠂⠡⣄⠀⠀⠀⠀⠘⣧⠀⠀⢉⡧⢀⠀⢹⡦⣀⠀⠈⢿⡇⠀⡀
⠀⠀⠀⡀⢸⠀⠎⢀⣸⣿⢳⣏⣤⠤⠚⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⢇⣆⣷⢀⠁⠘⡧⢸⣦⡀⠎⢷⡴⢻⡆
⠀⠀⠀⣧⠀⡆⠀⡸⢋⡿⣾⣉⣆⢠⢠⡠⣴⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢿⠳⠷⣧⡄⣣⡑⡄⢼⣷⣾⠁
⠀⠀⢀⠸⡔⡉⢶⡟⣹⣱⡟⠓⠁⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⠂⠳⣄⣏⠘⠻⢷⣿⣀⣿⡃⣨
⠀⢳⠈⡦⢻⣦⡟⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⢸⣿⡝⣿⡷⡴⠂
⠀⠈⢷⡄⠈⢿⣾⢃⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠳⣿⡇⢻⣇⢽⠄
⣄⠀⣸⢿⣆⣼⣟⣱⣿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⢻⡷⣼⣿⣷
⠘⣧⡽⣎⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⣸⣿⣼⣿⠏
⠀⠘⣧⣿⢸⣿⣿⢀⣄⠀⢠⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⡏
⠀⢀⢹⣾⢾⣿⣿⣨⠋⠡⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣀⠀⡓⢾⣿⣿⢳
⠐⢾⡤⣿⣤⣿⣿⡄⠀⢸⣿⣫⡀⠀⢠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⡻⡟⣾⣿⣿⢸⠇
⠀⠸⣿⢏⢿⣿⣿⣧⠀⢒⢸⣟⡆⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⡇⢈⣿⣿⡇⢸⠀⠠
⠀⠀⢹⡥⡂⢻⣿⣿⣧⠀⢖⣿⢩⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣿⠥⣼⣿⣿⣇⡏⠀⠏
⠀⠀⠀⠘⢷⡈⣿⣿⣿⣷⡨⣯⣾⣿⢘⣠⣀⡆⠀⠀⠀⠀⠀⠀⠀⢶⣷⣆⡀⠀⠈⢀⣤⡸⣿⣏⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣛⠛⣿⣻⣿⣶⣄⢀⠀⢀⠀⠀⠘⢝⢯⣇⢆⣇⡞⣿⠩⢿⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠻⣿⣷⣾⠼⠿⠿⠿⠯⣄⣠⣤⡄⢠⠴⠓⢉⣩⣍⠙⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠓⠦⠤⣼⣿⣥⠤⠄⣨⡤⠐⠀⠀⢈⠗⣅⠀⣲⣊⣹⣥⣾⣿⣿⣿⣿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡏⠉⢻⣿⣟⣩⣹⣷⣶⣊⣠⠶⢻⣯⠟⠉⠀⠀⢤⣤⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠿⠏⠀⠊⠁⠐⢤⠞⠂⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠉⠉⠉⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⠄⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢰⡁⠀⠀⠀⠤⠠⠤⠐⠈⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠠⠸⠅⣀⠀⠀⠀⠀⠀⡀⣀⠀⠠⠤⠌⠂⣰⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠈⠠⣆⠀⣤⡄⠀⢀⡀⠀⣠⣄⠀⢀⠔⠈⠁⠀⠗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠌⠀⠩⠡⢀⠋⠈⠂⠈⠁⠐⠁⠀⠀⠒⠈⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇⠀⠀⠀⠀⠑⢄⠀⠀⠀⠂⠀⠀⠀⠀⢀⠜⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠀⠀⠃⠀⠀⠑⠠⣀⠀⠀⣀⠠⠔⢡⠁⠈⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠄⠠⠀⠠⠀⠠⠀⠀⠀⠃⠀⠀⠀⠐⡀⠀⠀⠀⠐⠠⠀⢐⠀⠀⡠⠃⠇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⢁⠀⠀⠀⠀⡑⢄⠸⠀⠎⠀⠰⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⢰⠒⠲⠲⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⢂⠀⠀⠀⠡⠀⠑⡇⠀⠀⡄⠀⠀⠀⠠⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡱⠶⡈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⢂⠀⢀⠀⡐⠀⠀⠀⢀⣆⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣰⢰⠀⠀⠀⢀⡀⡇⠀⠇⣀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⢡⠀⢲⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠉⠏⢸⠀⠠⠤⠰⠀⠀⠀⠀⠈⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⣀⢀⠀⠠⠀⠈⠢⡀
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠒⠒⠒⡀⠱⡀⠀⠈⢂
⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠒⠂⠐⠀⠁⠀⠀⠀⠑⢄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘

⠀⠈⠉⠉⠛⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠓⠢⢀⠀⠀⠀⠀⡄⠀⠀⣀⡀⠀⠀⠀⡔⠀⠀⠀⠠⠐⠛⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠐⢦⣾⣿⣿⣿⣿⣦⡤⠂⣠⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣾⣾⣿⣿⣿⣿⣿⣿⣿⡛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢿⣯⣿⡿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⣿⣿⣿⣿⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢰⡖⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡶⠋⠀⢀⢸⠀⡠⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⡴⠿⠛⠛⢛⠛⠛⠋⠈⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⠖⠉⢰⡴⠚⠁⠀⠀⠀⠘⠾⠊⠀⡠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠐⡀⣰⠁⠀⠀⡠⡀
⠀⠀⠀⠀⡀⠄⢠⣤⠔⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠳⠿⠥⠀⠀⠶⠃⠸⠀⠀⠈⠣⣀⠀⠀⢀⣨⠔⠁⠀⠀⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⠋⠀⠀⠀⠀⠶⠂⠀⢠⠏⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⡤⡸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠿⠀⠀⠀⠀⠸⢦⣾⣥⢤⣄⠀⠀⢆⠠⢴⢀⢀⠎⠀⠉⠒⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠙⣿⡤⣤
⠀⠀⠀⠀⠀⠀⠋⠀⢰⣖⡒⢤⡀⠀⣄⢠⠀⠀⠀⣾⢁⣀⣠⣟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠟⠢⠀⣠⠀⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⢹⠗⠋⡀⠐⠂⠂⠀⠀⠉⠛⢡⠏⢀⣽⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⢀⠤⠐⠋⠁⢀⠏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⡿⠋⠉⢳⡄⠀⠀⠈⠢⡐⠀⠀⠠⢀⡸⠀⠀⠀⠀⢀⠀⣹⠧⢒⠆
⠀⠀⠀⢰⣿⣶⣤⣄⡀⠘⢄⠀⠀⡆⢀⠀⠀⢠⡄⠀⠀⠀⠸⣅⠀⠀⠚⠀⠀⠀⠀⠀⠘⡀⠒⠊⠉⠀⠀⠀⠀⠀⢺⡷⠛⠊⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡼⠀⠀⡏⠙⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡞⠙⡆⠀⠼⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢄⣀⠀⢠⣤⡌⢀⡄⠀⠀⠀⠸⡿⠀⠀⠀⢀⣼⠙⡣
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠖⠛⠃⡀⣀⠀⠀⠀⣞⣽⣿⣿⣿⢶⠚⠁⠘⠀⠉⠀⠁⠀⠀⠀⠀⢿⠀⢀⣴⠟⠊⢹⡅
⠀⠀⠀⠀⠄⠸⣔⡽⠀⠀⠠⢀⣘⣧⣤⠤⠴⠞⠁⠀⠀⠀⠀⢹⢹⠁⣀⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠭⡟⠁⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢳⣏⠉⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠉⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⠹⣧⠀⠀⠂⢉⣻⣦⣤⡼⠀⠀⣀⡀⠀⠀⠀⠀⢃⢿⣿⠀⣿⠀⠀⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠸⣍⣀⠈⡧⠀⠀⠘⠉⠀⠃⠀⠀⠄⠸⡸⣿⡇⢻⡇⠘⠋⠉⠻⡁⢘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠧⡡⠃
⠀⠀⠀⠀⣀⡀⠀⠀⢈⡴⠒⠛⠻⣏⠃⠀⠀⠀⣀⡠⢠⡀⠀⠠⠀⡇⢿⣿⣘⣿⠀⠀⠀⠀⢸⢎⠀⠀⠀⠀⠑⠁⠈
⠀⠀⠀⠀⠛⠁⠀⠀⠾⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢼⣟⡩⠋⠀⠀⠀⠰⠃⠀⠳⣄⠀⠀⣠⣐⣒⣒⢒⡄
⠀⠀⠀⠀⢞⣹⠀⢴⡦⠀⠀⠐⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⠆⠀⢀⡠⠖⠉⠀⠀⠈⡟⠛⠛⡟
⠀⠀⠀⠀⠀⣀⣶⠶⠦⢤⣤⡤⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⠙⠈⠂⠾⠃⠀⠀⢰⣹⠆⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣀⣤⣤⣤⣤⣖⠚⠉⠉⠉⠉⠉⣷⠴⠶⠶⠶⠶⠚⠃⢀⠀⠀⢠⢊⣁⣀⣨⣌⣲
⠀⠀⠀⠀⡀⠸⣄⣀⣀⣠⠇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠸⢿⣿⣿⣿⣿⠟⠰⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠘⠒⠒⠒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣍⣡⡍⠒⠒⠒⢈⡙⠒⠒⠚⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡉⢱⢤⡴⠂⠥⢤⣀⡸⠀⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡤⠤⠊⠈⣆⠀⠠⢀⠏⡛⠀⣠⠴⣇⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠓⢄⡳⠖⠉⠙⠚⠉⠀⠈⣋⡤⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡳⢄⠀⠀⠀⠀⡌⠑⢖⣒⣶⠂⡛⠩⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⢘⢀⠋⠐⠴⠈⡁⠸⠀⠀⠆⠎⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠈⢫⡀⠀⠀⠀⢇⡀⠀⠀⡌⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢀⡜⠀⠁⠀⠈⠘⠀⠀⠀⠁⡠⠆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠀⠀⠀⡠⢎⠀⠀⠀⢀⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡒⠀⣸⠆⠀⢈⠦⠔⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠓⠚⠥⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⢸⠀⠈⠁⠐⠒⠂⢰⠁⠀⠈⠀⢀⠁⠀⠀⢈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠁⠒⠀⡎⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠈⠢⣀⣀⣀⣠⠉⠒⠠⠤⢀⣀⡀⠀⡁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠈⠀⠢⠀⠀⠀⠣⣀⣀⣀⣀⣀⠤⠜⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠄⠐⢀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣿⣟⣻⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⠠⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠒⠒⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠖⢲⠎⠀⠀⠀⢹⡤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢒⠒⠒⠒⣶⡒⠒⠒⠒⠒⠒⠒⠒⠺⣄⠀⠀⢀⡼⠓⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠰⡻⠆⢤⣄⠿⠛⣄⠀⠀⠀⠀⠀⠀⠀⠈⣷⠚⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠐⠂⠀⠀⡔⠂⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡈⠄⠠⡀⠐⣂⡖⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠪⠴⠁⠈⣦⠟⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣤⣀⣀⣀⣀⣀⣠⣔⣁⣀⡀⠀⠀⠀⠀⢀⡽⠒⠿⡀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠞⠭⠭⠭⠭⠁⠸⣀⠀⣀⠛⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡈⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣄⣀⣠⠄⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠨⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠆

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⠉⡆⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠵⡒⠁⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢦⣀⡼⠀⠀⠸⡯⠀⠁⠀⠀⢀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠓⠀⠀⠠⠄⠀⠈⠛⢇⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣼⠁⠀⠁⠀⠀⢸⠀⠀⠘⡏⡇⠀⢀⣤⡈⠀⠑⠀⠀⠀⡀⠀⠀⠀⢱⠀⣸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠘⠻⢤⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⢀⠊⠈⠁⠀⠀⠃⠀⠀⠙⠿⠿⠿⠋⠀⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡖⠀⠀⡀⠀⠹⡆⠀⠀⡇⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢣⠀⠀⠅⠀⣠⠇⠀⠀⡇⠀⠀⠀⠀⠀⣸⠘⣦⠀⠀⠀⠀⡄⠀⠈⢩⠉⠉⡇⠀⠀⢠⡮⡀⠀⠀⢘
⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠈⠟⠛⠟⠛⠏⠀⠀⠀⡇⠀⠀⠀⠀⠉⢻⠀⠉⠻⠉⠉⠋⠁⠀⠀⢸⠀⣗⡇⠀⡖⠉⠀⠀⢀
⠀⠀⣠⣤⣿⣀⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣶⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣷⣧⣤⣷⣤⣤⣤⣼⣤⣬⣤⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢂⣴⣄⡄⠀⠁⣼⡦⡳⡯⡫⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠃⠀⣙⣯⠙⠛⢊⡄⠰⢦⡢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠷⠀⠁⠄⠘⣴⠈⠸⡀⠁⢁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⠄
⠀⠀⠀⠀⢀⠄⡀⠀⠀⡀⠄⢂⠰⠀⠄⠁⠀⠢⢂⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠮⡏
⠀⠀⠀⠀⢠⡀⠱⡀⠀⠻⠖⠀⠀⠀⢀⠐⢦⡀⠀⠁⠀⠀⠀⡀⠀⠀⠀⢆⠀⠠⣄⢳⢄⠑⠙⠇⢈⠁⠀⣉
⠀⠀⠀⠀⠠⡗⠒⠁⠈⠀⢀⠀⠈⠢⠀⠀⠁⠀⠀⠀⠀⡀⠀⠹⣄⠀⠀⠰⡁⠄⣀⣧⣹⠝⠁⣚⡑⠒⢩⠄
⠀⠀⠀⠀⠀⠐⠋⠡⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠳⠷⠤⠀⠘⣎⢇⣙⠳⣷⠉⠈⠆⠀⠁
⠀⠀⠀⠀⡆⠘⠂⠄⠲⢄⡀⠀⠘⠂⠀⣄⠀⠀⠀⠀⠀⠀⠆⠘⠆⠘⣬⣘⠠⡈⠻⠻⡞⠁⠁⠈⠁⠘⠁
⠀⠀⠀⠀⠁⠀⠀⠈⠂⠤⠀⠀⠀⠀⠀⠈⢳⣦⠄⢀⡀⠀⠈⠀⡀⠰⠄⡡⢆⠀⠀⡄⠙⣈⣀⣁⡉⣬⡨⠼⠛⠁
⠀⠀⡀⠀⠀⠁⠀⠂⠀⡜⢂⠀⠠⠀⡀⠀⠀⠁⠾⠁⠤⠀⠀⠀⠐⠄⢀⣆⠀⠀⠸⢀⡈⠀⠈⠁
⠀⠀⠀⠀⠀⠃⠰⠀⣀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠈⠁⢀⠁⢀⠀⠀⡄⠰⢉⠄⡠⠁⠉⡙⠂⠈⠓⠑⡟⠒⡶⠶⠶⠂
⠀⠀⠀⠀⢀⠐⡀⠀⠉⡀⠈⠀⠠⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠈⠀⢀⡀⠎⢠⡎⠀⠀⠄⠀⠒⠥⠀⠈
⠀⠀⠂⠀⢩⠀⠀⢴⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠂⠔⠀⠀⠀⠀⠄⠈⠰⣥⠎⠀⠀⡂⠀⠀⠁⠀⠀⠀⠀⠂⠐⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠠⠀⠈⠀⠁⢀⠀⠀⠡⠛⠀⠀⠀⠀⠠
⠀⠊⠀⠠⠄⠀⠐⠀⠠⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠤⠖⠋
⠀⠀⠀⠐⠂⠈⡄⡀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠎⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠃⠒⠠⠀⠁⠀⠠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠢
⠀⠐⠀⠀⢀⠘⠀⠆⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠈⠀⢠⠀⠠⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠄⠘⠀⡀⠈
⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⠀⠐
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠠⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢐⠅⡃⠀⠈⠀⠀⠀⢀⣀⠠⠄⠉⠁⠐⠀⠡⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠂⠀⠀⠀⢸⠀⢓⡠⠤⠀⠓⠈⠁⠀⠀⠀⠀⠀⠀⠂⢂⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠦⠀⠀⠀⠠⠠⠄⠀⠐⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⡁⠀⠀⠀⠐⠀⠒⠂⠈⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡄
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠐⡁⠂⠀⢈⡀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⣃⠀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡙⢆⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠁⠀⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠐⢀⠄⠂⠈⠁⠈⠉⠀⠢⢄⠀⠈⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢠⠀⣆⣔⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠎⠁⠀⢈⠆⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠄⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠴⠠⠀⠀⠀⠊⠄⠀⠀⠀⠐⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠂⠀⢸⠀⠠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣽⠟⢻⣏⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢁⢠⢴⠊⠐⢀⣨⠉⠕⡢⢦⢬⡉⠁⠀⢁⠅⢤⣀⠀⢂⢤⣄
⠀⠀⠀⠀⠀⢀⠌⢠⠔⠚⣉⡀⠀⢠⡖⠗⢒⣦⣐⣂⣁⢄⣩⡆⣤⢷⠖⠢⡆⣐⣀⢌⠑⢿⣆
⠀⠀⠀⠀⠀⡈⠀⣎⠀⠞⣁⡅⢀⠏⠘⢠⠋⠀⠀⠀⠀⠀⠀⠀⡉⠉⢹⡇⢡⠀⢈⠽⠂⢈⠈
⠀⠀⠀⠀⠀⠠⡀⠈⠓⠤⠤⣉⣀⢤⣀⡆⡄⠉⠙⠀⠀⠀⠐⢡⡴⠾⢼⡧⣤⣭⢥⣤⣴⣶⣷
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠠⠀⠼⠯⣈⡻⠓⠲⣒⠲⠶⠴⠲⢾⠷⠶⠊⡀⠤⠄⠰⠼⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠐⠉⠠⠾⠅⠠⠀⠀⠢⠸⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠄⠂⠐⢀⠀⢠⠀⠀⡐⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⠈⠀⠌⡂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠀⢁⣀⡔⢐⠨⡀⠐⠒⠑⠀⢸⠀⣀⡄⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠉⠚⠛⠉⠄⠂⠔⠨⢘⠳⡦⠄⡠⠐⠜⠡⢐⠠⠀⠁⠈⠪⠐⠅

⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢫⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⢴⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡔
⠀⠀⠀⠀⠀⢄⠀⠰⣿⢋⠀⢠⣿⣦⡀⠀⠀⠀⠀⠒⠀⠟⠂⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠐⠉⠱⡀⢼⠷
⠀⠀⠀⠀⡀⣸⠇⠀⣭⣿⠂⠙⠛⠁⠀⠀⠀⠀⠀⠉⠠⠍⠱⠀⠀⠤⠀⠐⠊⠀⠈⡽⠋
⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢴⠎⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠙⣶⣶⣄⠀⠐⠀⡠⠐⡍
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⠀⠀⠀⠊
⠀⣤⣴⡌⠀⠀⠀⠀⠠⠋⠀⣀⠤⠆⠀⠀⠀⠀⠀⠀⡠⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂⠒
⠀⣿⣿⣧⣶⣶⡖⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢶⣿⣿⣿⡇⠀⠀⠀⠤⠴⠆⠀⡀
⠀⠈⣿⡿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣿⣿⣿⣿⡇⠀⠀⣀⠤⠔⠁⣸⠇
⠀⠰⣡⣶⣦⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣾⣿⣿⣿⠇⠀⠀⠁⠀⠀⠀⠃
⠸⠃⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⣻⣽⣿⣿⣿⣿⣿⣿⠶⣒⠦
⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢿⣿⣿⣏⣿⡿⠿⠷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢣⣦⣀⢰⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣋⡟⣿⣟⣧⠙⠄⠀⠀⠀⠀⣀⠀⢀⣀⠀⣠⡶⠛⠉⠉
⠀⠀⠀⠀⢛⡏⣼⠁⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⣿⠁⠀⢀⡀⢲⣶⣿⣧⠀⡼⠿⠏⠙⠇⠀⠀⠀⣀
⠀⠀⠀⠀⣨⣷⣟⢻⠟⠛⠁⠀⢀⠆⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠐⠂⣌⣭⢿⠿⢷⣄⡀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⣴⢿⡿⠋⠀⠀⣠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦
⠀⠀⠠⢈⠈⣀⠄⠐⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⣀⡠⠁⠈⠁⠁⠀⣄⡆⢰⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣄
⢀⠟⠀⠀⠀⣀⠁⢤⢅⡯⡿⣿⣿⡿⠀⠀⠀⠀⣠⣾⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣽⡇
⠀⠀⠀⠀⢤⣏⣓⡾⣴⣿⣷⣿⠟⠁⠀⠀⢀⣼⠻⢿⠬⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⣼⠋⠣⢴⣲⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣁⣮⡀⠤⢤
⠀⠀⠒⠀⠁⡀⡀⠈⠁⠀⠀⠀⠀⠀⠀⢐⣿⡔⠂⢽⣪⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣬⣿⡇
⠀⠀⠀⠛⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣗⡮⠐⣻⣽⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠛⠛⠋⠀⣀⣀⡴⣴⣶⡀
⠀⠐⠂⠀⠙⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣯⣄⠮⣧⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⢾⣑⣳⣾⣿⣿⣿
⠀⠀⠀⠐⣺⡇⠻⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⢿⣺⣯⢽⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢨⣟⣿⣷⢿⣯⣿⡿⠁
⠀⠀⠀⠈⠀⡷⠾⠟⢿⣷⣀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⢄⡀⠈⣿⣷⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⠿⠉⠙⠋⠉

⠈⠂⢄⣀
⠀⠀⢠⠹⢗⣶
⠀⠀⠀⢵⠠⠢⠈⠀⡀⠀⠀⠀⠀⠐⠂⠼⠓⢅⠐⠢⢄⡀
⠀⠀⠀⠀⡀⠆⢤⢇⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡢⣬⠂⡐⢄⢀
⠀⠀⠀⠀⠀⠀⠈⠈⡀⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠚⣌⠂⢄⠢⡱⢦⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⡀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⡹⡄⠈⠁⠐⢄⠢⡄⠀⠀⠁⠹⣅⠂⠙⠇⡢
⠀⠀⠀⠀⠀⠀⠀⡣⡠⡀⠀⠃⡀⠈⠳⣦⠀⢤⡠⣤⠴⠓⠀⠈⠀⠑⠂⢁⢨⠂⠀⠀⢀⣸⠁⠀⠅⡀⠐
⠀⠀⠀⠀⠸⣄⠀⠰⣤⠀⠀⠀⠀⢌⠣⠈⠁⠀⠠⠀⢆⠈⠀⠀⢠⠀⢀⠤⠶⣔⣈⡀⡀⠄⠀⡠⠕⠈⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⢍⠓⡓⢍⠁⠀⠄⠄⠀⢁⠀⠂⢀⠂⠠⠄⠀⢀⠰⠄⠁⠈⠁⣐⣮⠝⠉⡀⠓⠄⡀⣐⣦⡀⢀⠢⠀⠠⠄⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠈⠊⠀⠈⠀⠀⠈⠒⠵⢅⡀⠀⣉⢀⠀⢗⠀⠈⠳⡂⠔⠌⠶⠊⢀⠈⠈⠘⣤⡀⡘⠛⠌⠀⡅⢀⡀⠈⠐⢈⣉⣪⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠑⢬⠙⢅⣢⣤⠄⠂⠀⡀⠀⠀⠀⠩⣤⡅⠫⠀⡂⠀⠀⠑⠑⠂⠀⢳⠀⠄⡀⠉⠂⢐⠒⠋⣈⣀⡠⠶⠭⠴⢬⣅⡁⠸⠇⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠈⠑⠐⠢⣀⣐⣀⠀⢢⣄⠀⠤⡀⣀⢍⠳⣌⢦⡂⠘⡲⠛⢙⠐⠘⠝⠓⡸⠿⠍⣁⣄⣄⠊⠀⠐⠂⠀⠈⠀⠒⢄⠢⡠⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⢒⠄⡂⢌⠐⢍⢳⣌⡀⢀⠐⡄⠀⠢⠉⢫⡴⠏⠀⢠⠞⠁⠀⢸⠃⠀⠀⠀⠀⠀⢐⣤⠄⡈⠢⠌⢽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠂⠐⡴⡀⢌⠃⠠⣛⢉⠀⡄⢠⡞⠁⠄⢘⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⣟⠉⠙⠈⢂⠀⠄⢙⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⡀⡢⠈⢠⠀⠑⠘⠄⠐⢰⡏⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠐⠀⢼⣣⠀⡈⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣔⠐⠌⢳⡑⣄⢼⢀⡎⠀⣄⠐⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⣢⡤⢟⠀⠘⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣘⠀⠁⡹⡙⠝⣎⢶⡆⡟⠟⠀⠆⠀⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠃⠀⣰⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠠⠈⢿⠢⡪⣤⡳⠰⠃⡘⡀⡁⠏⠓⠀⠀⠀⠀⠀⠀⢀⡄⠰⡀⠀⠒⢜⠆⠀⠀⣏⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡢⠳⠈⡂⠃⣐⠀⡐⡠⡘⠔⢄⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠤⠘⢂⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⢦⡁⡄⠡⠈⢄⠀⠀⠀⠀⣐⠀⠀⠁⠀⠀⠀⠱⣄⡐⢂⠌⠀⠀⢠⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠱⠌⣤⣀⠠⡀⠰⣢⡤⣤⠥⣄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡴⠃⡠⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⢒⡈⠑⣅⠈⠀⡿⣍⡀⠀⠈⠀⢳⠄⠀⠀⠀⠀⠀⡡⢖⠔⢀⠏⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠬⣀⠀⠩⠽⠦⣨⡙⢠⡤⠄⠓⠠⠄⣀⠥⠒⡊⠐⡁⠐⣁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢉⠁⢄⠀⠉⠩⠭⠉⠀⠀⠀⠁⠀⢐⡫⠀⣀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⠐⣀⣀⣀⣀⣀⣀⡠⠔⠂
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠿⠿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⣤⣤⡄⠀⣿⣿⠀⣤⣤⡄⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠿⠟⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⠾⠿⠟⠋⠉




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

⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢰⢋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠠⠁⠠⠬⠐⢂⠀⠀⠀⠀⡦⠀⡐⠉⢂⢀⡀⠀⠀⠀⣀⣧⡵⠖
⠀⠀⠀⠀⠀⣥⠜⠁⢢⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠸⡀⠁⠐⠀⠂⢉⡜⠀⠀⠀⠈⢢⡠⣯⡟⣍⣈⠏⠀⠀⢼⠁⢈⡇
⠀⠀⢀⠀⡀⠀⠀⠰⢀⠀⠀⠘⡁⣤⠁⠠⡀⢀⠀⠀⠑⠤⡄⠀⡠⠎⠀⠀⠀⠀⠐⣁⣸⠨⢵⡋⠑⡀⢀⡴⠚⢯⠉
⠀⠀⠈⡉⠅⠀⠠⢂⠌⠀⠀⠀⠐⢄⠀⠀⠐⣄⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠄⠈⠉⠀⠀⠈⠉⠚
⠀⠀⠀⢰⣶⣿⣷⣷⣀⠀⠀⠀⠀⠈⠰⢤⡾⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠤⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠀⠑⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⡈⢀⠀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠃⠀⠐⠃⠀⠀⠀⠠⠘⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⡠⢊⠆
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠉⡇⠠⠀⠀⠀⠀⠀⢻⣷⠄⠀⠠⠊⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡦⢄⠤⠖⠁⠀⠀⠀⠀⠀⠠⣠⣶⣶⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠢⠄⠄⠊
⠀⠀⠀⠀⠀⠠⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡡⠀⠀⠀⠀⠈⢤⡐⢀⠆
⠀⠀⠀⠀⢠⠁⠏⠀⠀⠀⠄⢀⠴⠀⠀⠀⢠⠿⢿⠿⣿⣿⡿⠷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠂⠐⠔⠁⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠈⠒⢀⠸⠈⠂⠀⠀⠀⠀⠀⠀⢂⡀⠀⡰⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣈⠁⢈⣤⣤⡗⠀⠀⠀⠀⠀⢠⠊⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡍⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂
⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⡆⠀⠄⣀⠀⠀⠀⠀⠀⠀⡠⢐⣤⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠠⠐⠁⠀⠑⢩⠁⠀⠀⠀⠀⠀⠀⠈⢿⡇⣀⣀⠀⡄⠀⠀⠀⢰⡸⠏⠟⢀⢰⠀⠀⠀⠈⡀⣬⢢⠀⠀⡠⡂⠥⠀⠠⠁
⠀⠀⠀⡁⡄⠀⠐⠒⠄⠅⠀⠀⠀⠀⠀⣠⣴⡾⠛⠻⢿⠃⠀⠀⠀⠀⠀⠃⠈⠄⢉⡀⠂⠀⠀⠀⠐⠠⢙⢠⣌⠜⢁⠠
⠀⠀⠀⠑⠈⠀⠒⠨⠈⠀⠀⠀⠀⠀⠠⡈⠛⠃⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⣀⣰⠘⠋⠈⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠓⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⡀
⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡁⢀⠀⣁⣠⢀⡅⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠤⠀⠤⠤⠤⠤⠜⡀⡀
⠀⠌⠀⡄⢠⠆⢀⡀⢠⠀⠀⢹⠁⠀⠉⠈⠀⠀⠀⠀⠈⡇⠀⠆⠰⠀⠠⠤⠄⠂⠁⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁
⠀⠉⠀⠁⠈⡏⢈⠀⠠⡀⠀⣸⠀⣀⠀⠀⡀⠀⠀⠤⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⡀⠠⣈⠃⠀⠀⡐⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⢀⠀⠀⠠⠀⠂⣀⠐
⠀⠀⠀⠀⠠⠆⠀⠀⠀⢀⡀⠀⢁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠒⠂⡑⡄⡅⠀⠀⠀⠐⠠⡤⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⣁⡒⠀⠠⠀⠒⠈⣀⠀⠐⠀⠀⠀⠀⠈⠀⠐⠄⠀⠀⠠⠄⠀⠆⡄⢀⠀⡆⠀⠑⠁⠀⠀⠀⢎⠀⠀⠀⣀⠘⠀⢀⡂⠶⡅
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠐⡱⠦⠤⠔⠊⠀⠀⠀⣇⢀⠙⣠⠀⢀⠠⠦⠀⢰⠀⠭⠃⢠⠠⡄⠀⠁⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⠁⠀⠀⠐⠀⠀⠀⠀⠘⢦⡀⠈⠁⠉⠁⢂⡠⠬⠀⠀⠉⠀⠋⠀⠠⡀⠀⠀⠐⠈⠐⠉⠐
⠀⠂⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠰⠀⠀⠀⠀⠀⠀⠉⡁⠒⠒⠊⠉⠀⢠⠀⠀⢰⠀⠑⠀⠠⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠔⠀⠈⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡊⠐⠀⠄⠀⠘⠀⠑⠁⠦⠀⠀⢀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠂⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣄⡀⢀⣀⣀⡀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠈⠉⠉⠁⠁⠀⠀⠀⠈⠁⠀⠀⠀⡀⢸⣿⠀⠀⢸⠟⠉⢻⡇⣿⡇⢹⡇⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠍⠀⠁
⠀⠀⠀⠀⢨⠈⡅⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠃⢸⣿⠀⠀⢸⣆⣀⣸⡇⢸⣧⣾⠇⠀⠀⢀⣀⣀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠆⠺⠀⠆⡀⠠⡄⠀⠀⠀⠀⠱⡀⢀⠔⠀⢸⣿⠀⠀⢸⡇⠀⢸⡇⢸⡏⣹⡇⠀⠀⢸⠉⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠘⠃⠀⠘⠁⠘⠛⠛⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠂
⢀⠀⠐⠉⠀⠀⠀⡆⠀⠂⠀⠀⠀⢠⢀⠀⠀⣀⠀⠀⢸⡛⡟⣻⠻⢿⠛⢟⣿⢻⡇⠀⠀⠀⡄⠀⠆⠐⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠈
⠀⠉⠀⠀⠒⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣷⣷⢾⡾⣾⡷⣷⡿⡾⡇⠀⠀⠀⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠑⠀⠀⢸⠀⠠⠀⠀⠀⣀⠀⠀⠠⠀⠀⠐⢀⠀⠌⠐⢆⡃⠂⠀⠡⠠⢀⡐⠀⠀⠀⠀⠀⠠⡀⠠⠂
⠀⢀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠵⠀⠀⠀⠀⠊⢔⠀⠀⠀⠀⠀⠙⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠀⠀⠁⠀⠂⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠂
⠀⠀⢰⡆⢰⡆⠀⠀⢠⡾⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠐⠁⠊⠁⡐⠀⠀⠀⠉
⠀⠀⢸⣧⣼⡇⡶⣦⠸⣧⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠈⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⢸⡇⢀⡿⠀⣿⣸⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⡄⣡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠈⠛⠘⠁⠙⠛⠀⠙⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⠂⡸⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⡝⠻⢧⣄⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⡏⢠⡎⠹⡆⠀⠀⠋⠒⢤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠡⡘⢷⣠⡇⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⠸⣿⡀⠀⠈⡢⣝⠛⠧⢀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠙⠷⠾⠮⣅⣉⡒⣤⣀⠁⠓⠺⢅⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⠞⠟⠓⣲⣦⣤⣄⡀⠈⠙⠺⣟⡲⣦⡂⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⢀⣽⡿⠛⠉⠈⠹⣆⠀⠀⠀⠹⡄⠙⢦⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⣸⣟⠂⠀⠀⠀⢠⡿⠀⠀⠀⠀⡇⠈⠈⢷⣁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⡋⠉⠙⢻⠒⢤⣾⡟⠁⠀⠀⣠⠞⠀⢀⠀⢸⣿⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢄⡈⢿⡻⠶⠃⠀⠃⢈⢿⠿⢷⣿⣅⡀⠀⠈⢀⣾⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⢦⢹⡿⢽⣶⣄⣀⠀⠈⠁⠀⠀⠀⠈⠉⠓⠶⢮⣈⡴⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠙⣿⠁⠄⠈⠹⣿⣭⡒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⣦⡀⠀⠀⠻⣷⡙⢦⡉⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣀⠀⠀⠀⠀⠀⢈⡄⠀⠈⡆⠉⢳⠢⠄⡘⢷⡼⠟⠋⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⣝⢦⠈⠳⢤⣀⠀⠀⠀⢇⡀⠀⢱⣀⣨⠦⠖⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⠀⠈⠓⢄⣀⠼⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⢀⠴⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠄⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⡗⣊⣉⣦⢠⠤⠤⠤⠀⠛⠚⠉⠙⠛⠓⠒⠠⠤⠤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣭⣭⡵⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⠐⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢉⠙⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠒⠂⠀⠀⠘⠒⠀⠤⡀
⠀⠀⠀⢀⣠⡤⠟⠓⠛⠉⠁⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⢀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⡞⠀⠀⠀⣀⠤⠴⣶⣻⡯⠥⠼⠥⠀⠀⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⢧⠀⣀⡤⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢠⠟⠁⠀⠀⠀⢀⣀⣤⡤⠤⠐⠒⠐⣒⡛⠩⠤⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣿⠀⠀⠀⢰⣼⡿⠷⠖⠒⠚⠉⠉⠉⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠂⠄⡄⠀⠀⠲⠀⠀⠻
⠘⡷⠖⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⢸
⣾⠁⠀⠀⣀⣠⠤⠶⣖⣛⣫⣭⠥⠦⠔⠂⠀⠈⠑⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠺⡈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢻⡀⠀⠊⢉⡴⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣹⢗⣽⠋⠀⠀⢀⣀⣤⠤⠶⠶⣲⠾⠿⠯⢥⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠃⢸⠇⠀⠀⢰⢟⠉⠈⠙⠻⣼⠃⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠈⠢⠤⠴⠋⢸⡀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣼⠄⠒⠚⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠁
⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⢀⠇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡸
⠀⠙⢆⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠂⠒⠀⠚⠀⠀⠀⠀⠤⠧⠠⠴⠒⡶⠁
⠀⠀⠀⢻⠛⠉⠉⠛⠉⠉⠙⠯⠉⠙⠯⠉⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣙⣓⠀⡇
⠀⠀⠀⢸⡆⠀⠀⠤⠤⠤⠤⠤⠤⠀⠄⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠠⠤⠤⠤⠤⢤⣤⠶⡶⠶⠀⡇
⠀⠀⠀⠺⡉⠀⠰⠶⠶⠶⠒⣒⣒⣛⡫⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠁⠀⠀⠀⠀⠠⠤⠤⠴⣶⣾⣿⠀⡆
⠀⠀⠀⢺⡅⠐⠶⠶⠶⠚⠛⣛⣚⣓⡭⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⠀⠀⣀⣀⣀⣀⣠⣵⣶⣶⢶⠀⡇
⠀⠀⠀⢾⡅⠀⠶⠶⠶⠒⠚⢛⣒⣛⠻⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⣤⣤⡶⣶⡃⣠⠇
⠀⠀⠀⠈⠳⣄⡀⠒⠒⠒⢚⣓⣛⣾⣥⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠈⠉⠭⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠻⡍⠉⠉⠉⡭⢉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣛⣛⣿⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣧⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⠛⠙⠛⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⢠⡞⠲⣽⣍⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⣼⠀⢀⡬⣅⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⣸⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠤⣤⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⣛⣉⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠋⠉⠀⠀⢀⣨⠿⠖⠒⠲⢦⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⣴⡆⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠹⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠘⠁⢠⡶⠛⠛⠒⠦⣏⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⡆
⠀⠀⠀⠀⢀⡤⠤⢤⣀⣠⢼⡇⠀⠀⠀⠀⠀⠀⣾⣤⣄⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢳⣔⣷⡆⠀⠀⠀⠀⡟⠀⣷⠀⠀⠀⠀⡏⠉⠙⡇
⠀⠀⠀⢰⡏⠀⠀⠀⠀⡏⣰⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⢶⣄⠀⢹⡄⠀⠀⠀⠀⠀⢀⣿⠉⠀⠀⠀⢀⡼⠁⠀⣿⠀⠀⢀⣤⡇⠠⡞⠓⢦
⠀⠀⠀⢸⡇⠀⠀⠀⢼⠳⣏⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⣧⠀⣻⣄⣀⣀⠀⠀⠈⢹⠷⠤⠤⢖⡯⠤⣄⠀⣿⠀⠀⣯⢠⡇⢠⠼⠧⣾⠁
⠀⠀⠀⠈⣧⠀⠀⠀⠈⠳⣝⡛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⣄⠀⠘⣇⠀⠀⠀⠈⠙⢦⣤⠞⠀⠀⠀⠜⠀⢀⡼⢰⠇⠀⠀⠸⣼⡇⢸⠃⠲⡼⠃
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣉⣉⡉⠀⠀⢀⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡟⠀⠀⠀⢀⣽⡇⠈⢹⣦⠞
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⡇⠀⠞⠓⠛⠉⡀⠀⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢠⡞⢹⡇⠀⢸⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢦⣤⣤⠴⠋⠹⡄⢸⡧⠝⣦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣴⠋⠀⢸⡇⠀⣾⠳⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠰⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠷⠛⠁⠉⠀⠀⠀⣠⠞⠁⠀⢀⣴⠟⠁⠀⠀⠸⠦⠤⠟⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠀⠀⠀⠀⢀⡤⠞⠁⠀⣀⡴⠋⠁⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⡠⡾⠃⢸⡄⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⡾⠀⠀⢀⣠⠶⠋⠀⣀⡤⠚⠉⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⡏⠳⠶⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⡷⠤⢰⠋⣷⠖⠒⠉⠁⠀⠀⣀⣤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⢥⡀⢣⠀⡼⠀⣼⣆⡠⠤⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢺⡀⢸⡀⠇⢠⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⣒⠒⠒⢒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠘⠀⣿⠀⠘⠀⠀⠀⠀⠀⠀⢫⠍⠉⢡⠝⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢹⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⣸⡀⠀⢸⡄⢠⡋⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠸⠀⠀⠇⠀⠀⠀⠀⣴⠃⠀⠀⠀⠹⡇⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠷⠶⠖⠛⠒⠒⠒⠚⠒⠒⠓⠒⠒⠒⡾⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠘⡗⠚⠛⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⣀⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⠶⠤⠤⠤⠤⠤⠤⠶⠋⠉⠉⠉

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⢰⠆⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠃⠀⠀⠀⠀⠀⢤⢰⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⢀⡎⠠⠀⢸⡁⠀⠀⠀⠀⠀⣄⠀⠺⢢⠚⠃⢀⡄⠀⠀⠀⠲⠀⣀⣀⠐⠃⠀⠀⠀⠠⠴⠀⣀⠄⠀⠀⠤⠀⠒⠂⠀⠀⠀⠈⡟⢻⠀⢐
⠀⠀⢶⣶⠟⡇⡏⠀⠀⠀⠀⠀⠘⡗⣬⣿⡹⡄⡯⠁⠀⢀⣐⠀⠃⢴⣄⠘⡁⢂⡀⠀⣰⣦⠀⣤⠟⠀⠚⡴⠂⠈⠀⠀⠀⠑⢘⣓⣘⡣⠊
⠀⠀⠨⣐⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠗⠉⠀⠀⠀⠀⠀⠠⠧⣙⣁⠴⠑⠂⠀⠈⠘⠁⠀⠀⠉⣀⡘⠁⠀⠀⠀⢠⠀⠀⠀⠏⠹⠄⠀⠀⢀⡀
⠀⠀⠀⢿⡵⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠘⠖⠀⠀⠀⡀⠀⠀⠀⠀⢭⡥⠀⠀⠀⠀⣡⢣⠀⠀⢀⣀⠀⢠⠌⠙⠆
⠀⠀⠀⣘⢠⠀⠀⠀⢀⡷⢯⡀⠀⠀⠀⢀⢀⠀⠀⣀⠤⠄⡄⡀⠀⠸⠗⠀⠀⡀⠠⠀⡁⠠⠀⠀⠀⢰⡆⠀⢀⠀⡘⠔⢥⡏⠀⠨⠍⠀⢰⢚⠀⠈⠀⠀⡀
⠀⠀⠀⢸⡖⠀⠠⣁⠁⣷⣯⡇⠀⠤⠀⠘⢉⠀⠮⢰⡶⠳⣶⠹⡄⠀⡂⠀⠀⠀⠛⠀⡅⠘⠃⠀⠀⠈⣷⠒⠋⠀⠀⣄⣢⠀⠀⢀⣆⠀⠀⠙⠶⣀⡈⠟⠁
⠀⠀⠀⢰⢺⠀⢄⡅⢰⢾⠿⡇⠤⠄⠀⠸⠚⠀⣇⢹⣦⣤⣟⢁⠃⠈⠋⠀⠠⠀⣀⠈⠂⢀⣀⠈⠀⠀⢸⠀⠀⠀⠀⠰⠖⠀⠀⠘⡞⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢬⡷⣾⠔⠡⠀⠀⢰⣠⠀⠀⠃⠠⡅⠄⠋⠀⠀⠀⠀⠀⠐⠁⠀⡀⠸⠁⠂⠀⠀⡟⠀⠀⠀⠀⠈⡏⠀⠀⢀⢦⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣴⠄⠀⢐⣸⠀⠐⠀⠀⢠⠀⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠰⠇⠀⠀⠀⡏⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢐⠀⠀⠀⠘⠿⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠁⠀⠀⠀⠘⠦⠆⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⡄⡄⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⡆⠀⠀⢠⠉⠄⠀⠀⠀⠘
⠀⠀⠀⢸⢉⠀⠀⠀⠖⠐⢠⠁⠀⠀⠀⠀⠇⠁⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠷⡆⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢦⡆⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢐⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠰⠀⢠⢠⠄⢄⠄⠀⠀⠀⠀⠀⠀⢠⢠⠄⠀⢀⠄
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠄⠰⠒⠚⠀⠀⠀⠀⠀⠞⠀⠐⠀⠰⠠⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠂⠰⠆⠀⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣒⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠙⠁
⠀⠀⠀⠀⠀⡀⢤⣀⡀
⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⣀⣤⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠛⠋⠉⠉⠉⠉⠙⠻⠷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⣀⡀⣀⠀⣀⠀⠀⠀⠀⠈⠙⣷⡆⠀⠀⠀⠀⠀⠠⢾⠿⠀⠘⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠁⠘⠋⣶⢪⡶⣡⣀⣤⠈⢿⣄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⣿⣇⠀⠀⠁⠀⠀⢀⣀⡀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⣻⣿⣦⠸⣯⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡌⠙⠃⠀⠀⠀⠀⠰⣿⣿⣿⡄⢠⣾⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣶⣿⠆⠀⠀⠀⠀⠈⠂⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⠸⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⠋⠀⠀⠀⠀⠀⠀⠚⠋⠀⠂⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠀⠀⠈⠵⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠃⣼⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠐⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⡤⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠁⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠺⡀⠀⠀⠀⡀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠶⠒⠀⠀⠻⢆⡈⠀⢀⠛⢀⡾⠟⠀⠀⠀⠸⠀⠔⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠑⠆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣯⣾⡇⠚⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠈⠙⢦⡇⣴⡉⠀⠤⡀⠀⠀⢀⠠⢤⣄⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣄⡀⠁⢠⠛⠳⣼⣷⣄⠀⠘⠲⣎⡀⠀⠏⠀⡄
⠀⠀⠀⠀⡀⠐⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠡⠴⣾⡇⢈⡟⢻⡆⠀⠀⠈⠻⢦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢰⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡌⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⣶⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡆⠀⠀⠀⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠒⠀⠄⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠁⠀⠀⠀⢸⣿⣧
⠀⠠⣄⣀⠀⣄⢀⣠⠀⣦⡄⠀⠃⠀⡐⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣷⣾⣿⠷⡿⣧⡀
⠀⠀⠻⠟⠀⠸⠷⠏⠀⢹⣇⠀⠤⠀⠀⠀⠄⠠⢀⠈⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠠⠀⠀⢰⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢤⡴⠋⢰⣂⢠⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠐⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠄⠂⠁⠀⠀⠁⠤⠠⠠⠂⠀⠀⠀⠀⠚⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠀⢀⠀⠀⠄⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠐⠂⠀⠁⠂⠀⠀⠀⠀⠠⠄⠀⠀⠀⣃
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠤⠊⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠁⠹⠁⢀⠀⠠⠂⠀⠀⠀⠤⠂⠀⠀⠀⠀⠒⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⢡⡄⠴⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⠰⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠌⠐⠀⢀⣉⠀⠰⡄⠈⠀⠉⠀⠀⠀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⢀⡄
⠀⠀⠀⠀⠠⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠂⠀⠃⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⡦⠀⠐⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠋⠀⢀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⢤⡄⠀⠀⠀⠈⠙⠀⠀⢀⡀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠇⠀⢈⣀⣀⣀⢀⡈⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⣁⣀⠀⠰⠀⠐⠂⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠱⠂⠈⠀⠀⠀⠆⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠁⠠⠑⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠉⠂⠰⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⣐⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠋⠀⠀⠰⠃⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡈⣐⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠓⠂⠊⠉⠀⢀⢀⡤⢘⡇⠀⠀⠀⠀⠈⠀⠀⠁⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠙⠄⠀⠀⠀⠀⠂⠐⠀⠒⠈⠀⠀⠀⠈⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠴⠀⠀⠀⠀⠰⠁⠀⠀⠈⡄⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠠⡀⠀⠀⠨⠀⠀⠀⠚⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⡰⠀⠁⠘⠀⠀⠀⠀⢉⠠⠄⠀⠰⡀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡠⡄⠒⠀⠀⠀⠀⠈⠁⠂⠀⠀⠤⠄⠀⠀⡀⠀⠁⠀⠐⠂⡄⠀⠀⠈⠁⠀⠀⠀⠀⠠⠂⠀⠀⠤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⠶⠿⠿⠿⠶⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣴⡾⠟⠉⢁⠤⢖⣒⣒⠒⠦⣄⣀⡀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⠟⠛⠛⠻⣿⣾⣿⣅⣀⠀⡰⠁⠀⠀⢀⣽⠿⠿⠿⣿⣿⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣄⣀⢀⣼⠟⠁⠈⠉⠙⠽⡇⠀⢀⣴⡏⠀⠠⡶⢦⠺⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠈⢉⠛⢦⠀⠀⠀⠀⠀⢻⢇⡞⡻⠇⠀⠀⠀⠀⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣿⠷⣦⣄⠀⠀⠀⠺⣷⣤⣄⠀⠀⠀⠀⠉⢿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢱⠀⠈⠻⣏⡽⢷⣦⣼⣀⠈⠑⠶⣶⢶⠖⠋⠀⠈⠻⣕⢄⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⡜⠀⠀⠀⣻⣿⠿⣿⣿⣿⣶⣮⣐⠾⣿⡗⠢⠄⣀⠻⠟⠒⠛⠐⠆⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠃⠀⢠⠎⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣦⣝⡻⢶⣾⣷⣾⠀⠀⠀⠸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠠⠀⡞⠀⢻⣿⣦⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣶⣿⢻⣿⣯⣤⢄⠀⢣⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢿⣿⡿⣿⢿⣿⣷⣄⠀⢸⣿⣿⢿⣿⣿⣿⣿⠉⠻⢿⣿⣿⠘⣷⠈⣆⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡉⠻⣮⢣⢻⣿⣿⣦⣸⣿⣿⡀⠉⠻⣿⣿⣷⣄⠀⠉⠻⢧⣿⡀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠃⠀⢻⣇⣸⢏⣿⣿⣿⡉⠻⣿⣦⡀⠈⠙⢿⣿⣷⣦⡰⠎⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⡀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠟⣻⣿⣷⣄⣿⣧⣙⢦⡰⠆⢹⣿⣿⣿⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢇⠀⠀⠀⠀⣠⣿⣿⠿⡇⠀⠈⢽⣿⣿⣿⣿⣿⣷⣝⠶⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠴⠚⠛⢷⣦⣄⣧⣀⡈⠒⠺⠿⣿⣿⣿⣿⣿⣷⣌⣀⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣟⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠈⣿⣧⠀⠀⠀⠀⠀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣆⠀⠀⢀⣤⣿⣿⡏⣴⣾⣿⣧⣤⣤⡀⣸⣿⡿⢫⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⢀⠹⣿⢿⣿⣿⣿⣿⣿⢻⢧⠞⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠐⠿⠿⢿⣟⠶⣤⣤⣤⣴⡶⢶⣿⣿⣿⣿⢿⣿⣿⣿⠟⠛⠉⠱⢌⣷⣼⣿⣿⣿⠇⠀⢿⣤⣴⣦⣤⡶⢾⣿⣯⣿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣷⣿⣿⣿⣷⣥⡿⠟⠁⠀⠀⠀⠀⠀⠉⠛⠿⣿⣇⣠⣶⠄⠔⠛⣩⣴⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣯⣅⣁⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡗⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣶⣶⣶⣶⣶⡶⠿⠿⠷⠶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠛⠉⠉⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠁⠀⠀⣀⣄⠀⠠⣈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⡀⠀⠀⠒⡜⡰⠀⠈⢻⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⣼⣍⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣤⢘⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⣶⣦⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠠⣿⣂⣭⣶⠄⠀⠀⣠⢖⢀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⠟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⡈⣿⣿⣿⣿⣾⣴⣾⣧⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣋⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠶⠶⠶⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠠

⠀⠀⠀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⠀⠀⢀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡄
⠀⠀⠒⠿⢷⡈⠯⢍⠛⠅⠐⠶⣄⠐⠆⠀⠐⠄⠀⠀⠀⠘⠁⠵⠄⠀⠀⠀⢀⠀⣀⢀⡈⠈⠉⠉⠉⠉⢙⣃⡉⠂⢉⡐⣋⣛⢛⣿⣿⣿⡿⢿⣿⣿⣟⣿⣿⣿
⠀⢠⣄⠉⢤⢹⡄⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢯⠿⣆⠻⣿⣿⣿⣆⠛⢿⣿⣿⣿⣿
⠀⠀⣉⠁⠒⠳⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⣻⣯⡿⢛⣀⠛⣿⣿⣿
⠀⠠⣯⣅⠀⠅⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡙⢉⢡⣇⣀⣭⣇
⠀⠀⣷⣆⡀⠀⠐⢆⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠶⢾⡿⡇
⠀⠀⣿⣮⣉⡘⠳⡈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⢾⣶⣶⣂⣀⠚⢿⣿⣧
⠀⠀⠓⠛⠂⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⡙⠢⠀⢂⠠⣄⡙⢿⣿⣦⣶⣶⣿⣿⠂
⠀⠀⠁⠀⠀⣀⣠⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣈⡑⢖⣬⣥⡙⢓⣀⠉⢿⣿⣭⣿⣿
⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲⡖⢞⣻⣟⣻⣎⢹⣽⣾⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢤⡘⢷⣿⣟⡿⣿⣿⣿⣷⠖⢻⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢂⡀⠈⠋⠑⣤⣥⣸⠲⠾⠿⢻⢿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣤⣤⡀⢠⡄⠀⡀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠉⠁⣾⡇⠙⢻⡟⣷⢒⣶⣤⣼⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⠛⣜⣹⡇⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡄⠀⠀⠁⠀⠀⠹⢯⣭⣿⣧⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⣷⣶⣦⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣠⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣷⣮⡁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣛⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⢾⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⢿⢻⣿⣿⣿⣷⣾⣷⣿⣿⣧⣾⣿⣿⣻⣿⣉⣛⣛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣷⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇
⠀⠉⠉⠉⠉⠉⠉⠀⠉⠀⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠙⠉⠀⠈⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡋⢙⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣏⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣽⣿⣷⣄⠀⠀⠀⠘⠛⠛⠛⠛⢿⠟⠛⢻⡟⠉⠉⠉⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⣀⣀⡀⣼⠀⠀⢸⡇⢀⣴⣿⡿⠟⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣷⣾⣿⣿⠀⢀⣴⣿⠟⣿⣿⣿⡀⠀⢸⣧⣾⣿⣿⣿⣦⣿⣿⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡍⠙⡏⠉⠉⠀⣴⣿⣿⣷⣦⣾⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢦⣄⠀⠈⡇⠀⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣷⣼⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣾⣿⣦⠀⣷⠀⢻⠀⣼⣿⣿⣿⣿⣯⡸⣿⣿⣿⣿⣿⡇⡿⠛⠛⣻⠛⠛⠛⡟⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣙⣿⣟⣡⣿⣿⣷⡰⡇⠘⠀⠘⠛⠛⠛⠻⡿⠿⠿⣿⠿⠿⠟⢡⡇⠀⠀⡏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠹⠉⠉⠀⣃⣄⣀⣾⠂⠀⠀⠀⠀⡇⠀⠀⡟⠀⠀⠠⢸⠇⠀⢸⠱⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠁⢣⠀⠙⡆⠀⠀⠀⢰⡇⠀⢠⡇⠀⢀⡀⣾⠀⢀⡏⠁⢀⣴⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⣴⣶⣦⡘⡆⠀⢸⡀⠀⠀⢸⠀⠀⠘⣡⡾⣿⣿⡆⠀⡼⠀⢠⣾⣟⣿⣅⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣷⠀⠈⡇⠀⠀⡞⠀⢰⣾⣿⣿⡿⣿⣿⡌⠁⠀⠘⣻⠛⠿⠿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⣿⠿⡟⠋⡇⠀⢸⣶⣶⡇⠀⢸⡟⣻⠛⢻⠿⢿⠇⠀⠀⢠⠇⡌⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⢹⡄⢹⢀⣿⣧⣿⣿⠆⢸⠁⠇⠀⣾⡴⠃⠀⠀⢠⠏⣸⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣄⢧⠘⢷⡘⡆⠀⡏⢸⠁⠀⣿⡜⠀⣴⠋⠀⠀⡠⣠⢳⣌⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣼⣟⠈⢆⠀⢳⣇⠀⡇⢸⠀⢠⡿⠁⢰⡏⠀⣠⢞⡴⠇⡁⠈⢳⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠈⢦⠘⣆⠀⠙⣄⡷⢸⠀⡼⠁⢀⡞⠀⡪⣐⢩⠴⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣄⠀⠀⠈⠣⡈⠧⠈⢧⠀⠈⠃⠘⠋⠀⠀⠚⠋⠉⠈⠀⠀⣠⠔⠋⠀⠀⢠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠆⠀⢸⣿⣷⡄⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠰⠀⠈⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⡀⠀⣼⣿⣿⣿⣿⣷⠀⢀⠀⠸⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠶⢦⣤⣄⣀⡀⠀⠘⡇⠈⡏⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣀⠉⠙⠛⠲⠮⢽⣿⣛⣺⡷⠶⣧⣤⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡷⢲⣦⣤⣄⣀⡈⠩⢿⡟⠲⠶⢭⣭⣛⡓⠶⠦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠿⠞⠃⣼⣿⣭⡽⢻⡶⢲⡦⣤⣄⣀⡈⠉⠙⠓⠲⢬⡟⣿⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⢀⡾⠁⠈⠉⠀⢸⡇⢸⡇⣸⣿⣏⢉⣿⣷⡶⢶⣼⣷⠟⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣤⣀⣀⣠⣤⠴⠞⠋⠁⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⢸⡇⣨⡟⢹⡏⠛⠋⣠⠿⣿⣶⠟⠉⠓⠶⠦⢤⣤⣤⣤⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⣁⣀⡀⠀⠀⠀⠀⠀⣸⡟⢹⡇⢸⡇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠁⣿⠫⢭⣉⡉⠛⠲⣦⣴⣏⣹⡇⢸⡇⢸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣄⣠⡽⠟⠿⢧⣤⣈⡉⠙⣻⡷⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠙⣷⣈⣽⠟⣷⣦⣤⣄⣉⣽⣟⠿⢶⣤⣌⣉⠛⠻⠶⣤⣄⣀
⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⢀⡿⢷⣤⠿⠛⣷⡾⣤⣄⣀⠈⠉⠙⠓⠶⢤⣌⣉⡽⣷⠀⠀⠀⢀⡀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣿⠀⢸⡏⢹⣿⡶⢦⣤⣤⣀⡀⣹⣀⣿⠖⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⢾⡟⠛⠋⠻⣿⣏⣽⠿⢯⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⢻⡇⢸⡇⠀⢀⡾⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⣿⠀⢸⡇⢸⣧⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠶⠶⠖⠒⠋⠉⠀⠀⠀⠀⣿⠀⣸⡧⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⣿⠋⢹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢻⠄⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣼⠶⠛

⠀⠸

⠀⠀⠀⠀⣠⣤⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠘⡄⢠⢃⡨⠛⠧⣽⡤⠃⠠⠿⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣧⡟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠛⠯⠤⠤⠔⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⣄⠫⠑⠀⡀⠀⠀⠀⠠⠀⠀⠈⠇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠐⠐⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠉
⠀⠀⠄⠀⠀⠀⠀⠾⠆⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠄⢀⣴⣿⠟⠁
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠁⠤⢘⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠘⠀⡒⠈⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⡀⠀⠀⠀⣾⡇⠀⠀⢠⡶⣆⠀⠀⠀⠛⠛⠛
⠀⠐⠂⠀⠀⠀⠀⠳⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠈⠀⠀⠀⢸⣽⣿⡇⠀⢀⢀
⠀⠀⠀⠀⠀⣀⡀⠳⠆⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⣠⣶⡧⠀⠀⠀⠀⠀⠻⠓⠀⠙⠛
⠠⠀⠀⠀⠀⢙⡃⠀⠀⠀⠐⠂⠀⢠⣤⡄⠀⠻⡟⠀⠀⠘⠁⠀⠀⡀⠀⢀⡴⡶⢢⠀⢀⣦⡀⠀⠀⠀⠀⢴⡷
⠀⠐⠢⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣤⣤⡄⠀⣾⠿⠀⠘⢷⣏⡿⠁⠈⠰
⠀⢈⠡⠀⠹⣾⡿⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠑⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠾⠮⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⢰⠀⠀⠆⠀⠀⠈⠀⢀⡤⠒⡻⣏⠑⠢⣄⠀⠀⠀⠀⢒⠀⠗⠀⣀
⣐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣏⣤⣤⡧⠼⣦⠤⢬⣇⠀⠀⠠⠈⠀⠀⠀⠐⠀⠀⢀⠠
⠀⠅⠀⠂⠀⢲⡶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠉⠲⣾⣀⠀⣹⡖⠉⢸⠀⠀⠙⠀⠀⠀⠁⣰⣰⡀⠘

⣿⣿⣿⣿⣶⣾⣷⣇⣸⣦⣈⣇⣠⣷⣄⣄⣠⣄⢙⣅⣡⣴⣿⣤⣌⣵⡌⣡⢊⣱⣶⣀⡙⣷⣄⠀⠰⣤⠈⢿⣈⣿⠗⣉⠛⢈⡙⢉⣌⣠⣠⠜⠷
⡟⢻⠿⣿⣷⣿⣿⣿⡟⠉⣿⣩⣿⣿⡙⢿⡿⢿⣿⡟⣿⢁⡿⢇⠙⢋⣿⣈⢻⣿⠻⡿⣯⣠⡿⠏⠰⠟⠓⠐⠛⢫⠟⠻⣷⡃⠙⡞⠻⠿⡷⠠⠾
⡿⣿⣦⣿⣿⣿⣧⣿⠿⣴⠿⢯⣸⣿⣿⣈⣧⠈⠛⠃⢁⠘⢠⠌⢃⠀⢳⣏⣧⣍⡰⠊⠄⠟⠉⡁⠀⠈⠂⠀⠀⠉⣯⠄⠈⠑⠦⢛⣦⠀⠀⠀⣀
⣸⣿⣶⡷⢿⠛⡿⠛⠁⢹⣦⠀⢦⣿⠈⠉⠛⠀⠘⠂⠀⢸⡌⢢⠚⠀⠈⢡⡈⠙⢅⠉⡐⢶⣆⠀⡄⠁⠀⠀⠀⠰⠀⠐⠀⠀⠀⠙⠁
⣿⣾⣿⠶⠇⢿⡶⣴⣿⢀⣿⢿⡛⣿⣿⠸⠀⣿⠀⣶⣧⣼⠁⡾⠟⣠⠀⠀⣐⠀⢸⣄⣙⠿⣿⣦⠐⡎⢠⣆⠐⢀⣄⠀⢀⠀⠀⠀⠀⠀⣀⠀⣀
⠘⢿⠛⠰⣶⣾⠳⣿⠏⣹⠇⠀⢁⡋⣷⠀⣶⡷⠀⢱⠴⡿⣶⣀⢸⡿⠀⣷⠉⣀⠈⢹⢏⠁⠙⠃⠶⡄⠀⠈⠀⠈⠉⠁⡈⠀⠘⣥⠒⠀⠙⠆⡈
⣀⣀⣀⣤⡅⠀⣤⠃⣸⠏⠀⢀⡀⢡⣬⢀⠈⣀⢀⡀⣠⠀⢸⡈⡀⠀⡄⢸⣄⣀⣠⠀⠀⠀⢀⠀⢀⠁⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⣻⣿⣬⢿⡗⢀⠹⣷⡿⢛⣷⡾⢛⡟⠀⢻⠇⡿⢻⡷⣿⡀⠾⢱⡇⡸⠧⣤⣹⠿⡇⠐⢁⣶⡎⢰⡆⠀⣰⠀⢀⡀⠈⢀⡀⢼⡀⠀⣤⠀⡈⠠⣄
⣷⣿⣉⡸⠃⠈⠗⣼⠓⠘⢃⢃⣼⣓⠶⣾⡀⠀⣾⡇⢸⣅⣄⠘⠛⣃⢲⣿⠉⠀⢓⠀⣌⡁⠀⠀⠀⠀⠉⢧⠀⠁⠀⢆⠁⠜⠓⠰⢴⠒⠉⠀⠈
⣿⣿⣿⣷⠈⢶⠿⣼⡇⣠⣤⣀⣿⣏⠠⣿⣧⣤⣿⣤⣬⣿⣏⠐⠀⣤⣿⣿⡟⠛⢁⡈⠛⠃⠾⡆⠀⠀⠠⠀⡆⠠⠀⢠⣤⠄⠀⠠⠞⢀
⣥⣬⣿⠀⣶⣿⡗⢹⣿⣋⣹⡏⣿⢙⡇⢹⡻⣿⠍⢻⠉⣿⣧⣴⣤⣿⣿⣿⣿⣟⡛⠓⣼⣷⡄⠃⠰⠃⠶⣾⠁⠀⠠⠠⣤⠳⠴⣶⠆⣼⡇⠀⡀
⣿⠛⣿⣀⣿⡿⢧⣼⡇⣿⠿⠃⡻⢘⡟⠻⠃⡇⠀⡸⣿⠋⠁⢿⣧⠘⣿⠉⠸⠿⣇⠘⠈⠛⣿⠀⠀⠀⠀⠉⡈⠀⠀⠀⠈⠒⠀⠙⠇⠙⠘⠃
⣿⣦⡟⠛⢹⣷⠘⠉⣿⢛⣷⣰⡁⣈⣹⡀⣀⠘⣶⣇⣿⡄⠀⡈⣿⡀⠁⠀⣀⡀⢉⣤⣶⣄⣼⣤⠂⠀⠀⡄⠉⠀⠀⠀⠀⠆⠁⢤⡜⠳⠗
⢿⡿⠟⣿⢿⣿⢾⣶⠟⠸⡿⠸⣿⡟⠉⣧⣤⠈⣿⠁⠹⣿⣷⠆⢿⣇⣰⣇⠟⣽⠿⠇⡄⠛⣤⢤⡖⠀⠀⢠⠀⠀⠤⠠⡦⢰⡆⣸⡵⠆⠘⢠⠚
⠀⡆⢠⡄⠀⢹⡄⡟⠘⠆⠀⠠⢤⠀⠀⣽⠀⡀⠀⠀⠀⠉⠀⠀⠈⠁⢩⡁⠀⠄⠀⠀⠀⠀⠻⠈⠃⠈⠂⠀⠠⠙⠄⠆⣤⠀⠀⠹⠩⠄⠰⡋⠠
⠀⠁⢈⠁⢠⡀⠀⢰⡄⡆⠠⠆⠀⠄⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢸
⠂⠐
⡀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⣀⣠⣄⠀⣠⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢘⣿⣿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⣠⣴⣿⣀⠀⢻⣿⣹⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢸⣿⡏⣩⡟⢶⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡾⣿⠇⣠⣾⣿⣿⣿⡿⠃⠉⠉⠛⠉⠉⠉⣤⢟⠻⢿⣿⣿⣿⣿
⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⡗⠀⢿⣿⣷⣿⣟⢿⣿⣿⣻⣯⣤⣤⠐⠀⢿⣧⠠⠆⠀⢿⣿⠀⠙⣿⣿⣿
⣿⣿⣦⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⡠⢿⠿⣷⣿⣿⣇⣈⣁⠀⢷⡿⠇⢼⣿⣽⣿⣧⣴⣦⣴⣾⣿⣶⠶⣶⣶⡼⠀⡈⠃⠈⢻
⣿⣿⣿⣷⡼⣿⣷⣷⣾⣦⡄⠀⢀⣾⡟⢉⠁⣹⣿⣟⣃⠐⣴⡟⠁⢀⠀⠻⣯⣤⣤⣤⣤⣤⡟⢿⣿⠛⢿⣿⠟⢻⣿⣿⣶⣿⣷⣶⣶⣦⣤⣤⠸
⢿⠛⣿⡿⡓⣿⣿⡿⣿⡹⢇⠠⢬⣾⣤⡶⠴⠻⠿⣏⣉⣉⣿⡟⠻⡟⢃⣤⡄⠸⠄⢀⠦⠈⡅⣿⣾⠀⢸⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⢾⣛⣿⢠
⡈⠁⢻⠟⠃⣿⣿⣇⣹⡇⣸⣤⣤⣤⣌⣀⠀⠀⣤⡈⠛⠋⠽⠷⠘⠋⠙⠿⠃⣀⠀⠀⠀⠠⣄⣉⡁⠀⠘⢫⣿⢠⣿⣿⠿⣿⣿⡿⣧⡘⢻⣿⣾
⣇⣠⣼⣦⣤⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠠⡦⢴⣶⡀⢸⠇⣿⠀⣦⣀⢀⣿⣯⡄⠀⠄⣰⣿⣿⡏⠀⠀⣼⣿⣷⣾⣇⣼⡏⣿
⠹⣿⡉⢹⣟⣿⣿⣿⣿⣿⣿⠛⢭⠙⢉⠉⠘⠋⠀⡀⠀⠂⠀⠛⠛⣻⣷⣾⡟⠛⢻⣉⣹⣿⣿⣏⡁⣠⠜⣿⣿⣿⣿⢴⣿⣿⣿⡷⣾⣿⡿⢷⠿
⣴⣿⡷⣿⡏⠻⠋⢻⣦⡸⢿⣷⣾⡟⣿⠀⣴⠦⠀⡛⠀⣤⣄⠀⣀⣾⣯⣰⡶⠆⣨⣿⡝⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣷⣾⣿⣷⡆⣄
⣿⣿⣷⣼⣿⠶⠆⠀⡈⣻⣦⣀⣸⣧⣼⠀⣰⡾⣶⢿⣦⣿⣿⡀⢿⣿⣿⠇⠀⠘⢻⣿⠃⠈⠉⠁⠙⢉⠁⣿⣿⣿⣿⡿⢻⡿⠿⣿⣿⣿⣿⣷⣽
⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⠁⠀⠀⠀⣰⢿⣶⣦⣾⣿⣿⣿⣧⣼⣿⣧⠀⠀⠀⢸⢿⡆⠐⠋⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣶⢷⠄⠀⠀⠀⠈
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣈⡁⠈⢻⡈⢿⣿⣿⣿⣯⣿⢻⡇⠀⠀⠀⠛⠚⠛⠖⠀⢉⣻⣿⣿⣯⣽⣍⣉⣉⣉⣡⣄⣀⣴⡖⢲⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣷⣼⣿⣻⣿⣿⣯⣾⣥⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⣉⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣦⣍⡉⠙⠛⠻⠻⠿⠿⢿⣿⢏⣿⣄⣿⣿⣿⣿⠁⣿⡏⢉⣉⣤⠀⣠⠀⢀⣀⣰⣾⣿⣿⣿⣯⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣭⣿⣿⣿⣯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠋⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⢀⣼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣙⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠻⣄⣿⣿⣿⡿⢟⡃⠀⠀⠀⠀⣤⢤⣤⣤⣤⣤⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⣀⣉⣁⣼⢿⠟⠀⠀⠀⠀⠀⠐⠀⠙⠛⠛⠋⠉⠙⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢷⣶⣶⣦⣦⢸⣧⣾⣿⠀⠀⠀⠀⠀⠀⠀⠰⠄⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣾⡏⢻⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⠃⢸⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣴⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣿⣿⣿⡿⠁⠀⠈⣿⣿⣇⣀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣗⡂⣸⣿⣏⣼⠿⠿⣿⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠙⠃⠉⠉⠉⠀⠈⠉⠉⠉⣿⠁
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠙⠙⠛⠛⠛⠛⠛⠛⠛

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣴⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠘⠈⠉⠋⢉⠈⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⠞⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣰⠗⠀⡇⠀⠀⠀⠀⣠⣼⣿⣤⡀⠀⠀⠀⠀⣟⣻⡇⠀⠀⠈⠣⡀⠀⢠⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀
⠀⠀⠀⢀⡀⠀⠀⠀⡇⠀⠀⠀⢰⠋⠉⢉⠉⢹⠀⠀⠀⠀⡏⢽⡇⠀⠀⠀⠀⠈⠲⣿⣿⣦⡀⠀⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⢠⣀⣀⣀⣀⣀⡇⠀⠀⠀⠘⣄⠐⠂⢀⡼⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠈⠻⣧⠟⠀⠀⠀⢸⡟⠛⠉⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠤⠀⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⡀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⢀⡅⡭⠦⡅⢘⡀⠀⠀⢴⢟⣟⣷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⠀⠀⠀⢸⡁⠀⠀⢹⠄⠀⠀⠀⠀⠈⠈⢿⡟⠁
⠀⠀⠃⠜⣌⣛⡜⠤⠋⠀⠀⠛⣷⢵⠟⣥⣄⠀⠀⠀⠈⢻⣿⣿⠟⠀⠀⠀⠘⠿⢤⡴⢿⡀⠀⠀⠀⠀⢰⣶⡞⢳⣶⡆
⠀⠀⠀⠂⠢⡠⠓⠚⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠀⠀⠀⠀⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡝⡻⣆⠀⠀⠀⠀⠀⣴⣿⡆
⠀⠐⠲⠿⢿⣿⣿⣿⣿⣶⣤⡀⠀⠀⡿⢿⠀⠀⠀⠛⢁⣾⣿⣿⣷⣚⡿⠂⠀⠀⠀⢴⠟⣿⠞⠋⠀⠀⢀⣶⠿⢿⣿⡇
⠀⢰⠀⠀⠘⠋⠉⠉⠋⠉⠀⠀⠀⠀⡇⢸⠀⠀⠰⢮⠥⠿⣿⣿⠟⣥⡀⠀⠀⢰⡟⠻⣿⠛⠀⠀⠀⠀⢸⡇⠀⠸⠿⠿
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠶⢿⡶⠾⠁⠀⠀⠀⠀⢸⣿⡖⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⣶⣶⢶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣶⣶⡶⠶⠶⠶⠷⠾⠷⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣿⢹⡇⠀⢸⡟⣿⡆⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣿⢸⡇⠀⢸⡇⣿⡇⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣼⡇⠀⠸⠷⠿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⣀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣿⢻⡿⠀⠀⠀⠀⠙⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⠀⠀⣠⡿⣱⡟⠁⢀⣼⢿⣶⣾⠛⣿⡄⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣯⣙⠻⣶⣟⣼⠟⠻⣶⡾⣣⣿⣷⣿⣿⣿⣷⣶⣶⣶⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠉⠛⢿⣿⣿⠻⢶⣴⡟⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⣿⣾⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣹⣿⣿⣿⡛⠛⣛⣛⡛⠛⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣿⡇⠀⣿⣿⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣿⡇⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠿⠷⡿⠃⠀⠛⠛⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⣦⣀⠀⠀⢀⣽⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠈⣻⣟⠁⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⣼⢿⡿⢶⡿⠃⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⢸⣏⣹⣧⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⡾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠶⠶⠶⠿⠿⠿⠿⠶⠶⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⣠⡾⠋⠀⠀⠘⢷⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⢀⣤⡾⠛⠁
⣠⣤⣤⣶⠶⠟⠛⠉⢀⣠⣴⠾⠛⠁
⠉⠁⣀⣀⣠⣤⡶⠾⠛⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⡟⣛⠛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣥⣴⣿⡟⠁⣀⣀⣀⠉⠐⠪⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠠⣿⢿⣿⣿⣷⡴⠛⠉⠉⣷⡄⠀⠀⠑⠘⢿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣘⣿⣿⣿⣿⣿⣄⡀⣀⣰⣾⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⠻⠘⣿⣿⣿⣿⣿⠟⠻⡟⠋⣤⣤⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣽⡿⠋⠛⠉⠀⠀⠀⠀⠛⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡔⢃⡄⠹⡆⠀⠀⠀⠀⠀⠀⠀⣀⣽⣷⣇⠀⢺⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠀⡀⠷⠂⠀⠀⠀⠀⠀⠀⢷⣾⣿⣿⡇⣀⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣶⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠟⠋⠙⠛⠋⠁⠀⠀⠀⠀⠈⠙⠿⢠⡀⠀⠀⠀⠀⠀⠀⠄⢀⣴⣿⣿⡿⠿⠛⠁⠀⠙⠻⠿⡿⠛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⠶⠶⠶⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⣯⣅⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢟⣽⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⣼⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠈⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢜⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂
⡒⠶⢶⠤⢄⠀⠀⠑⠊⠀⠀⠀⠀⠀⢀⠔⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠠
⠠⢀⠀⡇⠀⠀⠀⡠⢤⣶⣆⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡾⠀⠀⠀⠀⠱⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡸
⠀⢀⠆⠀⠀⠀⠀⠀⠉⢄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠙⠋⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠸⠀⠀⠠⠂⠀⠀⠀⠀⠑⠇⡀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠐⠄⠉⠉⠉⢠⠁⠀⠀⠀⠈⠳⣤⣀⣀⢴⢣⠀⠀⠀⠀⠀⠠⠎⠉⠑⡄⠀⠀⠀⠀⠸
⢀⠇⠀⠀⠐⠄⣀⡀⠀⠀⢀⡀⠈⡀⠤⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡼⠶⣄⠀⠰⠋⠙⠳⡄⠀⠀⠈⠧⣀⡴⠁⠀⠀⠀⠀⠠⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢺⡀⢀⡸⠀⠘⢤⣀⠴⠃⠀⠀⠀⠀⠀⡶⠖⠢⡀
⠀⡠⠶⢤⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡞
⠀⣇⠀⣠⡦⣀⣀⢄⡀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠚⠁
⢀⣈⠉⠁⡸⠋⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠁⠈⢳⠄⣇⠀⠀⠀⢠⠆⠀⠀⠀⢀⠄⢤⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠀⠈⠀⠀⠀⠘⠀⠙⢄⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⣀⠠
⢤⠴⠋⠀⠈⠲⠤⠖⠃⠀⠀⠀⠀⠹⢄⣀⠇⠀⠀⠀⠀⢀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢣⡀⠀⠀⠆⠻⠟⠀⠚⠂⣤⠄⠀⠀⠀⠀⠠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠁
⢀⣤⠆⢱⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠠⠉⠐
⠉⠀⠀⠀⢢⠀⠀⠘⢅⣀⡼⠓⠢⢼⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠄⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠾⢁⡤⠦⠠⣄⠀⠀⠀⡠⠄⢄⠀⠀⠀⡠⠲⠶⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⢄⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠈⡧⠀⠘⢅⣀⡼⠀⠀⠀⠈⡂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⠢⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠢⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠁
⠀⠀⠘⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢠⠋⠀⠀⠀⠉⢣⠀⠀⠀⠀⢠⠀⠲⡎⠉
⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⡄⠀⠀⠘⢄⡀⠀⠀⣠⡎⠀⠀⠀⠀⠸⡀⡀⠆
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠃⠀⠀⠀⣸⣙⠉⠉⢱⠼⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⢴⠘⠣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⢱⠀⢣⡀⠀⣨⠃
⠀⠀⠀⠀⠀⢠⠒⠒⠄⠀⠀⠀⠀⠀⣇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠡⠀⢀⠌⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⠀⡄⠀⠀⠠⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄