Bakery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠄⣦⢲⠆⠀⠀⠀⠀⠁⠀⠀⠂⠄⠀⠀⠀⠀⠀⢤⡄⡀⠀⠀⠙⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⢄⣀⣓⣠⢂⣘⣀⠂⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠘⢧⡀⠀⠰⠄⠀⠀⠀⢥⠁⡔⠊⢀⠄⠀⠀⠀⠘⣣⡔⠀⠀⣀⢄⡟⠂⣄⠀⠈⠁⠀⢹⡋⠀⠀⡈⠉⠁⠀⢙⡇
⠀⠀⠀⠀⢘⠃⠀⠀⠀⠘⠂⢀⣀⣴⡀⢀⠈⠖⢀⠞⠁⢀⡄⠊⠀⠀⠀⠀⠀⠠⣡⠜⢧⢗⡫⠂⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣼⠁⣀
⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⢀⠌⠈⠈⠁⠀⠀⠐⠦⠀⢀⠎⢠⠞⠆⠀⠀⠀⠠⣔⣄⣶⠨⠍⡠⠖⡧⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠀⠐⢤⡆⠀⢧⠀⠂⠀⠀⠄⠀⡅⢤⣥⠔⠚⢀⡠⠆⠀⠀⠀⠙⠠⠤⠄⠠⠤⠤⠂
⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⢤⠀⠀⣀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠸⢗⣸⢩⡍⢮⡛⠀⠀⣄⢶⠆⠀⠀⣀⠀⠀⢦⣆⡄⠈
⠀⠀⠀⠀⡶⠚⠁⢃⣀⣀⠀⣀⠀⠀⠘⢡⠾⣼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠈⠉⠛⠃⠉⠀⠀⠷⡉⠀⠀⠀⠀⠁⠀⠀⠀⢊⢱⡆
⠀⠀⠀⠀⠀⠀⡞⠋⢀⡠⠴⠬⢤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⡦⡀
⠀⠀⠀⠀⠀⠀⠻⣶⠃⠁⠀⠀⠀⠈⠆⠀⠀⣥⠀⡆⡄⢐⢰⠀⡄⢀⠇⠀⠂⢰⠀⠰⣀⠂⡦⢀⠀⠀⠀⠀⠀⠘⢼⣁⠄⡓⣧⢂
⠀⠀⠀⠀⠋⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠉⠀⠤⠐⠳⠁⠬⠸⠄⠇⠨⠤⠀⠀⠇⠱⠐⠻⠀⠗⠀⠇⠁⠀⢲⡦⡄⢩⢽⣶⠲⠨⠇⡰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠠⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠉⠹⢾⣤⡜⠿⢭⠘⣧
⠀⠀⠀⠀⣠⠀⠀⠢⡇⡀⣀⠀⣠⠅⠀⠀⠙⣣⡆⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠎⠃⠀⠀⣄⠀⠀⠀⠀⠘⠳⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⠚⠃⠀⢀⠀⠀⡠⠠⠎⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⢠⡄
⠀⠀⠀⢠⠀⡈⠀⠀⠀⢠⡀⢠⠔⠀⠀⠀⢄⠀⠀⠁⠀⠀⠁⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⢻⣿⣧
⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠉⠲⠀⠀⠀⠀⠘⠀⣴⡀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠻⡿⢤⠂⠀⢠⣿⣿⠃⢠
⠀⠀⠀⠀⠀⠘⡀⢀⠄⠎⠁⡀⠀⠰⠄⠀⢡⣹⠓⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣦⣟⠁⠀⠀⠂⠀⡜⠀⠀⠀⠀⠾⠋⠐⠀⡀
⠀⠀⠀⠀⠀⠲⠈⠈⢀⢀⠉⠈⠀⠙⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢉⣉⣉⣉⣉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠖⠉⠈⣠⢀⣠⠨⠝⠑⢢⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⢾⠀⠘⠢⠄⠀⠀⠀⠀⠀⠠⠤⠊⠀⢸⠶⠦⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⣠⠿⣄⠀⠀⢀⡼⢧⡀⠀⠀⣠⠿⣄⠀⠀⢀⡼⢧⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⢲⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠚⠒⠛⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠿⠅⠀⠠⠀⠀⠀⢀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣂⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠠⠄⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠄⡀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⣔⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⡄⠀⠀⠀⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡠⠠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⣶⠏
⠀⠀⠀⡁⠤⡀⠀⠀⠉⠒⠠⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡀⠀⠤⠄⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠓⢄⠀⠑⠂⠄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠈⠂⠤⣀⠈⠑⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠠⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⡀⠈⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⢀⣀⡤⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠄⣀⢀⠀⢀⣀⣀⣀⣠⠤⠦⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠓⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠲⢤⡀
⠀⠀⠀⡌⡀⠝⠲⢍⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⣄⣡
⠀⠀⠀⢣⠄⠈⡠⢘⠇⠀⠀⠐⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠤⠜⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠚⠛⠙⠟⠋⠛⠂⡀
⠀⠀⢰⠊⢾⡤⠤⢾⡶⠤⠤⠤⠾⠙⢷⡀⠀⠀⠀⠀⠀⢢⣠⡠⣆⣎⠐⢲⡀⣶⡟⠀⠀⠀⠀⠀⠀⠀⢢⠄⣀⣠⠀⠀⠂⠀⡶⠓
⠀⠀⢣⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⠀⡰⠛⠛⠣⢛⠀⠀⠉⠃⠻⠦⠀⠀⠀⠀⠀⠀⠠⢈⠀⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠞⠚⠒⠴⠧⠶⠤⠐⠲⠒⠚⠊⠀⠀⠀⠀⠀⠀⣱⡖⡐⣀⠀⠀⠀⠲⢶⣤⣖⠀⠀⠀⠀⠀⠀⠾⠯⠀⠀⠀⠀⠀⠀⢀⣀⡰⠶
⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠐⠻⡝⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢨⠁⠈⠁⠀⠀⠀⠈⠉⠀⢹⠃⠀⠀⠀⠀⠳⠤⠤⢦⣀⡄⠠⡤⢀⠄⠰⠴⠆⠀⠀⠀⠀⠓⠤⡤⠒⠀⠢⡄⠀⠈⠀⠀⠖⠀⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⢣⠀⠄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠐⠴⠄⡆⠀⡀⠀⠠⠼⠃⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠰⢅⠀⠀⢠⠀⢀⠀⠅
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠘⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠻⣄
⠀⠀⠀⠀⢀⡽⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⣠⣧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢈⡀⣀⠐⠓⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⣆⣻⡀⠀⢶⢾⣏⣛⡈⠈⠢⠀⠀⠀⠀⠀⠀⠊⠉⠁⠠⢶⠖⠚⠉⠉⠱
⠀⠀⠀⢀⢌⡩⠁⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣀⡀⠀⣀⢀⣀⣀⣴⡄
⠀⠀⢀⡁⠂⠂⢠⡀⠀⠀⠀⠁⠀⠙⠂⠀⠀⠀⠀⠆⠀⢠⠀⡄⢀⠀⠄⠀⠀⡀⠀⠒⠀⠀⠀⠀⠈⠑⠄⠈⠀⠉⠋⠙⠻⠉⢄⠀⠘⡀
⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⣄⣄⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠂⠀⠀⠈⣠⠀⡀
⠀⠀⢸⠷⠄⠚⠣⠀⠂⠠⠒⠀⠒⠰⠶⠀⠀⠀⠀⠃⠀⠁⠉⠂⠰⠶⠒⠂⠘⠋⠉⡝⠁⠀⠀⠀⠸⠖⠠⠷⠤⠀⡠⢦⡄⠀⢠⠷⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⠶⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠈⠀⠠⠤⡤⠦⠤⠦⠶⠢⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⢀⡀⣀⣀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡
⠀⢠⡈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠛⠉⠈⠁⠁⡀⠀⠀⠀⢀⣏⠉⠛⠑⠛⠒⠖⠒⠛⠛⠓⠐⢛⣇
⠀⠀⠷⠒⠦⢀⠀⢀⣀⣀⡠⡄⠀⠤⠊⡁⠀⠀⠀⠀⣤⣀⣤⠤⠄⠀⠀⠤⠤⣴⠞⡀⠀⠀⠀⠀⣟⣛⠛⠛⢓⠒⠒⡒⠲⢚⣛⣫⣛⡇
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠘⠁⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠈⠉⠋⠙⠀⠉⠉⢘⠅
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠂⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠊⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠒⠊⠁⠠⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢲⠁⣘⠀⠀⣀⣀⣠⡇⢉⣭⡄⠸⡄
⠀⢀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠜⠀⠀⢀⠀⠀⣀⢈⣤⡖⡦⢖⡞⠀⠇⠀⣾⠙⢯⠏⣿⣯⠽⠁⢠⣷
⠀⠈⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⡐⠁⠀⡰⠁⢰⠏⣽⠀⣽⣛⣿⢈⠃⠘⠀⠀⣧⣤⣄⣈⣀⣀⣠⠴⠫⠃
⠀⠀⠀⠀⠈⠐⠀⠂⠠⠂⠄⠀⠠⠂⠒⠀⠀⠀⢰⠁⣰⣏⡓⠯⠿⢼⡿⠐⠁⢠⠂⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⣷⣂⡃⠴⠔⠋⢀⡠⠒⠁
⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⡝⠓⠢⢀⠀⠀⠀⡜⠀⠜⠉⢁⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠠⡤⠆⠀⠀⠠
⠀⡠⠊⠁⠀⠀⠀⠀⠀⢰⡃⠀⠀⠈⠀⢌⢠⠇⡐⠂⠉⠁⠀⠀⠀⠀⠀⠀⡀⢠⣀⡆⠀⠀⠹⠅⠀⠀⠉⠀⠀⠁
⢰⣁⠀⣀⠀⠀⠀⠀⢈⡸⢻⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⠀⠀⠑⠀⠀⠀⠀⡀⠠⠄⠂
⠙⠀⠀⠀⣱⠤⠔⠊⠁⠀⢊⠀⠐⠁⠀⠀⠀⠀⢀⠄⠒⢖⡃⠀⠀⠀⠈⠀⠀⣀
⠰⡄⠀⠀⠉⠉⠁⠲⠀⠀⠀⠀⠀⡀⣀⠆⠀⠙⠽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠁⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡠⢐⣦⡴⠊⠀⡈⣯⠝⠉⠀⢈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢸⠟⠁⠀⢸⠟⠁⠀⠀⢠⣟⠭⠛⠳
⠀⠀⠀⠀⠀⣀⠠⠤⠤⠀⢀⠀⠀⠀⢀⠠⠀⢒⣀⢀⡐⠒⠀⠄⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀
⠀⠀⡠⠔⢁⣄⣈⣉⠙⠻⠦⣹⠀⡔⠁⢰⢚⣋⣸⣁⠋⣛⣻⢦⠈⠂⠈⡓⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠒⡏
⣠⡊⣐⡶⠦⢤⣌⠉⣳⠔⠋⠁⠀⠀⠀⠀⠀⠿⠠⣤⡤⠭⠓⠁⠀⠀⠀⢠⡁⠀⠀⠩⠉⠉⠉⠉⠉⠁⠄⠀⢀⡼
⢇⠶⠶⢶⡏⢢⡴⠊⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⠊⣀⠔⠁⠀⠀⠳⢮⣀⣀⠀⠀⠀⠀⠐⠀⣐⣨⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢩⡄⠀⡄⠈⣀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠁⠀⠀⣠⠆⠀⠠⠄⠀⠈⣄⣀⢀⣤⡴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⠁⠶⠀⣠⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡄⠀⣠⠀⠀⠖⠀⠀⠀⠄⢀⡾⢂⢀⡀⡀⡂⠀⠠⠒⡁⠐⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠀⠀⠀⡀⠠⠈⢀⡔⠛⡒⠒⠀⠐⠀⠀⠒⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠑⠀⠐⠂⠐⠠⠄⠀⠁⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠴⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠁⠀⠊⠀⠀⠤⠀⠀⠀⠀⠐⠀⠾⡀
⠀⠀⠀⠀⣱⠢⠄⠀⠀⠀⠤⡄⠀⠀⠀⠀⠊⠀⠂⠠⠀⠠⠀⠂⠐⡠⠀⠀⣅⡀⠀⢀⡰⠂
⠀⠀⠀⢠⡏⣈⣀⣀⣀⣀⣐⣋⠑⠀⠀⠀⡻⠔⠀⠀⠀⠀⣒⡢⠽⠁⠀⠀⠸⣵⣈⣷⣄⢤⣠⢤⡅
⠀⠀⠀⠑⠛⠠⠤⠀⠐⠊⠉⠀⠀⠀⠀⠈⠒⠤⠄⣀⣀⡀⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⢹⣭⣭⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠠⣀⣀⠀⠀⠀⠈⠉⣀⢢⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⢸⠂⠀⠀⠀⢀⠠⠊⠀⠙⢈⠖⠂⠠
⠀⢀⠀⢤⣀⣀⣉⠉⠁⢀⣀⣠⡴⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⢠⠎⠀⠀⡠⠀⠁⠀⠐⠀⠂⢀⠌⠁⠂
⠀⠀⢀⠀⡩⠉⠉⠉⠉⠉⣉⠔⠁⢀⠀⠀⠘⠙⢦⠀⢀⡠⠚⠁⠀⠀⠑⠑⠀⠀⠀⢀⠀⡰
⠀⠀⠀⠉⣤⠒⠀⡄⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⣐⠔
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠘⢧⠜⡀⠀⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⢩⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢷⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡶⠛⠉⠀⠀⠁⣱⣄⣀⠀⠀⠀⠀⢸⠀⠀⣈⡻⢃⢸
⠀⠀⢄⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣝⠆⠀⠀⠀⠃⢠⠐⠘⡋⣋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣀
⠀⠀⠀⢀⠔⠈⠹⣁⣀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠢⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠔⠀⢈⠚⠁⠀⠀⡢⢄
⠀⠀⠘⠁⠤⣀⣀⡀⠀⣈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠃⠀⠀⡌⠀⠀⠀⠐⠀⠀⠀⢄⠀⢠⠋⠉⡆
⠀⠀⡸⢄⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⢀⠃
⠀⢰⠒⢘⠁⠹⠉⠉⢃⠀⢹⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠁⠀⡎⣛⣟⢓
⠀⠀⢆⠈⡀⠀⡄⠀⠸⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⠉⠉⡁
⠀⠀⠈⠢⣐⡀⠰⡀⢰⢀⣃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠦⠀⣀⣀⣈⠑⣶⣻⠤⠔⠀⣉⣁⣀⠀⠈⠑⢢⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠐⠀⠀⠈⠐⠀⠠⡀⠀⠀⠀⠀⠀⠓⠋⠣⡐⠢⠄⣀⠀⠀⠀⠉⠰⢆⠀⠀⠉⠀⠀⠀⠀⡇
⠀⠀⢀⢀⡠⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⡀⠈⢁⠰⠃⠁⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⡂⠀⠈⠺⢤⠔⠊⠀⠀⠑⢄⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣀⣀⠇
⠀⠀⠘⣉⠀⠚⠾⠀⠀⡀⠄⠒⠈⠑⢄⠀⠀⠀⠢⠀⠄⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠶⠷⠆
⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠀⠀⣱⢲⡀⠀⠀⠀⠲⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡰⡟⠂⣈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠰⣷⠏⣈⡰⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⡰⠆⠛⠈⢩⠉⢶⠠⡄⠀⠀⠀⠀⠀⠀⠣⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⢓⡈⣅⠠⣆⡒⠃⠁⢠⡴⠂⢄
⠀⠀⡤⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠢⡀⠀⠀⠀⠀⠀⠀⢰⠂⠏⠙⣀⢠⡔⠁⠈⠛⠋⠀⡡⠱⠣⣽⢁
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢠⢄⢀⣀⠀⠘⡆⠀⠀⠀⠀⠀⠰⣇⢙⡁⣡⡌⢀⢤⡔⢲⠎⣉⠝⠃⢜⢘⠀⠆
⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠵⠯⠴⠮⠬⠭⠄⠄⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⡴⠇⡨⠓⢤⡌⢱⠎⣠⠋⢃⠸
⠀⠙⠒⠲⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⢲⠖⢲⠶⠶⠒⠒⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣉⡰⢆⣨⢓⣤⠩⠵⠞⠢⠃
⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠀⠀⠀⣸⣿⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⡀⠤⠀⠠⠄⡀
⠀⠀⠀⢰⠀⢠⠀⡇⠀⢰⡖⢒⣒⣒⣛⣛⣓⣚⣒⣒⣒⣦⠀⢰⣲⣒⣒⣒⣒⣒⣒⣒⣲⣒⣀⣀⢀⠈⡇⠀⡰⢁⠀⠂⠀⠀⠠⠀⠑⠄
⠀⠀⠀⣸⠀⢸⠀⢇⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠈⠓⠲⡀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠐⠸⠀⠄⢠⠂⠉⠁⠢⠀⠀⠈⡀
⠀⠀⢠⠃⠀⢸⠀⠘⡄⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢣⠀⠀⠑⠎⠙⢄⠌⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠇
⠀⣴⠣⠤⠤⠼⠤⠤⠽⠤⠤⠤⠭⠶⠤⠤⠤⠴⠮⠥⠤⠤⡄⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠄⠈⠈⡐⠀⢒⠤⣀⠎⡘
⠀⠱⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠔⠁⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠑⠎⠀⠁⠁⠀⠄⠊
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠖⠋⠉⠁⠀⣏⣉⣙⣛⠳⣶⣴⡏⠁⢤⡁⠛⢲⣤⠖⠋⢉⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⡇⣼⠁⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⢛⡎⣇⠁⣢⣀⣧⣾⣄⠁⠈⠀⢸⡇⠒⠤⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⢠⣼⣿⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣭⣍⡑⣛⣹⣷⣿⡟⢦⣀⠀⣸⣧⠀⠠⠼⢏⠦⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⣿⣷⣋⣉⢻⡿⣟⣳⢄⣀⠀⠀⠠⢤⣴⣫⣾⡟⡏⢯⠹⡇⢹⠈⡇⡟⠀⠈⠉⠛⠁⠀⠀⠵⢤⡼⠗⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣼⣟⣴⢻⡿⠿⠟⠀⠸⠽⢿⣍⠓⢯⣽⣋⣟⢻⣿⡻⣿⣷⣱⠸⡀⢦⠀⡄⠀⢻⡶⠒⢢⡄⠀⣤⠤⣤⣤⠤⢦⣄⣀⣈⣿⣛⡷
⠀⠀⠀⠀⠀⢀⠟⠛⣹⣧⠟⣹⣿⣽⣝⣓⣒⢦⣹⣷⠻⠿⣠⠮⠽⢿⣮⣽⣿⢦⢳⠸⡀⠇⢸⢸⣧⡄⠤⠷⣈⡷⠀⢤⣤⠤⠄⣤⡤⠍⣿⣶⠧⡀
⠀⠀⠀⠀⠠⠋⡰⢾⡟⣡⡞⠉⠀⠀⠈⠉⡻⠉⠉⣿⣛⣿⣿⠾⣟⡟⢋⡿⠿⠷⣷⣧⣇⣠⣸⠞⠻⣦⠤⠎⢵⡷⠴⠋⣌⣷⣾⣄⣵⣮⣼⣗⣶⡿⠷
⠀⠀⠀⣤⣾⣋⡹⠯⢾⣉⡩⣶⣄⠀⠀⣠⢶⡀⢸⡿⠿⠷⠶⠤⠚⠛⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠹⣦⣤⣤⠖⢶⣤⣯⣭⡀⡟⠀⠀⠉⠉⠛⠲⠾⢄⡀
⠀⠠⠞⠉⠛⠓⠒⠛⠻⠋⠉⠛⢙⡇⢠⣏⣾⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠾⡗⠛⠛⡇⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⢷⠒⠲⠶⠶⠶⠶⠖⠚⠚⢿⡇⠀⠈⠁⡞⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠂⢀⡤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢰⣦⢿⣷⠀⠀⠀⣰⠀⠀⢀⡞⠁⣤⡀
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡸⠁⠀⢀⣴⠖⠙⠋⠂⠀⠀⠀⣼⠃⠀⡾⢁⠂⢀⡀⠀⠀⣀⠀⠀⠀⠀⠈⡄⠹⡎⣿⡀⢀⡔⠋⠓⠒⠶⣷⣚⠅⡇
⠀⠀⢈⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣷⣤⡤⠃⠀⣰⡟⠁⠀⠀⠀⠀⠀⣀⢰⣯⠀⣸⡗⠂⢰⠏⠀⠀⡾⠁⠀⠀⠀⠀⠀⠹⠨⠡⣹⠟⠀⠕⠒⠀⠂⠀⠚⠻⣏
⠀⠀⢸⡋⠉⠉⠉⠉⡉⠩⢿⡀⡟⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣴⠏⠉⢹⢁⠀⣿⠀⠀⠹⠀⠀⠸⡇⠀⠔⠁⠀⠀⠀⠀⣇⣴⡗⠀⠂⢀⠈⠀⠈⠀⠀⣶⣿
⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⣼⣯⣵⡏⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠛⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⣀⣀⡴⢦⡾⠻⣦⡿⠘⡇
⠀⠀⠘⣷⠖⠛⠉⣋⠀⠀⠈⠀⠈⠉⠓⠦⡄⠀⠀⠀⠀⠀⢀⣶⢹⡄⠀⠀⠁⠀⠁⢀⡾⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣍⡩⣴⣞⡶⣤⣪⠔⠠⣿
⠀⢠⡞⠀⢀⣀⣨⠤⠴⠒⠲⠒⠢⣤⡄⠀⠈⡄⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⠀⠀⢀⣾⠁⢀⡴⠁⠃⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢉⠟⠛⣆⡸⢝⣡⡷⠞⠁
⠀⢾⠀⠐⠀⠙⡛⠒⢚⣛⡛⠛⠉⠁⠀⢀⠴⡇⠀⠀⠀⡠⠼⣿⢀⡤⠀⠀⠀⠀⣼⠇⢀⡿⠀⠀⢸⡑⣿⠀⠀⠀⠀⠀⠀⣠⡆⣀⣀⣬⠁⠀⢼⡿⠋⣡⠖⢛⣷
⠀⠀⢷⠒⠉⠒⠦⠚⠉⠀⠉⠢⠐⠉⠑⢎⣼⡀⠀⠀⡞⠁⢀⣿⡞⠁⠀⠀⠀⢠⡟⠀⠈⠿⠄⠀⠀⠀⢧⠀⠀⠀⠀⢠⠯⢿⡏⠁⠒⠛⠓⠛⡿⢁⣜⣻⣦⠴⠃
⠀⣠⣼⢷⡤⣄⣠⣤⣶⣶⣶⣲⣶⣶⣖⣋⢏⡽⡀⠀⠁⠀⠉⠻⠃⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⣾⣦⣤⣄⣀⣀⣸⣧⣾⣾⠥⠴⣶⡆
⠀⠙⠈⠙⢿⠿⠿⠿⠟⠛⠛⠁⠈⣃⢨⡿⠛⠙⢯⡖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢰⣄⠀⠀⠀⠀⠀⠀⡀⣠⣟⣇⢠⡟⢭⠉⣿⠟⡾⣏⠑⣶⠋⠁
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢰⣿⣾⣴⠓⢒⣿⢑⣾⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠟⠞⠣⣈⡲⢿⠛⠃⡔⠑⠓⠶⠿⢿⡿⢦⣾⡿⣸⢣⡌⢟⡅
⠀⠀⠀⠀⠀⣨⢶⡄⢀⣀⣠⡴⢚⣙⣥⡿⠉⠭⠉⠉⠻⡖⣰⡆⣶⡍⠲⡄⢠⡦⠵⣿⠓⢺⠒⢺⠃⠹⠃⢸⠄⡸⠁⠀⠦⠀⢀⣼⡧⠈⡼⢁⣿⡿⠖⠉
⠀⠀⠀⠀⠀⠳⠌⠠⠤⢻⣷⠞⠛⢉⣸⠃⠀⠀⠀⠀⠀⢷⢌⣀⣘⢰⠀⢙⣼⠻⡇⠈⡆⠘⠀⠀⠆⠀⡄⢸⡔⠀⢀⣄⠀⠀⡘⣹⠟⠊⠛⠛⢯
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠛⠉⢈⣄⣦⠀⠀⠀⣠⠖⠉⣹⠀⣌⣽⠶⠛⠛⠛⠻⢦⡸⢤⣧⣀⣤⣤⣷⣿⣁⡀⠀⠀⠀⡄⠀⡿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠰⠷⠛⠉⡟⠀⢹⠰⡟⠰⠂⠀⢉⡰⠿⠁⠀⠀⠀⠀⠠⠶⠷⣾⣯⢩⠁⣤⠰⡟⢣⣤⡙⢛⣚⣯⠺⠁⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⣼⡀⣀⠷⠊⢀⡇⠑⡶⠂⣹⡿⢁⡗⠀⠀⠀⡠⠀⠀⠀⠀⠈⡇⠀⠀⢰⠀⢸⡀⠿⢠⡏⠝⢩⡗⠠⠤⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣁⣀⣀⠾⠢⠤⠌⠒⣸⢏⠘⣀⣃⠀⠀⣰⠁⣀⣤⡴⠒⠛⣧⠈⠀⠘⡀⠀⣡⠈⠀⠛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠀⠀⠀⠈⠣⡀⡟⣿⣻⠟⢶⡛⠛⠋⠉⠛⠣⣀⡼⠟⠓⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠉⠁⠀⠀⠐⠒⠒⠉
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⠶⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠄⣲⣶⠀⠀⠀⠀⠀⠀⠀⠂⠄⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠉⠄⠈⠉⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠐⠈⠁⣀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⢃⣄⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣠⠄⠁⠀⠷⠂
⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢈⡀⠠⣶⠄⠀⠸⠏
⠀⠀⢠⣀⣤⣀⣀⣀⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠈⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈

⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠒⠚⠉⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠟⠛⢻⢿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠲⠦⣄⠀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠁⠢⢤⡀⠈⠑⠀⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡇⠀⡀⠊⠛⠿⠶⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣰⠁⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠤⠖⠋⠁⠀⠀⠙⠦⣤⣄⣀⣀⣀⣤⣤⣤⠶⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠖⠂⠀⠊⢹⡆
⠀⠀⠀⠀⢀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃⠀⠀⠀⠀⢴⡄
⠀⠀⡀⠀⠀⠀⠉⠛⠿⣴⣤⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠑⠂⠀⢀⠆⠀⠀⡜⠀⠀⣰⡇⠀⠀⠀⣽
⠀⠀⠿⣷⣦⣄⢀⣀⠀⢠⣄⣉⣉⣽⡟⠃⠀⠀⠀⠀⠠⢤⡀⠈⠑⠀⠀⠀⣀⠤⠒⠋⠁⢀⡴⠇⢣⡀⣠⠈⠀⠀⠀⢨⠏
⠀⠱⣦⣄⣀⠉⠈⠛⠁⣼⠅⠀⠈⠁⠀⢀⣀⠐⠒⠒⠄⠀⠀⢀⡀⠀⠒⠉⠀⠀⠀⠀⠀⢸⠀⠀⠠⠑⠇⠀⠀⢀⣠⠁
⠀⠀⠀⠉⠉⠂⠛⠶⠀⠋⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⣆⢠⡞⠉⠀⠀⠀⡸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢇⢀⣿⡬⠁⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠁⠀⠈⠙⠒⠠⢀⠀⠀⠀⠀⢺⣿⠀⢀⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣠⡄⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⠀⠀⠀⠻⠿⣿⣯⣛⠲⢤⣀⡀⠠⠀⠀⢉⡇⠀⠀⠀⠀⠀⣠⠤⠠⠄⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠉⠛⠿⢶⣏⢁⣤⠤⠒⠋⠁⠀⠀⠠⠂⠀⢤⣀⡀⠀⠀⣸⠶⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠚⠉⠹⣛⣿⠁⠀⢸⠄
⠀⠀⠈⠳⣤⣤⣀⣀⠀⣀⣀⣀⣀⣴⠎⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⡆⠀⠀⠀⢸⠃⠀⢀⡾
⠀⠀⠀⠀⠀⠉⠙⠛⠒⠂⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⢠⡀⠄⠀⠁⠀⠀⠀⠀⠀⠈⠳⢠⣀⣤⣤⠝⠛⠉

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠰⠼⠏⠀⠙⣀⠀⠀⠀⠀⣂⠀⠀⠀⠠⠀⠀⢀⢶⣅⠀⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠞⠉⠁
⠀⠀⠀⠇⠀⠀⠀⠀⠋⠀⠀⠂⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠒⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⠁⠃⠘⠒⠂⠀⠀⠚⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⣠⠀⠀⠀⠀⠧⠀⠀⠀⠆⠀⠰⠀⠀⠁⠀⠀⢀⣤⣶⣶⡀⠀⣸⡄
⠀⠀⠀⠀⢀⠘⢒⠦⡀⠀⡀⠀⠀⠀⠉⠉⣤⡀⠀⣠⠀⡄⢀⢠⠀⠀⡤⢀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠀⢤⠉⠓⠂
⠀⠀⠀⠀⠿⠤⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⣇⡗⢰⣻⡆⣧⠎⢸⣤⠄⣇⣸⠸⣆⠆⣠⡤⠀⠀⠀⠠⢄⡀⠀⠀⠙⠂
⠀⠀⠀⠀⠄⠤⠤⠒⠈⠁⠀⠀⠀⠀⠼⠀⡇⢹⢼⢸⡇⡏⣇⢸⠀⠀⡏⢳⠀⣿⠀⢻⣄⠀⠀⠀⠀⠒⠭⠔⠒⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠭⠤⠤⠧⠥⠬⠬⠭⠤⠥⠬⠤⠄⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠉⠉⡲⠈⠁
⠀⠀⠀⠠⠀⠂⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠄⠂⠀⠄⠀⠀⠠⠄⠒⠂⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠉
⠀⠀⠀⢀⡠⣤⣀⣀⡁⠀⠒⠀⠀⠀⠀⠀⠠⠊⠀⠀⡀⠐⠒⠈⠀⠐⠤⡀⠀⠈⠁⠒⠒⠀⠠⠤⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠋⠀⠘⠋⠁⠿⢿⠿⠊⡴⠤⠤⢤⠀⠀⡠⠎⠉⠉⠉⠐⢄⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠒⠔⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠠⠄⠤⠤⠐⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡬⠥⠴⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡀⣀⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀⡸⠣⠴⠒⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠛⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠞⣛⠩⠀⠀⣀⣀⣄⣀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠭⠭⠅⠐⠒⠂⠉⠁⠀⠀⠀⢸⠁⠀⠀⠀⠙⡆⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣠⣴⠟⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠟⠛⢉⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠳⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⣠⠤⣔⠊⠉
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠙⢦⡙⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠂⢄⠀⠉⠓⢄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⢴⠖⠉⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢳
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠬⠭⠭⠭⠭⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⠤⣀⣈⠁⠒⠂⠠⠤⠄⠀⠤⠠⠤⠀⠠⠤⠀⠐⠒⠈⢁⣀⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠤⠶⣄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠈⢄⠠⠀⣤⡶⠿⠀⣪⣍⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣱⠄⠩⣠⡀⠀⠈⠉⠓⠾⠛⠂⠀⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠉⠛⠧⡀⠀⠀⠀⠀⠀⢤⣌⣡⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⢰⢤⣴⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠺⢷⣌⠻⢷⣦⣬⣀⠀⠀⠀⢁⢀⠸⠀⠀⠀⠙⠛⣿⣿⢿⢻⣳⠂⣾
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠓⢹⣿⠛⠛⠛⠛⠒⠂⠉⠹⠀⠀⠀⠀⡀⡙⣿⣅⣾⢱⣼⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⢰⠰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠶⠛⠁⠀⠀⠀⢶⣶⡄⡄⣄⢠⡠⡀⣈⢑⣂⣛⠥⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣦⠤⢮⢹⡜⣿⣺⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠯⠽⠞⠓⣿⠉

⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣤⣤⣤⣤⣀⡀
⠀⣾⣟⡯⠍⠓⠒⠒⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣽⣿⣧
⠀⣿⠈⠉⠻⠓⠒⢶⣶⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⣶⣶⣶⡶⠟⠛⠉⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣠⣤⣤⣀⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠟⠋⣉⣉⣉⣙⠻⣷⣄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠟⠋⠉⠉⠛⣷⡌⢿⣆
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠃⠀⠀⠀⠀⠀⠘⣿⠸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⡿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣼⡟⢠⡿⠃
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣠⣾⠋⣰⡿⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣠⣴⡾⠋⣡⡾⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠛⠋⣁⣴⡿⠋
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣴⡾⠛⠁
⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁
⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣽⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⡭⠵⠖⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣍⣓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⢀⣀⣠⣤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠶⠤⢤⣄⡀⠀⠉⠛⢦⡙⢦
⠀⠀⠀⠀⠀⢠⡏⡏⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠉⠙⠲⣄⠀⣿⢸⡆
⠀⠀⠀⠀⠀⢸⣇⢣⡞⠉⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠋⠀⡤⠤⡄⢹⡀⠀⠀⠀⠀⠀⢀⡿⣡⢾⡇⣀⣤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⢸⡈⠳⣌⡳⢤⣀⡀⠀⠀⠸⡄⠀⠀⢰⠖⠒⠚⠁⠀⢹⢸⡇⠀⢀⣠⡴⢞⣡⠞⣡⠞⠋⠁⠀⣀⣀⣀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠓⠮⣍⣛⠒⠶⠿⠦⢤⣬⣷⣤⣤⣤⠤⠿⠾⠒⢋⣩⡤⠖⠉⠀⠀⣧⣀⡤⠖⠋⠁⠀⠉⠙⣦⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢧⣄⣀⣀⣀⣀⡤⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠈⠉⠉⠁⣀⡠⠔⠋
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠻⣍⠛⠋⠉⠉⠁
⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢸⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⣌⡙⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⣋⡥⠞⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⠤⠤⠤⠤⠤⠴⠶⠒⠋⠉⠀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠙⠪⣝⡲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣚⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠺⠭⣍⣓⣒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠴⣖⣒⣻⠭⠷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠙⠛⠛⠛⠛⠻⠿⢿⣿⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡭⠶⠶⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠉⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠉⠁⠀⠀⠀⠛⠛⠛⠲⠶⠶⣤⣤⣀⣀⠢⣄⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣁⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠉⠁⠀⠐⠒⠛⠲⠶⢦⣤⣈⣉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢼⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠉⣭⣉⣙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⣬⣍⣛⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠉
⠀⠀⠀⠀⠰⠋⠠⠖⠚⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣶⡄⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⢀⠀⠀⠀⠘⠓⠶⣤⣀⠈⠙⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠷⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⢠⡤⠭⠀⠀⠀⠀⠀⠀⠀⠭⠄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠒⠀⠀⠀⠁⠀⠀⠀⠈⢉⠆⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠠⠊⣿⣿⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠃⠀⠀⠀⠀⠱⠒⠉⠙⠲⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⣀⡀⡀⢀⠁⢀⡀⢀⡀⢀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠤⢈⠈⣠⢍⣀⢡⡀⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⠀⠀⠼⠄⢀⡁⡇⠀⢸⠀⠄⠀⠀⠀⡆⣂⢠⣠⡇⠀⣀⠀⠀⠀⠒⢰⠀⡈⠸⢄⢘⡇⠤
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠈⣀⡀⠉⠠⠁⠊⠁⠀⠀⠉⠀⠀⠀⠀⠀⠈⢠⡄⠈⠉⠈⠁⠈⠁⠀⠄⠁
⠙⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠐⠛⡛⠈⠄⠂⠀⠀⠐⠒⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⢰⠰⠈⠉⠀⠀⠀⠀⠠⠀⢀⠀⠸⠂
⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠶⢆⠀⠀⠀⠄⠀⠠⠤⠀⠀⠀⢀⡠⠄⠠⠀⠀⠀⡠⠐⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣠⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢨⣦⣉⣁⠠⡍⠁⠄⠀⠈⠉⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⣀⠠⠐⠊⠉⠀⠀⠍⠹⢻⡇⠴⠿⠖⠀⠀⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠐⠶⣶⣀⠀⢀⠀⠀⠄⠀⠀⢀⠈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠌⠀⠀⠀⠠⠆⠒⢦⠀⠄⠀⠀⢒⠀⠠⢀⢄⡏
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠲⠤⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢴⠀⣀⢩⠓⠠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⠁⠀⡾⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠇⠀⣸⠃⠀⢠⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡟⠀⢰⠇⠀⢠⠏⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠖⣾⠀⢸⠃⠀⡿⠀⢠⡟⠀⢀⡏⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣭⠴⠒⠀⠀⡏⠀⣿⠀⢸⡇⠀⢸⠁⠀⣼⠀⠀⠠⣌⣙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢾⣿⣶⣞⣋⣥⣤⣿⣤⣿⢠⣼⡇⣤⣼⢠⣤⣿⣀⡀⠒⠦⣭⣛⠆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠈⢉⣠⠟⢑⣶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣍⠓⠂⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⣉⣀⣤⡴⠾⣛⣵⡆⣚⣛⠧⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢋⣉⣉⣭⣴⡶⠿⣛⣭⠀⠉⠉⠙⣾⡇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠃⢸⣟⡳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣉⣉⣥⣴⡶⠿⣛⡅⠈⠑⣂⡴⣻⡣⢠⡏
⠀⠀⠀⠀⠀⢀⣤⠞⣋⡥⢒⡠⠄⠀⠀⢻⣟⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣉⣉⣉⣩⣭⣴⠶⢟⡋⢡⣞⣛⣽⣾⢟⣵⠟⢶⣄
⠀⠀⠀⠀⣰⠟⣡⡞⢡⡞⢉⡴⠊⡀⠀⠈⢿⣟⠒⠄⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣭⣭⣴⡶⢿⡛⢡⡿⢿⣛⣭⡶⠛⠁⣀⢢⡈⢷⡄
⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⡀⢾⡀⠀⠀⠀⠻⣯⡒⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣭⣥⣤⠴⠶⣞⡛⣱⣿⣿⣿⣿⣿⢿⡌⢳⡈⣆⢳⠈⡇
⠀⠀⠀⠀⠻⣆⠹⣧⣌⠳⢮⣛⠶⣬⣁⠀⠀⠀⠈⠻⣥⣄⣀⠀⠀⠀⠀⠀⠤⠤⠶⢶⣶⣾⣿⣿⣿⣿⣿⢸⣿⡜⣿⢎⡇⢸⠇⡏⢀⡼⠃
⠀⠀⠀⠀⠀⠈⣳⣮⣙⠷⣦⣍⣙⠓⠦⠄⠀⠀⠀⠀⠈⠙⠻⢯⣿⣛⣛⣛⣛⣛⣯⣽⡿⠿⢛⣫⣵⡿⢋⣾⠟⣰⠟⠘⠁⢋⣠⣶⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠨⠽⠿⠶⢮⣭⣙⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠽⠷⠶⠶⠶⣚⣛⣋⣭⡵⠾⠛⢁⣈⣡⣤⣶⣾⣿⣿⠿⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣹⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣟⣛⣛⣛⣛⠛⠛⠛⠛⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⣩⣭⣭⣭⣭⣭⣭⣉⣉⡉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠐⡃⢀⡬⠑⣦⠀⠀⠀⠀⠀⠐⠐⣀
⠀⠀⠀⢦⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠅⠀⠇⡡⠀⠀⡀⠀⠠⠤⠖⠁⠈
⠀⠀⠀⠀⠉⠛⠛⠿⠧⠀⠀⠄⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀⠾⠂⠡⣮⡭⠝⢃⡐⠷⠦⠀⣀⡁⠀⠀⠀⢀⠀⠠⠄
⠀⠀⠀⠨⠵⢦⣄⣠⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠓⢠⣀⠀⠐⠛⠻⠁⠴⠦⠬⠍⠉⠴⠖⠂⠁⠠⠀⠀⠄⠀⠢⠦
⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠿⠀⠘
⠀⠀⠀⠀⠰⠠⠀⠲⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⡀⠀⢂⠀⠀⠀⠐⠦⠤⠄⠀⠀⠀⠀⠀⠁⢀⡤⠀⠀⠀⠠⠐
⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⠸⠈⣁⠀⠀⠄⠇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠆⠀⠀⠄⡀⢀
⠀⠀⠀⠠⣄⠀⠑⠀⠀⠀⠢⡅⠠⠐⢀⢄⠀⠀⠑⠖⢂⣈⣀⠴⠁⢴⣿⣿⣿⢿⣾⣶⣄⠀⠀⠀⠈⠉⠓⠂⠀⠄⠀⠤⠀⠜
⠀⠀⢠⠀⣈⠉⠓⠦⡀⠀⠀⠈⠂⠀⠀⠀⠠⠒⠢⠀⠀⠀⠀⠀⠀⠈⡙⣿⣿⣶⣿⣏⣿⠆
⠀⠀⠸⠀⠀⠀⠀⢀⡐⠄⠀⠀⠀⠀⠀⠑⠤⣄⡉⠉⠡⠦⢄⠀⠀⠀⠈⠁⠀⠠⠬⠙⠉⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠉⠒⠦⣀⠀⠈⠑⢄⠀⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠑⠀⠈⠳⡤⠀⠈⠉⠒⠠⠀⠀⠀⠀⠐⠃⢀⠀⠀⠀⠀⠀⡈⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⡇⡘⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠖⠁⢀⠀⠀⢰⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠁⠀⠀⠀⠀⠀⠙⠛⠋⠉⠙⠛⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⣠⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠂⠊⠉⡍⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⢈⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⡐⠘⠀⠀⠀⠰⢈⠘⠀⠀⠀⠀⠸⠀⠤⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠑⠆⠐⢀⠀⠀⠀⢍⢢⠘⡀⠀⢠⡈⠜⠀⠀⠀⠀⠇⡁⠜⠀⠀⢀⠰⠀⠔⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠁⣀⠁⡀⢰⡀⠀⢨⠐⡔⢀⠀⢄⠘⡐⠂⠀⠀⠀⢘⠡⠂⠀⢠⠈⠠⠊⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⣄⢸⢄⠀⠁⢂⠘⡀⡎⠱⠁⠆⠀⢠⠉⠎⣠⠀⢠⠀⣆⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠈⢦⠀⣇⠑⠠⠀⢇⠘⢀⠇⣰⠀⡈⢡⠉⡀⢰⡇⢡⠅⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠐⢴⠈⡷⠄⡃⢸⢳⡀⠆⢁⢀⠃⣰⠂⣡⠊⢁⡄⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⢄⠛⣆⠱⠋⣧⠘⡀⠞⢸⡄⣣⠊⡁⠀⡬⠂⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⠘⣄⠛⠀⡅⠀⠃⠰⡇⠘⠁⠨⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠃⣌⢀⠀⠃⠀⠈⢠⠃⠄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠐⡆⠀⡄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⡀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣻⣻⣻⣻⣛⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣟⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣡⠶⠋⡹⠋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣠⠞⠂⠀⣼⠁⢠⠀⠀⠀⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠛⠀⠀⣴⢃⣠⡦⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠂⠀⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⡤⠚⠀⣠⣦⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢾⠆⠀⠀⠀⠀⠀⠀⠌⠃⠀⠁⠈⠉⢒⡆⠀⠙⣿⠀⡆⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠳⣤⢀⡉⠻⠀⢇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⡿⠀⠀⢠⠗⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠱⣤⠦⠈⠢⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠏⣰⡿⠚⠁⠰⠟⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠉⠻⠆⠐⠶⠚⠾⠃⠀⠀⠶⠀⠀⠒⠛⠉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠠⡟⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣦⡀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⠈⠁⠀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣧⠀⠀⠶⣦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠉⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠐⠒⠲⠚⠀⠀⠀⠀⠀⠀⢀⣤⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣶⣶⣶⣶⣶⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘






⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣾⣶⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣻⡟⢿⡿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡤⠑⠛⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⣦⣀⡴⡤⢄⣐⣒⡒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠂⠀⠀⠐⠒⠲⢦⣤⣀⠀⠀⠀⠀⢀⣬⡉⣀⣐⣂⣐⣒⣒⡂⠀⡒⠒⠒⣒⠂
⠀⡼⠀⣿⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⣤⣀⠄⠂⠠⡀⠀⠀⡀⠲⢰⣹⣿⡆⠀⠀⠀⠛⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⡿⣭⣭⣭⣭⣭⣉⠉⠂
⠀⠀⠀⠩⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡚⠿⠭⠿⠍⠁⠉⠁⠉⠉⠉⣹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⢰⠚⠀⡡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠁
⠀⢸⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠛⢿⢶⣶⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⣿⡄⣤⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢈⠀⠀⠀⢀
⠀⠀⢻⠁⠻⣿⣿⣿⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡇⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠉⠁⠀⠈⠉⠉⠠⢀⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡄⠀⠀⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⠀⠀⢀⣀⣀⡀⠀⣀⣠⣔⣀⣀⣀⡄⠀⣀⢀⣀⣠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡄⠜
⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠰⠶⠦⢶⣀⣴⣿⣿⠿⡿⠯⣻⠿⠖⢿⢿⡽⢿⣿⡩⣖⠀⠙⠛⠈⠉⠒⢤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡚⠉⣽⠋⢉⣴⠞⢁⡾⠀⣸⠃⢺⡅⠹⡄⠓⡌⠠⠍⡠⠀⠀⠀⠀⠀⠈⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣶⠿⠋⠁⣸⠟⠁⣠⡿⠁⠀⣿⠀⣺⡇⠀⢿⡀⠹⣦⠀⠈⣤⠂⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⣴⣾⡟⠛⠁⠀⣼⣿⠋⠀⢰⣿⠁⠀⣸⡿⠀⣿⡷⠀⢻⡇⠲⣿⡮⠀⠻⠃⠤⢀⠷⠀⠙⠒
⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠛⠁⠀⠙⠓⠀⠊⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢶⣿⣿⡿⠛⣿⣿⠛⠛⢷⠶⠶⠶⢦⣤⣀⡀
⠀⠀⣠⡶⠻⠉⠈⠀⠀⠠⠆⠁⠀⡀⣀⠉⠀⠀⡀⣿⠿⠓⠒⠶⠤⠉⠛⠷⣦⣀
⠀⣸⠟⠀⠪⠀⠀⡀⠀⠀⠀⠀⠈⠀⠉⠀⠠⠨⠀⠀⢀⣤⡴⠶⠛⢛⡛⠛⠛⠛⠿⢶⣄
⠀⣿⡌⠀⠀⡁⡜⡍⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡩⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠠⠙⣧
⠀⢻⣷⣾⡆⣠⢰⢸⢰⢾⡜⡎⢀⢀⢬⠡⠠⣸⡏⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢻⠟⠿⢿⣿⣾⣿⣿⣿⣿⣧⣿⣾⣀⠸⣿⡇⠀⠀⠀⠀⠅⠀⠁⠀⣀⣀⣀⣀⡀⠀⣾⠃
⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣶⣿⠿⢛⡉⠉⠉⠙⠻⣄
⠀⠀⣸⠇⠂⠀⠀⠀⠀⠐⠀⠄⠐⠂⠦⠄⡈⠉⠙⢷⡰⡠⢠⣿⣿⠟⠁⠀⠀⠁⠀⠀⢀⣠⣽⡷⠟⢛⡉⠉⠩⠛⠳⣄
⠀⢀⣿⢀⡀⠰⠀⠃⠰⠀⠐⠀⠄⠀⠀⠀⠀⡄⠀⢨⣷⠀⣼⠿⡇⡄⠠⠀⠀⠀⢉⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢂⠀⢸⡇
⠀⢼⣯⣼⡗⣆⢀⢀⠈⢡⠀⠀⠀⠀⠀⠀⢰⢀⡖⢾⢹⠀⢸⡆⢡⡱⠀⠀⠀⠀⣾⢻⡇⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠿⢿⣿⣿⣿⣷⣼⣰⡄⣴⡇⣀⠀⢸⢨⢻⣿⣿⠀⠀⠻⣿⣿⣶⣤⡐⠀⢿⡸⡄⠄⠠⠀⢀⠀⠀⠀⠀⠈⠐⠘⣇
⠀⠀⠀⠈⠉⠉⠛⢿⣟⣿⣿⣧⣿⣧⣿⣷⣧⣾⣿⣿⣯⠀⠀⠀⠈⠻⡏⠙⡇⠀⡈⠻⢿⣦⣄⡀⠀⠀⣀⠀⠁⠒⠂⢀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠩⠭⠭⠭⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡹⠀⠀⠀⣀⣠⣿⣦⣵⢣⡀⠀⠀⢻⠛⢻⠀⠀⠒⠃⠀⠀⠀⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠲⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⣝⣂⣀⣸⣷⣼⣇⢀⠀⠀⠀⠀⠀⠀⠀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣛⣻⡟⠛⠛⠛⠛⠛⢻⣿⣿⣦⣓⡀⠀⢀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠀⠀⠀⠶⠰⠒⠆⠐⠐⠂⠐⠐⠰⠀⠀⠂⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢁⠈⠀⠀⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠂⠀⠈⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⢺⡀⠀⢁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⣹⠀⠀⣏⠉⢵⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢋⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠒⠡⠐⢧⠀⠱⣀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣀⡀⠀⡈⡗⢤⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡜⢀⢊⠐⠁⠀⠀⠀⠑⢤⡈⠑⠂⠷⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠴⠊⠉⠀⠀⠀⢀⠻⠲⡐⠄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⡼⠉⠑⠂⠠⠀⢤⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠡⠁⠀⠀⠀⠀⠀⣠⠞⠀⠃⠀⢨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⡈⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢒⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣁⠤⠖⣒⠼⠶⠶⠦⠤⠶⠚⠁⠀⠀⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠠⠆⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⣠⠴⠶⠒⢉⣡⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠌⡁⠂⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠉⠀⠀⠔⠊⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠴⠒⢈⠠⢐⡮⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠀⠈⠉⠁⠒⠒⠀⠤⠤⠤⠤⠤⠤⠠⠤⠤⠶⠶⠾⠛⠛⠓⠊⠉⠉⠠⠀⠂⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠃⠐⠒⠒⠒⠒⠒⠒⠒⠂⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⡀⠘⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠈⠁⠀⠘⢿⣦⠈⢻⡇⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣳⣄⡀⠀⠈⢷⢷⡄⠙⡄⠘⡟⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠙⢮⣿⣦⣀⢀⠙⢿⡄⠈⢂⠻⡄
⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⡉⠢⣄⡀⠠⣈⠛⠿⠧⡉⠂⠈⠂⠀⠁⠁⠀⠂⢀⣠⣶⣦⣤⡄
⠀⠀⠀⠀⣠⣯⣿⣿⡟⣧⣟⡋⠁⠀⣛⢦⡀⠉⠒⠤⢌⣐⠤⣀⠀⠀⠀⢀⣴⣿⣯⣿⣿⣿⡾⢻⣷⡐
⠀⠀⣠⣾⣿⣿⣿⣟⣟⣿⢿⠱⡂⠄⠀⣠⣼⡽⠻⡤⢀⡶⡉⠐⠙⢂⡤⣿⣻⣿⡿⢿⣿⡻⡿⣙⠾⠯⡇⣄
⢠⡿⢿⣭⣍⠿⠓⢆⡩⠻⠴⠀⢃⡤⢿⣽⡛⣷⠿⣽⠋⡓⠚⣯⢶⣿⣷⣿⣹⣿⣟⡻⣽⢠⣼⣷⣿⡟⢷⡴⣱
⠐⠋⠁⡈⠂⠡⣁⡀⠀⠉⣤⢾⣽⣿⣿⣧⣏⣹⣿⣩⠸⠄⠘⢖⠻⠾⠾⣿⣿⣿⢿⡵⢶⣦⣭⣵⣬⠻⡯⠗
⠀⠀⠀⠈⠁⠀⠀⠄⠰⠍⣿⢽⣾⢳⡾⣷⣾⣿⣿⣿⡧⠀⠢⠌⠲⣀⢀⠉⠇⠂⢬⣶⠃⠰⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠻⡏⢩⡿⣿⣎⠓⢤⡉⠯⡤⠀⢯⠀⠴⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣄⣠⠤⠤⠶⠶⠶⠦⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⣠⣴⣶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⢭⡝⠉⠀⠀⠞⡡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⣤⡀⠀⢀⣀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠈⢠⠏⠀⠀⠰⢁⠜⠀⠀⠀⠀⢀⠰⠂⠀⠠⠒⠋⣉⠁⣠⣤⣤⣄⣀⣀⠀⠉⠂⠠⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢠⡇⠀⡀⠠⢀⠎⠀⠀⠀⢀⡴⠋⠀⠂⠀⢀⡢⠔⢛⣉⠁⠠⠀⠀⠀⠠⠉⢲⣬⡀⢤⡀⠘
⠀⠀⠀⡠⠊⠁⠀⡏⠀⠀⠆⣾⠀⢠⠁⢀⡞⠀⠀⠀⠀⡚⠁⠀⠀⣠⠚⠥⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡄
⠀⠀⣸⠁⠀⠀⠐⡇⠀⡀⡆⣿⡁⣾⠠⢸⠃⠀⠀⠀⠈⠀⠀⠄⣼⠗⠁⠀⠠⠀⣀⡀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠢⡜⣧
⠀⠀⢻⢠⠀⠀⠀⣧⢂⣥⣄⣿⣧⠙⠸⣿⠀⠀⠀⠀⢠⠀⢆⡾⠃⢠⣔⡁⠐⠋⣁⠀⠀⠀⠀⠄⠀⢄⡀⠀⠂⠀⠠⡘⠼
⡀⣀⢉⣯⣀⡁⣘⡜⢯⣿⣿⣿⣇⠈⢸⣿⠰⠀⠀⠀⡄⣰⡾⠁⢠⡿⠋⣠⠖⡈⠡⠄⢂⣀⣀⣀⡀⠀⠠⠀⠢⣄⠠⡹⡄
⠀⠀⠀⠀⠐⠋⠙⠻⠾⠿⢶⣬⣿⣧⣘⣿⢘⢨⣨⠸⠃⣿⡧⢠⠏⣠⠂⣴⣯⠵⠚⠋⡉⠁⠀⠀⠈⠩⢓⠤⡰⡌⢧⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠌⠭⠻⣿⠟⢿⣿⣷⣤⢰⠀⣟⢠⢏⣾⣣⠞⠉⠠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⢿⡈⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢚⠂⣿⣿⣿⢸⠀⣿⡏⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⡘⠋⢸⡄⢻⣇⡟⢠⣠⠄⢈⣁⡠⠤⠄⠀⠀⠀⠀⠠⠀⠀⢀⠰⡌⣛⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢡⡷⢴⣿⣥⣾⣿⣱⡟⣡⢞⣯⠖⠂⠈⠉⠀⠠⠌⠐⢦⡀⠳⠀⢃⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⢘⠛⣿⣿⢰⢣⡟⠡⠂⠀⠀⠀⠀⠀⠀⠉⠀⠙⣦⢸⡼⡟⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠽⢿⣿⢿⡿⠖⠚⠀⠀⠀⠀⠀⠀⠄⠀⢢⠘⣿⡇⠈⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⠟⠛⠟⠓⠲⢄⠀⠈⠂⠠⠸⡆⣸⢠⣟⣥⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⠀⡈⣇⠀⡷⢐⠀⠁⣩⠟⡛⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⠀⡀⢀⢨⢄⡇⣿⣼⣃⣞⣠⠾⠯⠠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣬⣑⣋⣋⣬⡞⡟⡛⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢸⠏⠷⣄⠀⣾⡛⠛⠻⠟⠛⠷⣶⣿⣟⢋⣷⠶⠶⢯⡿⢁⠷⢒⢍⣷⡴⠶⣶⡶⣤⣀
⠀⠀⠀⠀⠀⢠⡟⠐⣴⠉⠷⠿⡇⠀⠐⢲⣍⣉⡉⠉⠉⣻⡁⠀⣀⠀⢠⠘⠤⠍⢢⣾⣧⡀⢸⣿⣷⣿⣷⡄
⠀⠀⠀⠀⢠⠟⡀⣒⠠⠶⠂⡈⢤⠀⢝⡩⠙⠓⠚⠿⠛⢛⡀⢈⣁⣤⣪⣿⣲⠶⠻⢯⣹⣿⡿⠿⢻⡴⡀⡿⠹⡆
⠀⠀⢠⡟⢿⣦⡀⠤⠄⠁⠈⣁⠘⣤⠜⠴⠀⠀⠀⠀⠀⠾⠉⠁⠂⡌⠠⠛⣿⡇⣇⣨⡽⢟⣃⠂⣸⢱⡗⠃⢀⣿
⠀⠀⠈⢻⡿⢛⡁⠀⠆⠀⠀⠀⢀⣃⠀⠂⠀⠙⠐⠀⢃⡄⠐⠗⢤⣤⢀⡄⠀⢣⣿⣉⢀⠆⠈⠳⣅⣟⣀⢀⣾⣧⡀
⠀⠀⢰⡏⢠⠈⠘⢆⠀⢒⣀⡴⡤⠽⠂⠀⠀⣄⢀⣠⡴⢷⣤⣄⣀⡀⠀⣀⣀⢺⡿⢆⡤⠀⠀⠀⠀⠠⠀⣨⣟⣾⠁
⠀⠀⣸⠃⣈⠸⠀⡙⠁⠜⡏⠁⡂⡀⢄⡀⠠⣸⣍⡿⠛⠈⠙⠛⠙⠛⠛⠛⣭⣿⣷⣾⢃⡁⠀⠀⠀⠀⢀⣾⢾⣅
⠀⠀⢸⡄⠁⠦⢈⡃⠄⠘⣾⠁⠀⠀⠀⠀⡰⢸⡟⠁⠀⠀⠀⠡⢰⠆⠐⠋⡭⠛⡋⠉⠀⢀⣀⡀⠱⠠⢾⣷⣤⡏
⠀⠀⠈⣷⣤⣥⡈⣅⢀⠞⠂⠑⠁⢀⠀⠀⠲⣼⡄⡀⠀⠀⠀⠀⠂⠁⢠⣎⠀⣀⣤⣶⠿⠛⠉⠀⠀⣿⠆⣿⢯⡄
⠀⠀⢰⣿⣟⢰⣶⠈⠡⡐⠐⡆⢠⠄⣦⠴⠿⣟⠛⠗⠲⠄⣴⠆⣿⣄⠀⠈⡆⠂⢀⡀⠀⠄⠘⠀⠀⢄⣾⣿⣼⣇
⠀⠀⠈⢿⣿⣼⣿⣧⡴⠄⡄⠀⠂⠐⢛⠦⢀⠄⢀⡶⠠⣠⡤⠔⠋⠋⠉⠀⠀⠀⠤⢀⣀⠠⠐⢈⠐⠃⠻⡿⠷⠛
⠀⠀⢠⣻⣿⣷⣧⣀⣷⣄⠢⠐⠆⣸⠂⠀⢀⢈⣿⣇⡔⠹⠲⠂⠀⣠⠄⣀⠴⠆⠀⠮⣄⢀⣶⠿⣤⠀⣱⣷
⠀⠀⠘⣿⠿⠿⠏⠙⠈⣿⡟⠆⢠⣼⣤⠊⠉⠛⢷⠿⠲⢂⡽⠄⠀⠄⠀⠉⠀⠀⡏⢠⣦⠈⣠⡙⢩⠉⣿⣹⡇
⠀⠀⢼⠃⠀⠀⠧⠀⣚⢹⠇⠁⢀⣹⠇⠀⠀⢀⠲⢀⣄⠐⠂⣠⣄⠀⠈⣿⣙⣯⣀⡿⢇⢠⣿⠁⣼⠼⠅⠈⣷
⠀⠀⣸⣧⡠⢀⠬⣀⠠⠤⡧⠂⣾⠅⠙⢦⠯⡏⠀⢻⣿⣦⣴⣿⡿⠀⣰⢿⡟⠓⠀⠰⠠⠤⢥⢀⣧⡀⢐⣠⣿
⠀⢠⡿⠟⣿⠀⠀⠈⠃⠀⢹⠊⡑⢦⢭⣁⠠⣟⣤⡀⠉⠛⠛⠋⢀⡆⠰⠠⠆⠰⠀⣷⣤⠄⢨⣴⡄⠋⠙⣿⠃
⠀⠈⣛⣾⣿⣦⣄⣀⣉⡀⢈⡠⠀⠐⠀⣹⠰⢋⡍⠁⢰⡿⠿⢿⣿⣤⠀⢄⡤⠄⣐⣭⣴⣮⠶⠃⠀⣀⢀⣾⣧
⠀⠘⢧⠄⠚⠁⠈⠟⢁⣴⡿⣩⡾⠒⣃⢹⣶⣋⣴⡿⢼⡧⠦⠀⠰⣦⣾⠟⡿⠿⠿⠛⠛⣡⠀⠿⢂⣽⣿⣿⣟
⠀⠀⠸⣦⣀⡀⠀⣰⣿⣷⠿⡋⠰⠆⠀⢨⣟⠻⠀⠣⣬⡀⠠⠔⡂⠰⣿⡆⠀⠀⠀⠾⠂⠁⢀⡿⢯⠝⢿⣿⣿⡆
⠀⠀⠀⢸⣿⣧⡄⠛⠉⢠⠀⠙⠀⠈⢀⡼⢿⣾⣍⠀⣤⠹⠀⠀⠀⢀⣯⡽⠟⡚⠷⣶⠞⢴⠉⠀⠀⢠⡼⣿⣿⣧
⠀⠀⠀⠀⣿⢟⣡⡌⣃⡀⠀⠈⡠⠈⠁⠀⠈⢳⣹⡄⠘⡐⠁⢠⣿⡿⣽⡧⠄⠀⠠⡇⢈⠘⣶⢛⡊⠍⢓⣛⣩⠿
⠀⠀⠀⠀⣟⠈⠻⣧⠈⣻⡿⠋⠰⠿⣤⣀⣤⠈⣏⠶⣶⡅⠈⢸⣝⣦⡹⠰⠢⠐⠄⣿⡶⣫⢕⠢⡴⢾⣟⣿⣽⠆
⠀⠀⠀⢠⣿⣄⠸⣿⠇⠛⠀⠀⠰⠀⠀⢀⠁⠀⢸⡨⣿⣿⢾⣿⣻⣫⢷⣦⣀⢄⣴⣫⣞⠿⠶⣻⠟⠁⠀⠈⢻⡀
⠀⠀⠀⠸⣭⡿⠗⠒⢯⣄⡀⠀⠀⠀⠀⠈⠀⠀⠈⣇⣿⣿⡐⠗⠦⠚⣂⣿⣿⣷⡟⠁⠈⠇⠀⡡⠳⠘⠢⠀⢸⠇
⠀⠀⠀⠀⠈⠓⢶⣄⡂⠀⠈⠛⠶⠤⣤⣠⣴⠐⠶⠖⠒⢾⡛⣿⣻⣿⣟⣿⣿⣿⣿⣟⣇⣀⣰⢿⣦⣤⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢤⡴⠶⠛⠋⠉⠳⠶⠤⠴⠶⠚⠁⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡴⠀⠀⠰⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡎⠀⠀⠀⢀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠠⠀⡘⢡⡷⢤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⡄⢖⠀⣠⣴⣶⣶⣿⡿⢷⣼⣿⣿⣿⣿⣻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠷⢂⢹⣧⣤⣬⠍⠉⠉⠁⠉⠉⠉⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠑⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠠⠐⠞⠻⣦⡀⠀⠀⠀⠀⠀⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠷⣤⣍⣓⣶⣶⡤⠴⡋⠁⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣌⠻⣿⣿⣿⣿⣦⣌⣉⣉⣉⣁⡀⠔⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠀⢠⡴⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠋⠉⠉⠀⠀⠀⣀⣀⣤⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠉⠁⠀⠈⠁


⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠒⠂⠉⠉⠉⠐⠒⠂⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡐⢁⠠⣈⢻⡄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣟⡛⠛⠛⠛⡛⠛⠛⢛⡶⠶⢶⣤⣀⠀⠀⠠⢋⡠⢈⡹⠧⠉⢠⠼⢱⠇
⠀⠀⠀⠀⠀⠀⢿⣯⠀⠀⠀⠀⠀⠘⣍⡉⠻⣌⢉⣉⡥⠴⠚⠁⣨⡿⠇⠀⠀⠸⢄⡸⣀⣤⡄⣸⡀⠁
⠀⠀⠀⠀⣠⣴⣦⠙⠷⣤⡀⢰⠒⠒⠋⠉⠘⠵⠻⣄⠀⣀⣤⠾⠋⠁⢀⣀⣀⠀⠀⠐⢃⡬⠛⣤⢳
⠀⠀⠀⠸⢿⣇⠀⠀⠀⠈⠙⠻⠶⢤⣤⣤⣤⠤⠶⠞⠛⢉⣡⠴⠀⡐⢁⠠⣨⠱⣄⣠⠄⠃⠆⢋⠞
⠀⠀⠀⠀⠈⠙⢷⣄⡀⡎⠙⠃⠀⠀⠠⠀⠠⣄⣀⣠⡾⠛⠁⠀⠀⢀⡹⢠⠸⢡⠏⡤⠦⣄⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⢤⡤⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠈⠟⠋⢹⣷⡌⠓⠄⢛⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⣿⠆⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠊



⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡀
⠀⠀⠀⠀⠀⢀⡆⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⠃⠀⠀⠀⠀⠀⠀⢸⡔⠀⠀⠀⠀⠀⡠⠔⠀⢰
⠀⠀⠀⠀⠀⠸⠃⠀⠈⠖⠀⢺⠀⠀⠀⠁⠀⡰⠂⠀⣀⠀⠸⣆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠀⠀⣀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠀⢸⡇⠀⡄⠀⠘⠁⠀⠀⠉⠀⠀⠈⡇⠀⠀⠀⠀⣷⠞⠁⠀⠀⡀⢠⠔⠉
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠄⠀⠈⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⢁⠁⢀⡠⠄⢰
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠲⠂⠀⠘⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠀⠀⠀⢹⡶⠃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡄⠀⠀⠀⠀⠀⠈⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠴⠀⠀⠈⣿⣴⠂⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠔⠒⠂⠐⠚⠁⠀⠒⠠⠔⠉
⠀⠀⠀⠀⠀⠀⣔⠅⠂⠀⠈⣂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡀⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠘⠂⠒⠂⠐⠃⠀⠀⠀⠈⠛⠓⠐⠂⠐⠀⠀⠒⠒

⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠄⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⢄⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠦⣍⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⣸⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠔⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⢀⢤⣶⠿⠛⠉⠀⠀⢀⢠⠃
⠀⠀⠀⠈⢇⠀⣈⣉⠐⠠⣀⢮⠢⡐⠄⠀⠀⠀⠀⠀⠙⠓⠲⢦⡴⢒⡵⠟⠁⠀⠀⠀⠀⢄⡴⠃
⠀⠀⠀⠀⠀⠑⠄⡀⠁⠲⣈⣧⠦⠬⠱⡾⣽⡴⡦⡄⣀⣰⣯⣥⣔⣉⡀⡀⠠⢀⡂⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣉⣗⣾⡿⣿⠬⡯⢑⢔⡉⣀⠛⣧⣶⡖⡖⠒⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠤⠠⡿⠿⠹⣞⣛⢯⡉⣯⣽⣿⣘⢣⢻⣯⢏⣿⣾⣤⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠜⠀⢘⢐⣝⡭⠨⣽⢛⠖⢚⣿⣓⠾⠏⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠤⠂⠈⠑⠋⠉⠒⠃⠘⠯⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢦⠹⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⡄⣿⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢰⠃⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⠏⣸⠇⠀⢰⢿⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟⠀⠀⡞⢈⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣾⠁⠀⡼⠁⣼⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣰⠏⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠶⠖⠚⢻⡀⠈⠁⣿⠀⠈⠀⠀⠀⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣋⣥⣤⠴⠶⠶⠒⠈⠻⠦⡘⠙⢧⡘⠛⠳⠶⠶⠤⢤⣀⠉⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣥⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠾⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⣀⣼⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⡇⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⡇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠖⢋⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⡁
⠀⠀⠀⢀⣀⣤⣶⠾⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⡶⠶⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄
⠀⢸⣿⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣄⠀⠀⠀⠀⠀⣹
⠀⠈⢿⣦⡀⠀⠀⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⠿⣶⣄⣈⠙⠿⢷⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠞⠋⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣤⣬⣉⣉⡙⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠋⠉⠉⠁⣀⣀⣠⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠋⠉⠉⠉⠁

⣦⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣿⣵⣮⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣶⣶⣾⣷⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⣛⣛⣭⣭⣛⣛⣒⠶⢤⣄⡀⠀⠀⢀⣠⡤⠶⣒⣛⣛⣭⣭⣛⣓⡲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢭⣓⣚⡭⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠈⢦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣉⠉⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠈⠈⠀⠘⠀⠀⠀⠘⡇⣷
⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢆⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣟⢹
⠀⠀⠀⠀⠀⠀⠀⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠛⠀⣇⠀⠃⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣀⡔⠹⣄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠉⠛⠋⠉⠀⠀⠈⠙⠛⠉⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⠇⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸
⠀⠀⠀⠀⠀⣀⡤⢶⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡶⢤⣀
⠀⠀⠀⣠⠞⠁⣠⢼⠇⡇⠀⠀⠠⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡧⣄⠈⠳⣄
⠀⠀⣼⠁⢀⡞⠁⢸⢰⡇⠀⠀⠈⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⡇⠈⢳⡀⠈⣧
⠀⢠⡇⠀⢸⠀⠀⢸⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠀⢸⡄
⠀⠘⡁⠀⠸⢦⡀⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡇⢀⡴⠃⠀⢈⠃
⢀⡞⠁⠀⠀⠀⢧⣀⣳⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣞⣠⡼⠀⠀⠀⠈⢳
⣼⠀⢀⣴⡦⣄⣀⣠⠇⠙⢮⣑⡢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢔⣫⡵⠋⠸⣄⣀⣠⢴⣦⡀
⡇⠀⢸⠇⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⣶⠶⡶⢶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠸⡇
⠙⠲⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠈⠉⠙⠓⠿⠀⡇⢸⠀⠿⠚⠋⠉⠁⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡗⢺⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡟
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢿⣿⣿⣷⣶⣬⠿⠶⠶⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⡙⢯⣾⡿⠿⣿⣟⣀⣀⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⣿⣯⡟⣖⣿⣾⡆⣻⣿⡿⣳⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢺⣳⢼⣿⣦⡭⣋⠻⠃⢠⣿⠟⠳⠨⠿
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣯⣑⣴⣾⣿⣿⡿⡇⣀⢈⠙⠶⠂⠘⠙⠋
⠀⠀⠀⠀⠀⠀⠀⢳⣉⠁⠀⣶⣿⣿⣿⣯⢟⣾⣻⣿⠂
⠀⠀⠀⠀⠀⠀⢱⡟⣷⣤⣤⣿⠛⣉⣽⣟⣿⡴⡾⢽⣧⡄
⠀⠀⠀⠀⠀⠀⠸⢵⡟⢿⣿⣇⠘⠿⣿⣸⣧⣿⠿⣿⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡉⡼⠻⣿⣤⠀⠿⢃⡥⣥⢷⣺⠟⣁⣭⡀⣴⡦⣀⢠⠤⣄⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⠒⡀⢸⡜⠋⠀⠀⢤⢿⣿⣿⣿⣿⣷⣧⡴⠚⠓⠟⠾⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣷⡗⣽⠯⣭⣿⣿⣿⣿⣾⢀⠀⠂⣿⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣯⣍⣳⡒⢿⣝⡛⠛⢻⣷⣶⣾⣟⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⣯⣹⣯⡏⢷⠻⣿⣿⡗⢈⣿⣿⣟⣹⡧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡀⣿⠯⡛⠿⠿⠽⢯⡃⠀⣹⣿⡟⢧⡁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡑⠙⠻⣽⠗⣶⣹⠶⠁⢀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠑⠾⠀⠜⠀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄

⠀⠀⠀⢀⣀⣰⣶⣶⣶⣦⣄⠀⠀⠀⠀⠔⠀⠰⡀⠀⠀⠀⠀⢀⣀⣠⣤⣠⣀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⡴⠆⠀⢀⡴⠂⠀⢀⡰⠆⠀⣀
⠀⠀⠐⠛⠿⠿⡿⠟⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠈⠠⢈⡯⢻⣷⣧⠀⠀⠀⠈⠉⣷⠀⠀⠀⣀⡀⠀⢁⣀⠀⠀⣀⠀⢀⣈⠀⢀⡈⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠇⠀⠀⠀⠈⠀⠁⠀⠈⣟⣻⣾⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣷⢺⣾⢟⣷⠒⣿⠻⠶⣖⠛⠛⠷⠲⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠁⠀⠀⠀⠈⢀⡿⠀⠀⠀⠈⠉⠀⠒⠒⠚⠂⠀⠘⠓⠛⠒⠛⠓⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠁⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⢀⢔⣡⣶⣾⠿⠿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣻⣳⣴⣾⣿⣷⣿⣿⡷⠀⠈⠒⠒⠉⢹
⠀⠀⠀⠀⣀⠂⠄⢀⠀⠠⢀⣐⠢⠀⠀⠀⠀⠀⠀⢤⣵⠿⠋⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⡿⠿⠛⠛⠀⠈⠁⠀⠀⠀⠀⠀⠨⡄
⠀⠀⠀⠢⠤⣉⠐⠀⠈⣁⠀⢈⠔⠃⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⠀⢠⠁⠀⢀⡀
⠀⠀⣶⠤⢄⣀⠈⠑⠂⢈⠐⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠋⠀⠀⠀⠀⢘⠀⠄⠀⢰⠁⣿
⠀⠀⠙⠛⠛⢻⣌⣹⠶⠋⠀⠀⠀⠀⠀⣰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣀⢄⣄⠀⠀⠐⠒⠀⠂⠀⠀⠐⠁⠀⠀⢈⡜⠀⢀⠘⠓⠛⣴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⢨⡷⠈⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡇⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠶⢶⣶⡶⣶⠶⢚⠂⠀⠀⠀⠰⡀⠁⠀⠀⣾⣿⡏⢀⣮⠀⠀⠀⠀⠀⠀⠞⠀⠀⠘⡁⡛⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⢀⡿⠿⠾⠿⠾⡿⠿⢿⠀⠀⠀⠀⠀⡈⣴⠂⠀⠘⠿⠷⠄⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠃⠀⡇
⠀⠀⠀⠀⠀⢤⠦⠄⠀⡄⣠⡀⠀⠀⡠⠾⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠁⠀⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠄⠀⡇⡄⠠⡇
⠀⠀⡀⠀⠀⠀⣰⠏⠀⡔⠉⢧⠙⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢸⡇⠀⠀⡀⣀⣴⣴⣶⡆⠀⢀⣀⠀⠿⠆⠀⠀⢣⡅⢸⡇
⠀⠀⠀⠀⠀⠀⠁⢰⠞⠀⠀⠈⠇⠘⣁⠤⠀⠀⠀⠀⠀⣠⣴⢆⡜⢉⠝⠗⠦⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡛⠋⠋⠉⠙⠇⠀⠀⠉⠁⠀⠀⠀⠀⠸⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣴⣽⢿⣶⣭⣏⣷⣄⣬⣵⣤⠀⠰⠀⠀⣠⠋⠀⠀⠘⡧⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣯⣟⡻⢶⣤⡀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⢀⡴⠊⢁⠶⠀⠀⠀⢲⡈⠀⠰⠀⢀⠀⠉⢻⡀⠀⠸⣧⣤⣤⣉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⣤⡙⡿⣿⠟⢱⡶⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠂⢀⡎⠀⢠⡾⠁⠀⠑⠦⠈⡻⢟⣁⡿
⠀⠀⠀⠀⠠⣤⣤⡀⠀⠈⠙⢿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠃⢀⡾⡀⢰⡿⠁
⠀⠀⣼⠀⠀⢸⡏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠀⠂⠀⠀⠀⣰⣶⣺⠟⠀⠀⠀⠀⠀⠌⠀⢠⡿⠁⠀⠀⠀⠀⢤⡂
⠀⠀⣹⠀⠀⢈⡁⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡷⠎⠁⠀⠀⠀⠀⠀⠀⠠⢤⡾⠁⠀⠀⠀⠀⡆⠸⢁⡐⡇
⠀⠀⣿⠀⠀⠈⣿⠄⡄⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⢀⡴⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⠀⠀⢀⠃⠸⠀⡇⡇⢄⠔
⠀⠀⣿⠀⠀⠀⠡⡆⠁⠀⠀⠀⠀⠀⠒⠀⠒⠐⠒⠀⠒⠒⠀⠐⠀⠀⠀⢐⣿⡷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠈⠀⠀⠀⠀⠘⠀⠂⠚⣛⣽⡌
⠀⠀⢿⠀⠀⠸⣷⠀⠈⠀⠀⠀⠀⠀⠠⣀⣤⠀⣄⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⡀⢂⠐⡀⣂⠀⠀⠀⠀⠀⠀⠀⢸⣶⠆
⠀⠀⠸⡀⠀⣸⢡⠄⡄⠀⢀⡀⠢⠄⣻⣾⠏⣹⣁⡼⣤⣾⡚⣩⣤⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⡟⡌⠁⠉⡀⢆⠰⡐⢂⠀⠀⠀⠀⠀⠀⠈⣿⡶
⠀⠀⠀⠈⠰⢯⠎⠉⠀⠀⠈⠡⠤⠈⠭⠭⠬⠩⠍⠠⠭⠌⠭⠉⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠉⠁⠉⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⣠⡤⠀⠀⢀
⠀⠀⠀⠀⢀⣶⡠⢤⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠉⠢⡀⠀⡿⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⣼⡏⠀⣾⠇⠀⠀⠀⠀⣾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢃⡀⠀⢠⠴⠒⠲⣦⣴⠊⠁⠀⠠⣀⠈⡆
⠀⠀⠀⠀⣿⠓⠚⣏⢠⠞⢳⡧⢠⣿⢶⡅⢀⡾⢁⠆⡞⣶⠇⢰⡇⢰⡿⠀⠀⠀⠸⣸⡇⣰⠋⠀⠀⠀⠈⡿⠀⠀⠀⠀⠸⡞⡇
⠀⠀⠀⠀⡿⠀⢀⣿⢿⡠⢸⣇⣼⠇⢸⣇⢸⠁⡠⠊⢸⡏⣠⣾⡧⣾⠇⠀⠀⠀⠀⠣⣸⠡⣀⠀⠀⠀⠀⣿⠠⠀⢀⡤⢀⡿⠃⠀⠀⡸⡓⠂⣰⠧
⠀⠀⠀⠰⢤⣤⠾⠃⠀⠀⠈⣡⠏⠀⠈⠁⠀⠉⠀⠀⠈⠉⠁⠈⣰⠏⠀⠀⠀⠀⠀⠀⠉⠀⣈⠳⠶⢬⠀⣿⡔⢋⣩⠕⠋⠀⣴⠥⢠⠞⠁⠀⢳⡀⢨⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠉⠁⠀⠀⠀⠀⠈⡌⠠⡉⣥⠁⡄⢩⠉⣭⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠐⠀⣰⣿⠟⠁⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠸⡄⢃⡘⠀⠇⠜⢀⢧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠁⢠⡟⠁⠀⠀⢠⠟⠁⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣁⣀⣀⡈⠨⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢂⠁⠀⠀⠁⠒⣄⠀⠀⠀⠌⡀⠀⠀⠀⠊⠀⠀⠀⠀⠃⢤⣀⣀⠀⠐⠃⠀⠄⢂⡄
⠀⠀⠀⠀⠀⠀⢀⠎⢠⢀⡤⠄⠀⠀⠀⠈⢧⠀⠈⠀⠠⣀⣀⣀⣀⣠⡤⠀⢘⡉⠉⠀⡐⠒⣒⠒⠈⠩⠭⠊⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⢦⠠⣤⠇
⠀⠀⠀⠀⡴⠊⡝⢀⠀⢸⠀⣀⠈⣶⡄⠈⣾⣇⠀⠀⠀⠀⠀⠨⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠊⠉⠁⠀⠀⠠⠈⢃
⠀⠀⠀⣼⠁⠀⣇⠀⠀⣾⣧⠈⢛⡟⢸⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢌⡙⠛⠳⢶⠽⢭⣤⣭⣁⣀⣀⣀⣤
⠀⠀⠰⡇⠀⠀⠻⡄⠤⢏⣿⠀⠀⡰⠃⠰⢣⡏⠀⠀⠀⠀⠀⠀⣴⣿⣟⠩⣶⠲⣦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⣤⣤⣶⣡⣄⡈⠁⠈⠁⢍⠩⢉⣛
⠀⠀⠀⢣⠀⠀⠁⢈⠙⠛⣁⠴⠊⠀⡀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣷⠬⢗⠲⠶⠶⠞⠀⠀⣠⡀⠀⠀⠀⠀⠀⢉⡀⠒⠀⠈⠛⠶⠼⠷⠶⠶⣶⠇
⠀⠀⠀⠈⠃⠀⢄⣀⡈⣉⣠⠴⠖⣋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠓⠒⠒⣶⣤⣦⠟⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠤⠔⠊⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠐⠒⠒⠂⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠙⢿⡄⠈⢣⠀⡀
⠀⠀⠀⠀⠀⠀⣀⡤⢶⣬⣍⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢈⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠻⣷⡄⠀⠀⠀⠄⠘⣇⠀⣸⠀⠈⢢
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠰⢀⠠⠀⠁⠂⢀⠀⠀⣀⣀⣤⡴⠶⠿⠛⣓⣼⡇⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠈⠷⠘⡆⠀⢈⠁⠁⠁⠛⢘⠔⠊
⠀⠀⠀⠀⠀⠀⡞⠀⠄⠀⢀⡀⢁⠀⢠⠠⠇⣈⣉⣤⠴⠶⠶⠛⢛⣉⢹⠀⠀⠀⠀⠀⠀⡄⢠⡀⢀⡶⠂⠀⠰⢷⠈⠨⠂
⠀⠀⠀⠀⠀⢸⡇⠁⠀⢃⠀⠀⠈⠀⠀⠂⢀⣀⣠⡤⠤⠀⡠⠾⠛⠁⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⢸⢠⡀⠀⠀⠀⡆⠀⠃⠀⠀⠈⣿⠀⠀⠀⠀⢀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⡄⠤⣤⠄⠀⠰⢶⠐⣴⠶⡆⠶⢶⡒⠤⢄
⠀⠀⠀⠀⠀⠸⠈⠁⠆⢂⠀⡀⠃⡤⠀⠀⠀⠟⠀⠀⢀⣀⣘⡭⠶⢂⠇⠀⢀⣤⠄⠒⠒⠻⣯⠘⠀⢙⡆⠚⠀⢈⡇⠉⠀⣨⡇⠁⠠⠿⠀⠶⠃⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠃⠆⡤⠀⡇⠐⠿⢖⣿⠙⣿⡃⠤⠒⠁⠀⠐⠁⠀⣀⣁⣀⣀⠛⠀⣀⣈⣁⣀⠀⠈⠡⠤⠤⠒⣀⣐⣠⠴⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡼⠤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣤⣤⣦⣴⣶⣾⣷⣦⣤⣴⣦⣤⣴⣷⣶⣿⣶⣶⣾⣦⣤⣶⣤⡀
⠀⠀⠀⠀⠀⢀⣤⣿⣯⣴⣶⣶⣬⣭⣤⣤⣶⣶⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣶⣦⣤⣤⣤⣿⣷⣤⡀
⠀⠀⠀⠀⠀⢸⣿⠉⠁⣤⡀⠀⠙⠉⠁⠀⡦⠀⠀⠉⠉⠛⠃⠀⠀⣀⠀⠀⠀⠈⠋⠉⢁⡀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠋⠀⠀⠀⠀⣀⠀⠈⠁⡀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠰⠾⠿⠿⣧⣤⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠉⠀⠀⠈⠋⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⣦⠀⠀⠀⠀⠀⣍⠉⠉⠀⠈⢉⠁⠀⠀⠶⠀⠀⢶⣦⣤⣶⠶⣿⣦⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⠆⠀⠀⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⣤⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠟⠛⢿⠷⠶⠾⠷⠶⠀⠐⠗⠀⠀⠾⢟⡛⠻⠿⠶⠶⠀⠀⠀⠰⠆⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣿⡇






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠉⢛⣓⣲⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠀⣀⣀⡤⠤⠼⠓⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠖⠋⠁⣀⣠⠤⠖⠒⠋⠉⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠛⢓⣢⣤⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠠⠾⠕⠒⠚⠉⠁⠀⠀⠀⠀⣀⡴⠖⠋⠉⠁⠀⠀⣀⣠⠴⠖⠚⠉⠉⠉⠉⠉⠉⠉⠙⠒⢤⣀
⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣀⡠⠴⠒⠊⠉⠁⠀⠀⠀⣀⣤⠤⠖⠒⠒⠛⠛⠛⠒⠒⠮⠷⣄
⠀⠀⠀⠀⠀⢻⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠽⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢷⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⣀⣀⣠⠤⠤⠖⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠶⠶⠶⠦⠤⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠯⣤⣀⠤⠀⣠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢶⣇⣔⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⠶⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣥⣔⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠧⣄⣤⣀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠺⠷⠶⠶⠶⠾⠗⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⣞⣷⢻⡟⣸⣷⠘⡟⢲⣹⠆⢾⣙⣿⣾⣸⣹⠟⣺⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡆⠉⢥⡉⣉⡉⠉⠋⠀⡟⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⢀⣴⣟⣻⠭⠠⠤⢴⠀⠐⠈⠁⠀⠀⡗⠴⠚⢿⣿⣦⣄
⠀⠀⠀⢠⠊⠀⠀⠠⠄⡀⠀⠀⢠⣾⠉⠉⠀⠀⠀⠀⠈⠡⠠⠤⣄⣀⢈⠖⠉⠉⠀⠈⠙⢿⣷
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢸⠉⡧⠄⠀⠀⠤⡀⠀⠈⢤⢀⡠⠀⠠⣀⠀⠀⠀⠀⠀⠠⢻
⠀⠀⠀⠀⠀⠁⠚⠻⠶⣶⡀⠀⢈⠗⠁⠀⠀⠀⠀⡔⠀⠀⠈⢁⣀⣀⣈⠀⢀⠠⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢄⠀⠀⢀⠠⡞⠀⠄⣠⡚⠁⠀⠀⠀⠉⣒⠎⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠉⣡⠔⠀⠐⡀⠈⠁⠘⠒⠢⠂⠀⢸⠁⢀⠄⠀⠀⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⢈⣑⣢⠤⠔⠀⠀⠀⡀⠉⠥⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⠠⠀⠀⠀⠰⠈⠑⠒⠒⠒⠪⣀⠀⠀⠀⠀⠀⠲⠤⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠄⠀⠀⠢⣀⣀⣀⡠⠖⠒⠀⠂⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠚⠛⠉⠁⠀⠀⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠒⠒⠶⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢄⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⢇⠀⠀⠀⠈⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠉⠉⠙⠛⠶⣤⡀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠰⠆⠀⠀⠸⡆⠀⠀⠐⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠋⠀⠀⠀⢹⠀⠀⠀⢁⠀⠀⠀⠀⠀⠈⡧⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠠⠄⣀⡀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⢻⡀⠀⢀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡀⠀⠂⠀⠀⢠⠄⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣄⠀⠀⠀⠻⡄⠀⠀⠈⢷⠀⠈⣷⠀⠀⠀⠀⠀⢷⠀⠀⠀⡇⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠹⣆⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁⠀⡠⠂⠁⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠶⠀⠀⠘⣆⠀⠀⠹⡆⠀⠀⢹⡄⠀⠀⠀⢀⠀⠀⠈⡆⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⢠⠟⢦⣀⠀⠀⠀⠈⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢿⠀⠀⠀⠁⠀⠀⠰⠈⠁⠀⢀⡧⠤⠴⠖⠛⠦⢤⡠⠔⠈⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⡏⠀⠀⠈⠓⠒⠦⣄⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⢀⡧⠖⠒⠛⠛⠉⠀⠀⠀⡼
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⢀⣀⣤⣤⣤⢿⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠈⠉⠐⠂⠤⠀⠈⠙⡶⠚⠋⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⡤⠚⠁
⠀⠀⠀⠈⢳⡀⠀⠀⠀⣀⠠⠤⠀⠠⠄⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶
⠀⠀⠀⠀⢸⠁⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠰⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⠛⠛⠲⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⠤⠴⠶⢤⡀⠀⠀⠀⠆⠀⠀⠀⠀⢠⠟⠉⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠾⣄⣀⠀⠀⠀⣮⣤⡤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣰⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠍
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣿⣷⣷⣶⣶⣾⣿⡿⢿⣿⣿⡿⠿⠿⠛⠋⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣛⠶⠶⠦⠤⠅⠀⠀⠀⠠⠄⠤⠤⠤⠄⠒⠒⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⠊⡁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠿⢿⠿⠿⠟⠛⠻⠶⠓⠚⠲⡶⠚⠿⠋⠁⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣖⣄⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣻⡛⠽⠛⠿⢷⣤⣀⣀⣀⣀⣀⣠⠤⠖⠒⠚⠋⠉⠁⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣠⣤⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠚⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⢶⢶⣶⢿⡿⠉⠁⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠿⣿⣿⣿⣿⣉⣈⠉⠀⢀⠀⡈⣉⣉⢀⣀⣠⣴⡤⠶⢚⡉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⡁⠪⠽⢛⡛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠄⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⣄⣀⣀⠀⠀⠀⠈⠀⠀⣀⣀⡤⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠠⠠⣀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠉⠉⠛⠛⢛⠒⠢⠤⡀⠀⠀⠀⠀⠀⣠⡤⠶⠲⢤⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⣀⣠⣤⣨⡾⠳⠦⣄⠀⣏⢮⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣈⣆⠀⢀⡤⠻⢿⡄⠀⠀⢸⡿⠓⠦⡀
⠀⠀⠀⠀⠀⠀⢿⡦⡊⠁⠀⠉⠟⠛⠀⡀⢀⠸⡆⠸⣷⠇⠀⢠⣴⣟⣗⡆⠀⠀⢨⣽⣿⠋⢀⡾⠆⠀⠀⠃⠀⠀⢸⠀⠀⣠⡿⡄
⠀⠀⠀⠀⠀⠀⠈⣷⡇⠀⠀⡸⢀⠀⠀⠈⠳⣿⠂⠀⢨⠀⠀⠀⠈⠏⠁⠀⠀⠀⠀⣹⠏⠀⣎⠀⣈⡶⠤⠾⠶⠶⠛⠒⠾⢧⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣠⣜⣇⣑⣐⣀⣤⠟⠀⠀⠘⠳⢤⣤⣴⠀⢀⣀⣠⣤⡬⠏⠀⠀⠰⠜⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣴⣾⠛⢻⣿⣮⡵⣄
⠀⠀⠀⠀⠀⢀⡤⠤⡤⠀⡶⢤⣤⠖⠒⣶⢶⣶⠶⠋⢉⣩⣟⡲⠚⠉⣹⢒⣳⣶⠾⠉⠓⠒⢆⠀⢠⠓⠒⠉⠉⢻⣿⡟⠉⠙⠇⠀⢷
⠀⠀⠀⠀⠀⣏⡀⠠⠴⠋⠛⠁⠤⠒⠛⠛⠉⠀⠐⠚⠙⠉⡉⢀⣒⢉⡋⢉⡉⠀⢀⠀⣀⢄⡼⠀⠸⡀⠀⠀⠀⠟⠀⠙⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠙⠛⠛⠒⠓⠒⠓⠻⠿⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠒⠶⣤⣤⣀⣤⣤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⢒⡲⠶⠶⠖⢒⣢⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣠⠤⣤⣀⣀⣀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣎⢀⣷⡦⣰⣯⣄⣀⡴⣮⢬⣉⣀⣀⣀⣱⡄⠀⠀⢀⠤⠂⠉⢡⣫⠟⠋⢁⣴⡫⠿⡋⢀⡴⡿⠟⠋⠁⠢⡀
⠀⠀⠀⠀⠀⠀⣾⢸⡟⠻⣆⠙⠽⢧⡌⠛⠷⣌⣀⠈⠳⢤⡈⠉⠙⢦⠀⢺⣠⠀⠀⠟⠁⠀⠀⣸⡿⠁⠀⠀⠚⠉⠂⠀⠀⡀⠩⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣄⣘⣤⣄⠈⠻⡀⠀⠈⠛⢅⡂⠀⣙⣦⠴⠋⠀⠀⠙⠷⣆⣀⠀⢀⣤⡅⠀⠀⢀⣀⣀⠀⣀⣤⣯⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠓⠒⠚⠑⠒⠛⠚⠉⠉⠉⠁⣀⣀⣀⣀⣠⣤⣀⡈⠉⠉⠙⠛⠒⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⡠⠒⢗⠖⢛⠍⡭⠊⢡⠔⠂⠈⠛⡆⠀⠀⠀⠀⠀⣀⣤⡤⠀⡒⢢⣤⢄⡀
⠀⠀⠀⠀⠀⠀⣰⢇⡴⠊⠛⢄⠙⣆⠀⠀⠀⢀⠎⢰⠫⠊⡠⣣⣿⣴⠞⠁⠀⠀⠁⢠⠃⠀⠀⢀⢔⠟⢛⣽⠛⡄⡦⢠⢘⡦⠙⣆
⠀⠀⠀⠀⠀⠀⡏⣼⢇⣀⡤⠤⠶⢿⡀⠀⠀⣾⢾⡇⣾⠸⡃⡇⠘⣷⠀⠂⠀⠀⠂⠘⠀⠀⣴⠃⡆⢠⡋⣂⡬⢔⡥⠂⢼⡗⠀⢼
⠀⠀⠀⠀⠀⠀⣇⠸⡃⣌⣉⣓⣶⠶⡈⢦⠀⠹⣌⠣⡱⠄⠳⡘⢷⡝⡆⠀⠠⠀⠀⢰⠀⢸⠁⡀⠑⢀⣀⣀⣠⠵⠂⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠘⢦⢷⣅⠙⠈⠀⠀⢸⠋⢧⠀⠈⠱⡌⣎⢆⠘⡀⠃⡇⠀⠀⠀⢁⡎⠀⠘⣷⡈⠲⣦⣤⣤⣤⣤⡤⢴⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡁⠗⠰⠖⢁⡰⠃⠀⠀⠀⠸⣌⣘⡄⡇⡄⢿⡄⠀⡠⠊⠀⠀⠀⠈⠑⠲⠼⠿⠾⠷⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠃⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠠⠆⠉⠈⡈⠉⣁⠉⠀⠀⠀⠀⣼⣿⣿⠿⣽⣶⣶⣶⣮⣉⠙⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠴⠀⠀⠀⠀⢀⠀⢲⣂⣀⣤⣤⣶⠂⠀⡀⠀⠁⠘⠛⣩⠉⠿⣿⣿⡆⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⠀⣸⠃⠀⠀⠀⠀⠀⢈⡀⠁⣙⡂⠐⠛⢿⢷⣄⡀⠈⠃⣬⣿⡿⠁⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢌⣙⠀⠤⣄⣀⠀⠈⠉⠀⠩⠁⣠⡀⠀⢐⠛⢛⣛⡻⠞⠋⣤⡞⢾⣏⣀⣄⣈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣶⣶⠄⠀⠀⠀⡀⠐⠓⠛⠓⠂⣙⡋⠩⣷⣴⡀⢠⡿⣧⣿⡟⠁⠀⠙⣯⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠁⠀⠀⠉⠄⠈⢸⠏⣿⠇⠀⠀⣠⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠶⠶⠛⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠷⠟⠛⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡴⣿⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⢀⣶⣿⡿⢟⣳⡄⠈⠉⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢘⣿⣉⣻⣷⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠀⠀⣛⡾⣿⣟⣩⣿⣥⡀⠀⠱⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢁⣯⣽⡟⠉⣻⠏⣿⣾⣧⣤⣀⣀⠀⣀⢀⠀⣀⣁⣠⣶⣿⣫⢊⡽⣒⣿⣿⣷⠞⠀⠀⠀⢘⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣥⡀⣌⠉⢙⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⣿⣟⢍⣯⣱⣝⠋⠁⠀⠀⠀⢀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠰⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⠉⢁⠀⢀⡮⢶⡋⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠤⠦⠤⠤⠤⣄⣢⣤⣄⣤⡐⠿⠯⠁⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠍⠑⠒⠻⠥⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⡢⣄⡀
⠀⠀⠀⠀⢀⣰⣷⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠾⠛⠉⣉⣴⠦⠤⢄
⠀⠀⠀⢰⣋⠏⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠜⢚⣭⠗⠚⠁⠀⠀⠀⣀⣀⡀⠱⡀
⠀⠀⠀⠈⠻⣿⡿⠀⠀⣀⣶⠀⠀⠀⣰⡞⠁⠐⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡟⢿⡄⢳⡀
⠀⠀⠀⠀⠀⠘⣿⡤⡾⣿⡏⠁⢠⣠⣿⡴⠀⣀⣠⣦⡶⡟⢿⣿⣿⣿⣿⣿⣿⣮⢿⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠈⠳⢿⣛⣿⢠⣼⣿⣿⡍⠀⠉⢻⡿⣷⡯⣚⢯⡳⢯⠿⣟⡿⣿⣬⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣏⣿⢿⣷⣆⠄⠙⢿⣯⡇⡍⠫⣞⡙⣱⣳⢶⢻⢛⡓⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠈⠛⠻⢿⣷⣌⣦⣿⢦⠸⡱⣓⢶⡝⡾⡞⢻⠸⡽⡟⣿⢦⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠐⣂⢿⠢⣀⠀⢤⢔⡿⣾⣿⣻⣫⢃⡅⡳⣙⣯⣏⣣⣢⠧⣱⠡⠙⢾⣮⣳⣧⣯⡿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢆⡬⢲⣷⣆⠀⠀⠛⠉⠉⠹⠟⠚⠓⡿⠛⠿⢻⡋⣷⢏⣴⠟⠻⠏⣀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠽⠙⠶⠀⠄⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠀⠀⠛⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠀⢠⠄⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠀⠐⠹⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠶⣤⠀⠀⠈⠀⠰⡄⠀⠀⠠⡄⠀⢀⡠⠄⠥⡦⠤⠠⢄
⠀⠀⠀⠀⡤⠀⠀⠙⢢⡀⠘⠀⠀⠀⠐⣀⠊⣀⠄⠀⠀⡀⠀⠀⠓⠀⠀⠔⢠⢁⣰⡄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠒⠳⠀⠀⢠⣀⠁⠀⡰⢀⣤⠀⠀⠀⠀⠀⠚⡁⢌⠖⢁⢶⠀⣠⠀⠁⠀⠀⠀⠀⠀⢸⠀⠂
⠀⠀⠀⠤⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⣀⡈⢠⡊⠠⠀⠀⢀⠀⠛⣑⣋⡉⡄⠀⡨⠀⠀⠀⠇⢀⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠈⠱⣀⠁⠀⠀⠀⠀⠀⢰⠆⣱⣖⠠⠲⠀⠀⡀⣤⠄⠀⠀⠀⠀⢄⡄⡀⠐
⠀⠀⠀⢀⡜⠃⠁⠀⡀⡀⡀⠀⠀⠛⡴⢠⡀⠀⠀⠀⢀⠀⠀⠀⢤⠀⠀⠈⠘⠚⠒⠁⠀⢠⡛⠀⠀⠀⠈⠁⠀⠈⠘⢣⡆
⠀⠀⠀⠀⠀⢰⠋⢁⡠⠤⠨⢤⡀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠦⡄
⠀⠀⠀⢀⠀⠈⠷⠃⠀⠀⠀⠀⠰⢀⠀⠨⠀⡆⡆⡀⡄⢰⠀⡌⠀⠀⠰⠐⠰⠀⢰⠂⠀⣀⠀⠀⠀⠑⣫⡀⢈⢲⢂
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠐⠐⠑⠀⠂⠀⠀⠀⠐⠀⠀⠃⠁⠈⠂⠀⠀⠀⠀⠀⠸⣒⡆⠐⠓⣃⢂⠋⡄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⢀⡄⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠰⠄⠀⠀⢀⣀⢤⠀⠀⠀⠀⠊⠑⠢⣉⠱⠀⠵
⠀⠀⠀⠀⠂⠀⠈⠃⠀⠀⠀⠒⠀⢀⠀⠘⣣⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠶⠙⠈⠀⠀⠂⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠊⠀⠀⠀⠑⢁⠀⠀⠀⢀⠀⠀⠂⠀⠀⠂⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣷⠀⠀⠈⠁
⠀⠀⠀⠁⠀⠀⠄⠀⠈⠃⢤⠀⠀⠀⠐⠀⣠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⢴⠀⠀⠀⠀⠻⣿⡀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⢄⠀⠀⠄⠁⠀⠀⠄⠀⠀⣐⠮⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⣬⡛⠀⠀⠀⠀⠔⠀⠀⠀⠀⠟⠉
⠀⠀⠀⠀⠐⠂⠀⠡⢀⠁⠀⠀⠁⠀⠀⠉⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠃⢀⠈⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⡞⠁⠀⠀⠀⠀⠀⠀⢃⢠⡴⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢂⣁⡗⠢⠤⡀⠄⠒⢢⠤⠒⠧⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣠⣎⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠂⢁⡨⠀⢠⠤⠀⠈⠀⠠⠖⢂⠀⢸⡀⠀⡏⠢⠄⠀⠀⢀⢎⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠡⠄⠀⣠⡤⣀⠀⠀⣀⠀⠀⠑⠈⠁⠀⠐⠛⠉⠉⠀⠈⢱⡔⡑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢒⡞⡀⢤⡬⢤⣄⡇⠐⠉⠀⠀⠐⠀⠀⠤⣀⣀⡤⠀⠀⠀⣀⢄⡦⠪⢊⡘⣖⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢾⡓⠐⠒⠒⠒⠀⢘⢣⠀⣰⣓⣱⠀⠀⠀⠀⣄⠀⠀⠠⠾⡠⠥⠤⠖⠐⠁⣈⠆⢀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠈⠢⠄⣀⡀⠴⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠥⠤⠐⠒⠊⠉⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⢆⠠⠤⠤⠄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠤⠤⠄⡴⠖⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠐⠈


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠒⠀⢈⡉⠁⠀⡠⣙⡶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠨⠍⠉⢿⣿⠋⠀⠀⠀⠀⠁⠀⠀⡰⠁⣀⣤⢴⡷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⢅⠈⠙⣆⠀⠀⢸⡏⠀⣀⠀⠀⠀⠀⠀⠈⢠⠊⡡⠀⠈⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠙⠀⣾⠄⠀⢸⡇⢰⣹⠀⠀⡌⠀⢀⠀⡱⠋⢡⡤⠀⣀⠤⠒⠒⠾⠿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠐⠚⠁⠀⠀⠀⠀⢲⣿⡆⠀⢸⡇⣿⠇⠀⢸⡇⢀⡇⡤⡖⠀⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⡶⠿⠳⠦⡄⠀⢳⣄⠀⠀⢸⡏⣿⡀⢸⠁⡿⠀⠀⢸⠀⢸⣹⠁⠀⠀⠀⠂⡠⠔⠒⠒⠀⠛⠓⠶⣤⣸⡆
⠀⠀⠀⠀⠀⠀⢹⣷⡛⠛⠒⠀⠀⡀⣿⢂⠰⠈⡅⢸⣇⣼⣖⠃⠈⠀⠈⠀⣸⡇⠘⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⢻⣟⡧
⠀⠀⠀⠀⠀⠀⣼⡏⠃⠀⠀⠀⢐⣄⣼⠀⢡⣀⣧⣘⣿⣼⣿⣷⡀⠀⠀⠀⣼⣇⣤⠀⠀⠀⠠⠒⠉⡭⠉⠉⠓⠢⡀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⣾⡿⠛⠊⠉⠈⠀⠈⠉⠉⠹⠿⠿⠿⠶⠶⠿⢿⣿⣴⣶⣖⠀⠀⣀⣀⡀⠀⢒⠆⠈⣦⣺⠃
⠀⠀⠀⠀⠀⠀⠘⠿⠷⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢿⣿⠎⠉⠉⠛⠓⢤⡑⢘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⡇⠀⠛⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⠀⠀⠀⣧⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣇⠀⢸⡁⠙⡶⠙⡇⠀⠀⠀⠀⠀⠀⣠⠞⡇⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⢧⠀⠀⡴⢇⠀⠀⠀⠀⠀⣀⡇⠘⢋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢧⠀⠘⡟⠲⡀⠈⡇⠀⠀⠀⢰⠁⢱⠔⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡀⠸⡇⠀⣧⠀⠀⢸⠃⠀⠀⠀⢸⡄⠀⡰⠃⣀⡼⠉⠟⣦⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣻⣌⡏⠙⣄⠀⠀⠀⠀⡇⠀⠹⡄⣸⠣⣠⠟⣆⠀⠀⢰⠋⠸⠎⢹⠎⢹⣁⣤⡶⠁⠀⠀⠀⠀⣰⠋⡜⢷
⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⣇⠀⠉⠀⣸⠻⡄⠀⠀⢳⠀⠀⢱⣼⠀⠙⠀⢸⡀⠀⢾⡀⢠⠤⢟⠀⣀⡜⠀⠀⠀⠀⠀⣠⠞⡇⠀⣠⠟
⠀⠀⠀⠀⠈⢇⠳⡄⠀⠀⠈⠣⣄⡀⢃⠀⢻⣀⠀⢸⡀⠀⠀⢻⣦⡀⢀⢾⡀⠀⢠⠏⢯⠀⠹⠊⡇⠀⠀⢀⡴⡿⢀⡏⠠⠟⢹⠁
⠀⠀⠀⠀⠀⠈⢧⠙⢦⠀⠀⠀⣿⠈⠙⠂⠸⠉⢻⠀⡇⠀⠀⠀⣇⠘⡎⠀⡇⠀⢸⣤⢾⢀⢤⡞⠁⠀⣠⢋⠞⣡⠞⣇⣠⡴⠣
⠀⠀⠀⠀⠀⠀⠈⢳⡈⠳⣄⠀⠈⠳⣄⣀⢠⠀⠀⡇⢻⡀⠀⠀⢘⣆⠀⢀⣇⠀⠀⡇⠘⠁⢸⠇⢀⡜⢡⠏⢰⠃⠘⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⡀⠀⢯⡈⠙⠆⢀⠟⠻⡄⠀⠀⢸⡈⠳⠁⢘⡆⡴⢣⠀⠴⡏⣰⠏⢠⢃⡞⢹⠄⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⠢⡀⠙⣲⢄⣘⡀⠀⣷⠀⠀⠀⣳⢄⡠⠚⣶⡇⠀⠏⢠⡷⠃⢠⣯⣼⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠢⡸⣄⠈⠁⢠⡏⢻⠀⠀⣧⠀⠁⠀⣟⣇⠀⡠⢿⠁⢀⡞⠀⡴⠒⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠑⢄⠙⢮⡗⠒⠼⡇⢸⠶⡄⢸⡄⠀⣰⠃⠈⠎⢠⠏⡞⢙⢀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⠉⠳⣄⣀⣈⠱⣄⠙⣦⢄⡀⢸⠀⡇⠀⠙⣾⡽⣄⠀⡰⢻⢰⡇⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⣤⠬⢧⠈⢳⡬⢷⣼⣄⡈⠉⠀⣷⠀⠀⡿⣄⠈⠛⠀⡜⣠⠛⠉⠀⣀⣠⠤⠴⠒⠲⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⠴⠗⠀⠹⣧⡙⣟⠛⣎⣧⠀⡇⠈⢳⡴⠊⢠⠃⣠⠴⢊⡥⠖⠚⠛⠛⠓⠲⠦⣍⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡤⠴⠷⣝⣎⢦⠘⣿⡆⢧⠀⣼⠀⢠⡧⢚⡥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠛⠚⠻⢷⣷⡘⣿⣼⠀⡇⢠⢟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢀⣠⠤⠤⠒⠖⠒⠤⠤⣉⣳⡘⣿⡀⣧⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⣠⠤⢤⣉⠻⣿⣷⣿⢃⣠⠤⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⢙⣿⣿⣿⣉⡀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⣩⠟⢹⣿⣿⠳⣌⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⢠⠞⣿⣿⢧⡀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢸⠙⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣯⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠙⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢸⡶⣄
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢸⡇⠘⣇
⠀⠀⠀⠀⠀⠀⢸⣧⣶⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣼⠇⢀⡿⡄
⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠉⠙⢿⣿⣷⣄⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⣠⣤⣾⣿⣴⣾⢁⡇
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⢠⣿⣿⣦⣤⣤⣴⣶⣿⡿⠻⠿⠟⠛⠋⠉⠉⠉⠛⠋
⠀⠀⠀⠀⠀⣿⣀⣀⣤⣶⣤⡀⠀⠀⢸⣿⣷⣴⣶⣾⡿⠛⠛⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠙⣿⡟⠉⠉⠻⣿⣤⣶⡿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢻⣧⣄⣀⣤⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠒⠒⠒⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⢤⣄⣁⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠉⠳⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡏⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⡇⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠶⠦⢤⣉⠳⢄⠀⠀⠀⠀⠀⠀⣧⠀⠃⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣸⠁⢀⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⠳⣌⠳⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣠⠾⢥⣤⣎⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠘⣆⠁⠀⠀⠀⠀⣸⣇⠀⢀⣀⣀⣤⠴⠞⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣠⣤⣔⡂⠀⠀⠀⣹⣄⣀⣠⡤⠞⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠙⣦⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠰⠶⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⣊⣉⠭⡤⠤⢤⠤⠬⢭⣙⡒⠦⣀⠀⠻⠷⣀⣀
⠀⠀⠀⠀⠀⡰⣡⣶⣋⣭⣥⣴⣶⣶⣶⣶⣧⣔⠀⠈⠑⠪⡻⣄⠀⠀⠈⠑⣄⣀⣠⠄⠀⠤⠄⠠⢄
⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣺⠗⠀⠀⠀⡹⣏⣹⠦⠤⠚⡁⠀⣀⡴⠂⠈⠀⠠⠊
⡴⢊⡭⠭⣙⣿⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢀⣠⠤⣚⣹⡟⠋⢀⠄⣸⣷⣚⡉⠉⠀⠀⣠⣆
⣇⢸⡀⢀⡼⣿⣿⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⣍⣴⣿⣿⣿⢧⣤⡷⢞⣉⠁⠀⠀⠀⣴⣉⣠⣄⣙⡢⢄
⠘⢦⡙⠯⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠀⣌⢧⡀⠭⠀⢠⢶⡉⠻⠀⠉⠈⠉⠂⢘
⠀⣼⠙⡷⠦⣽⣟⠣⠀⠀⠀⠀⠀⠀⠀⠀⣌⠙⣿⣻⣿⣿⠇⢀⡿⣧⢿⣯⣭⣓⢦⣉⣀⣠⠤⠤⠶⠋⠉
⠀⢿⠠⠂⠀⠀⠙⢦⡀⣠⣄⣀⣄⣠⣀⣦⣿⣼⣿⣿⣿⣿⣶⣄⣠⡿⣻⣧⣩⣿⠟⠁
⠀⠘⢆⠠⠀⠀⠀⠀⠙⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⠤⠆⣱⣿⣍⣧⣽⣀⡀
⠀⠀⠈⠓⢤⡀⠀⢀⡀⠀⠀⠈⠙⠛⠿⠟⠿⠿⠟⠛⠉⠉⢀⣠⣾⣿⠛⢽⣿⣭⣿⢿⡆
⠀⠀⠀⠀⠀⠈⠓⠲⠤⣍⣁⣀⣀⣀⢀⣀⣀⣀⣠⣤⣶⣞⣩⣿⣿⣿⢀⡘⠿⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠛⠉⠉⠉⠈⠿⣯⠭⠶⣿⢿⣝⢧⣀⣾⣯⣽⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢿⣼⠏⠳⠬⡅⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣤⡤⠐⠒⣒⣶⣤⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⡠⣺⠉⣀⠔⡪⢁⡠⢤⣤⣤⣄⣀⣀⡒⠋⢉⣉⠤⠬⢭⣶⠤⣀
⠀⠀⠀⠀⡀⣼⢃⠞⡱⠊⡔⠁⠼⡳⠄⢒⣒⣒⣚⣛⡳⠦⣄⣐⠀⠀⣀⣀⣀⠱⡀
⠀⠀⠀⠀⢇⠀⠁⠊⠀⢸⠀⠀⠤⠒⠉⠁⠀⠀⢀⡠⠤⠤⠤⠬⠍⣒⣤⣀⠀⠀⡇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠸⠀⠀⠀⠀⠤⠶⠤⠤⠒⠒⠉⢉⣉⣉⠀⠠⢀⣈⡑⠦⡁
⠀⠀⠀⠀⢀⠤⢀⠔⠀⠐⠢⣀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⠤⠒⠒⠉⠉⠉⠛⠋⠺⠶⣄
⠀⠀⠀⠀⠇⢠⡁⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠈⠁⠀⠀⠀⢀⡠⠤⠀⠀⢈⣉⣁⣒⠢⢬⡳⡄
⠀⠀⠀⠀⢗⡸⣈⠑⠢⣄⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠘⠋⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠚⢆
⠀⠀⠀⠀⠀⠑⢨⡛⠓⠺⣗⠤⠤⠤⠤⣔⡇⠠⢄⡀⠀⠀⠀⠀⠀⠀⠶⠶⢀⣀⣈⣉⡁⠒⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⣟⠿⠿⢭⣴⠞⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠔⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⣦⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⣟⡿⠋⡁⠄⠀⣠⡀⠈⠁⠒⠬⢝⡺⢷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠕⣿⡷⠉⢂⠕⠊⠀⠀⠈⣃⠐⠀⠀⠀⠐⢍⠲⣝⢷⣌⠷⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡴⣫⠞⠁⣾⠏⡄⡔⠁⠠⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠈⠎⢿⣦⣤⠖⢘
⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⢸⣼⠘⠨⠀⠀⠀⠁⡀⠀⠀⣴⠄⡀⢁⠀⠀⠀⠀⠀⠀⠘⣼⡇⣠⢾⣧⡀
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿⢿⢀⠀⠐⡀⡀⠀⠘⠦⠄⣀⣄⠀⠈⠀⠀⠸⠀⠀⠀⠀⡇⣿⣥⣀⡀⠀⠈⠀⠒⠄
⠀⠀⠀⠀⢰⠃⠁⠀⠀⠀⢻⠸⡈⠌⢆⢳⣕⢄⡀⠀⠀⢈⠃⡴⣋⢔⠵⠁⠀⠀⡸⢸⢹⣿⠟⠻⠉⢗⡶⠦⠤⠃
⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠈⣧⠱⡀⠀⠀⠙⠻⢟⣓⠶⣤⡁⣴⡿⠃⠁⠀⢀⠜⡱⢣⣿⠛⠃⠀⠀⠈⣧
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⣷⣙⢦⡈⠲⢄⡀⠀⠉⠢⢱⠇⠀⠀⠀⠔⣡⢞⣵⣿⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⢍⡲⠤⣌⣁⣀⣀⣀⣀⣠⠤⢖⣫⠴⣻⠞⠁⠀⠀⠀⠂⠀⠀⡟
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢂⠈⠻⡷⣍⣙⡒⠲⠾⠭⠶⠶⠒⢛⣉⡴⠞⠁⠀⡀⠠⠀⠌⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠠⡣⡈⠮⡛⠻⠷⠶⠶⠶⠖⠛⠋⠉⠀⠀⠠⠊⠀⢀⠌⠄⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠓⠀⢀⠀⠀⠀⠀⠀⠀⡀⠄⡪⢀⠕⡡⠊⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠈⠂⢅⡀⠀⢀⠀⠈⠀⠀⠀⠂⠉⢀⠁⠊⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠄⣢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣗⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣖⣫⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠯⠭⣿⣿⠿⠭⠭⠷⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐
⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣠⠴⠐⢁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⡠⠀⠤⠂⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠐⠒
⠀⠄⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠆
⠀⠠⠀⠀⠀⠀⠀⠀⠨⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⠀⠀⠀⠀⠀⠀⠂⠐⠊⠂
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠴⠏⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠁⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠘⠄⠰⠅
⠀⠀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡤⠢⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄
⠀⠘⠀⠁⠁⠑⠀⠀⠀⠀⢀⠒⠀⠃⠴⠁⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀⠐⠂⢄
⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠐⠌⠀⠚⠈⠈⠀⠸⠀⠀⠀⠀⠁⠃⠀⠈⠀⠀⠀⠀⠀⠐⠀⠐⠂⠐⠀⠒⢈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠐⠠⠤⠥⠤⠔
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠠⠾⠿⠀⠀⠀⣤⡄⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡼⠒⠒⠢⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠄⠀⡜⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⠀⣇⠀⠀⠄⠤⠀⡇⠠⠀⠄⢨⡀⢀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢦⣀⠀⣠⠎⠑⢄⠀⣀⠞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⠤⠠⠆⠀⠀⠀⠀⠀⠒⠦⠄⢄⡀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢴⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡿⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠴⠖⠒⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠒⠲⢤⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⡜⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠙⠄⠀⠱⡀
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⡃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⡏⠀⠀⠉⠓⢄
⠀⠀⠀⠀⢰⠋⠀⡴⡶⡄⠀⠣⡀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡇⠀⠀⠀⡠⠃⠀⡴⠶⡄⠀⢣
⠀⠀⠀⠀⠈⠢⠾⡡⠃⠘⠒⠒⠁⠀⠀⢸⡇⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠒⠊⠀⠣⣽⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠒⠚⠓⣶⠲⡖⡶⢲⡖⠛⠒⠚⠛⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⡀⣿⢸⡇⡇⢸⡇⣀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠈⠙⠛⠸⡇⡧⠘⠋⠉⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠀⠆⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡄⡀⢠⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⢠⡇⠁⠘⡆⡃⢰⠗⠁⡴⢤⠀⠱⠼⠁⡈⢦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡇⠀⠘⡇⢀⠀⢸⠃⢀⢆⠀⣷⠀⠀⠆⠀⠀⠳⡈⠀⠨
⠀⠀⠀⠀⠤⡀⠀⠀⠰⠀⠀⠀⠂⡐⡂⡀⠈⠀⣬⡇⠂⢸⠀⢐⠀⠀⠈⡄⠀⡀⢡⠇⠀⡀⡠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢘⣰⠆⢁⠄⠈⢧⢼⠁⠆⠀⠀⠈⢻⠀⡔⠀⠀⠀⣧⠀⠀⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⢼⣿⣄⠨⣆⣾⠊⢇⠓⣘⠀⢠⣰⢛⠀⠇⠀⢠⢠⣿⢠⣀⢸⣇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠊⠙⠙⠛⠐⠛⠙⠁⠈⠁⠉⠁⠀⠉⠈⠀⠁⠈⠉⠉⠛⠉⠉⠙⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⠄
⠀⠀⠀⠀⠀⠀⠚⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣤⣤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣄⡤⠤⢀
⠀⠀⠀⠀⠀⢀⣠⠔⠒⠉⣷⠂⠄⠘⢦⡐⠄⠙⣿⢢⡀⠀⠀⡀⣾⠋⡠⢒⣚⣱⣶⣄⠀⠀⢠⠎⠀⢀⡀⠼⠀⢢⣀⠀⠑⡄
⠀⠀⢀⠴⢪⢅⠈⣇⠑⣄⠹⣆⠀⠀⠈⣧⠘⠀⠸⣀⡇⠀⢠⠁⠓⠀⡄⠉⠛⠉⠉⠉⡀⠀⣾⠀⠖⠀⠀⣤⢀⠀⠀⠱⡄⢸
⠀⢠⠃⠀⢿⠀⠁⠘⢦⠈⡄⠹⣦⠀⠀⠸⡄⣇⣴⡿⠁⠀⠘⢧⡀⠘⠤⠤⠒⠚⠉⢻⡇⠀⣿⣆⡀⠀⠀⢸⠌⠀⠀⠀⣀⡾
⠀⢀⠀⠀⠈⠳⢄⢢⡈⢣⣼⡀⣙⣦⣦⣴⡿⠟⠉⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⡤⠟⠀⠀⠙⣿⣷⣶⣤⣤⣤⣴⣶⣿⡿⠃
⠀⠈⠓⠶⠶⠤⠴⠾⠿⠷⠿⠟⠛⠋⠉⣀⠤⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⢛⣛⣿⢟⣉⠁
⠀⠀⠀⡠⢴⡂⠐⠒⠲⣤⣄⡀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢱⠀⠀⡠⠀⠀⠙⢾⡟⠓⠄⠀⠀⠀⠀⣰⠺⠁⠀⠀⠀⠈⡋⠑⡒⢲
⠀⣠⣎⡁⠐⢌⠆⠀⠀⢸⠅⠹⣄⢸⡄⠂⠀⠀⠀⠀⠀⢠⠄⢰⣧⣄⡀⠀⡼⠁⠀⠘⡄⠀⢠⠞⠉⠳⡱⡄⠀⠀⢠⡇⠰⠗⠉
⠈⠒⠒⠒⢬⣸⣷⣆⣼⣯⣠⣏⢘⠀⢧⠀⠀⠀⠈⠀⣠⠞⠀⣾⠉⠉⠙⠿⠁⠀⣀⣴⡏⠠⠉⢱⣤⡀⣸⣾⣄⣤⠞⠁
⢠⣁⣀⡤⠿⠟⠛⠋⠀⠀⠀⠈⠉⠀⠀⠉⠓⠒⠒⠊⠁⠀⠀⠸⡀⡀⠀⢘⡀⠀⢀⡜⠁⠈⠈⠉⢉⣩⣭⡑⠒⠒⠒⠤⢄⡀
⠀⠁⢀⠤⠖⠒⠈⠉⠈⠉⢹⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⠤⠾⠃⠀⠀⠀⢀⡤⠀⠉⠀⠉⠉⠙⠢⣄⠀⠀⠙⢆
⠀⠀⠺⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠻⠿⣿⡓⠂⢄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⡼
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡄⠱⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢮⡿⠛⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⣴⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⡇
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⡿⠀⠀⠈⠙⠒⠀⠤⢀⣀⠀⠀⠀⠀⠀⣸⠿⠋⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣠⠴⠃
⠀⠀⠀⠀⠉⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠓⠚⠲⠶⠔⠈⠘⠋
⣟⠉⣹⣛⣟⣟⣛⣻⣿⣛⣛⣻⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣟⣛⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠶⠒⠒⠶⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠉⠉⠉⠉⠁⠈⠉⠙⠒⠦⣍⠒⠌⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⡀⠀⠈⢧⠩⡐⢄
⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡰⡀⠀⠀⣧⢰⠀⠣
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢇⡄⠀⢸⢘⠆⠀⣇⢀⡀
⠀⠀⠀⡜⠀⠀⢠⠴⠒⠉⠉⠉⠉⠓⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⡆⠃⠀⣸⠈⠀⠀⢸⠀⠀⠑⢄
⠀⠀⢠⠁⢀⠄⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⢀⠙⠢⣄⠀⠀⠀⠀⠆⠐⠀⠀⠁⡇⢠⡀⣿⢰⠁⢀⡞⠀⠀⠀⢸
⠀⠀⢸⠀⠂⡠⠊⢀⡠⠴⠒⠒⠲⠤⠤⣀⡀⠙⠢⡀⠙⠢⡀⠀⠀⠀⠀⠀⡀⡇⢊⣼⢇⠞⣠⠟⢐⡔⠀⢀⠆
⠀⠀⢸⡘⡐⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠐⠄⠱⠈⡄⠀⠁⠀⠾⢸⣡⠾⣿⣭⠥⠷⠖⠈⠉⠈⠁
⠀⠀⠀⠳⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢷⠋⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⣯⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢣⢸⢆⠀⠄⠀⣸⠁
⠀⠀⠀⠀⣿⢠⢂⣾⠆⣠⠔⠒⠈⠉⠉⠉⠀⠲⢴⣍⢮⡜⣸⢮⣘⣃⣠⠇
⠀⠀⠀⠀⢇⠈⣾⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣧⡏⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠢⣤⢸⠀⠀⠀⠀⠀⢀⠴⠊⠉⠑⠢⡀⠿⠿
⠀⠀⠀⠀⠀⠀⠈⠺⡄⠀⠀⠀⢀⠏⡠⠖⠋⠈⠉⠑⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣂⡁⢸⣰⢀⠀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⢧⣴⣆⢤⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⡤⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠈⡉⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡧⠀⠀⠀⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠀⠁⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡋⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣠⢤⠔⠒⠂⠛⠛⠛⢿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠃
⠀⠀⠀⢀⡼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢘⣿⡯
⠀⠀⠀⢸⣷⠀⠋⢀⡀⢀⠀⠀⠀⣀⠀⠀⠀⠉⢻⣿⡲⢄⣀⣀⡠⠄⠒⠀⠀⠁⠄⠀⠀⠀⠀⠀⢸⣿⣷⣄⣆⡀
⠀⠀⠀⠈⡿⠘⠀⠀⠙⠧⠛⠛⠁⠉⠀⠀⠀⠀⠀⢻⣇⣥⠁⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣠⠀⢀⡰⠊⠙⢢⡀
⠀⠀⠀⠀⠲⣀⣠⣇⠀⠀⠈⠈⠱⠤⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣖⠀⠀⠀⣨⣿⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠙⠮⡻⣇⠠⣆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⣿⠖⣾⣿⡯⢁⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣿⡀⠀⠀⣠⠀⠀⠀⠐⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣂⣄⠀⠀⠁⠀⢄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠠⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠀⠠⠀⢀⠀⠀⠀⠉⠉⠉⠙⠛⠛⢿⣻⡎⠀⢾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⢀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣌⠄⣀⠤⠤⠠⡄⠀⠈⠈⠐⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠞⠁
⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⠉⠀⠀⣼⠁⠀⠀⠀⢠⠀⠀⠀⢀⠐⡇
⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡀⠂⠐⠋⠀⡀⠀⠔⣺⠆⢈⣀⠄⠈
⠀⠀⠀⠀⣿⣿⡆⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⠄⠀⠶⠒⠃⠎⠙⠁⠒⠁
⠀⠀⠀⠀⠹⣿⣧⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠶⣂⠒
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠠⠂⠡⣆⠲⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠶⡖⠂⠀⠀⢀⣀⡀⠀⠀⠀⢠⡤⢤⡄⠀⠀⠀⠀⠀⠀⢀⡤⢒⡀⠀⠀⠀⠌⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣧⣬⠀⠈⡷⢈⠀⠁⠀⠀⣾⢷⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠟⢀⡄⠀⠀⡀⣰⣆⣀⣀⡄⠴⠀⠀⠀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠛⠁⠀⠀⠀⠀⣿⣿⣿⣇⠠⠀⡄⠛⠀⠀⠀⠀⠀⠀⢠⠀⠀⢈⡱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣼⠒⣡⠆⡀⠀⢴⡀⠀⠀⣴⣶⠂⠋⠁⠀⢀⠀⠀⠀⠀⠀⣄⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠀⠁⣠⠏⡠⠊⠁⠈⠻⠆⣀⠂⠒⠃⠀⢀⣠⡀⢘⢃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠷⡤⠤⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⠤⣄⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣎⣀⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⣀⣠⠤⠴⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠙⢤⣀⡤⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣀⡤⠤⠶⠒⠊⡟⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡶⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠳⠤⠖⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⢤⣠⣞⣠⠇
⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠣⣀⣀⡰⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢹⠀⣀⣀⡤⠤⠒⠚⠉⠉
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠿⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⡇⠀⣀⣀⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⣠⠄⠄⢀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡠⠨⠍⠁⠤⠈⠀⠀⢀⣀⡴⡐⡄⠀⠈⡀⠰⠄⡀⠈⠂⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠛⢂⠆⠀⠀⠀⠀⠁⠀⠃⠀⠀⠰⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠀⠀⠀⠀⢠⣤⠄⡄⣠⣤⢠⣤⣤⡀⡤⠄⠀⠀⢤⠀⢾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⢁⡀
⠀⠀⠀⠀⠘⢦⣤⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠠⠀⠂⠀⠀⠀⠀⠀⢤⠀⠀⢨⣐⣀⠂
⠀⠀⠀⠀⡀⠀⠑⠄⠠⠄⠈⠒⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢴⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠐⠀⠀⠀⠀⠠⠀⠛⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠠⡀⠀⠀⠀⠐⠀⠀⠀⢀⢤⣀⣀⠀⡀⠀⠀⠄⢸⡆⠀⠀⠀⠀⠀⣀⠀⠈⠱⠀⠀⠀⡀⣲⣴⠀⠈⡐⠦⠠⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢴⠾⠥⠺⠏⠀⠀⠀⠀⠈⠉⠋⠉⠊⠀⠀⠀⠀⠉⠀⠀⠀⠈⠣⠌⢢⡀⠀⠘⠀⠈⠟⠅⠁⠀⠀⠘⠳⢤⣚⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⠃⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡼⢻⡆⠀⣰⠃
⠀⠀⠀⠀⠀⠀⡇⢸⣷⡞⢀⠘⣷⠞⡟
⠀⠀⠀⠀⡆⠀⢇⣾⠈⢳⣾⠞⠁⢰⣧⠁
⠀⠀⠀⠀⢃⠀⢸⣿⠠⠀⣿⡴⣡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠸⡀⡎⠘⢷⣧⣿⡿⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⠔⠁⠀⠀⢀⡠⠖⠁
⠀⠀⠀⡀⠀⣧⣿⢀⠀⢿⠏⡀⢸⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⢏⣠⢶⣏⣤⠴⢶⡾⠋
⠀⠀⠀⢰⠀⣿⢿⣦⣧⣸⡞⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣀⣴⣷⢋⠁⣼⡯⢀⣰⠟⠀⢀⣀⡀
⠀⠀⡀⠀⣇⢸⠀⠙⢿⣿⡿⠋⣹⣃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡞⠋⢹⣇⡎⣠⡿⢛⠉⢉⡽⠟⠉
⠀⠀⢰⠀⢸⣾⣇⢀⠘⡿⡡⢀⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡸⢀⡴⢿⡟⡔⠀⣼⣿⣿⣿⣿⣶⡾⠿⠒⠂⠉
⠀⠀⠀⢣⠀⡏⠹⣮⣦⣿⣡⡿⢿⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣰⣷⠏⠀⢸⣷⣥⣞⡩⠀⣠⡴⢋⣡⠤
⠀⠠⠀⠘⣧⣷⡀⠘⣿⣿⠋⠀⣸⡟⠀⢀⠀⠀⠀⠀⠀⠀⣰⢃⡾⢹⡇⡌⠀⣾⣿⠿⠷⢶⣿⠟⠉⠁
⠀⠀⢇⠀⣏⠻⣷⣤⣼⣧⠄⣠⣿⡇⢀⠂⠀⠀⠀⡘⠀⣠⣷⡎⠀⠀⣧⣦⣎⠁⠀⢀⣴⠈⠤⠒⠂
⠀⠀⠈⣆⢹⡀⠈⢿⣿⣯⡴⠋⢹⢁⠎⠀⠀⠀⠀⢀⡞⠁⢸⡄⢀⣼⠿⠟⠒⠒⡿⠋⠁
⠀⠀⠀⠘⣯⣷⡐⣄⢿⡿⠁⠀⣾⡟⠀⠀⠀⠀⣼⣿⢀⠀⢨⣿⡿⠅⠒⣀⣴⡪⠤⠂⠉
⠀⠀⠀⠀⢸⡟⣿⣾⣿⣵⠃⣴⣿⡇⠀⠀⣠⡾⢻⣏⣸⣠⡿⠿⠿⠟⣿⠟⠋⢀⠄
⠀⠀⠀⠀⠀⡇⠈⢻⣿⣧⡾⠋⠀⡗⠀⣰⠋⠀⢸⣿⡿⠧⠐⢀⣠⢞⣡⠔⠊⠁
⠀⠀⠀⠀⠀⢹⡀⣄⢻⡿⢁⠀⣰⠇⠀⡏⢸⠀⣼⡿⠷⠶⠿⢿⡟⠋
⠀⠀⠀⠀⠀⠈⢻⣌⣾⣿⢋⡴⠋⠀⠀⢷⣾⡿⠿⠖⠂⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠋⠀⠀⠀⢀⡾⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⣰⠃
⠀⠀⠀⢰⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠀⠀⠒⡂⠐⠒⠦⠤⣋⣉⠉⠩⠉⠙⠒⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣚⣋⡀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓⢦⣀⣀⠀⢄⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠌⠠⠒⠔⠲⠈⠍⠩⠉⠙⠛⠛⠛⠛⠒⠒⠤⣌⡀⠠⡀⠉⠁⠀⠈⠙⠲⣄⢀⠀⡴⠐⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡈⣀⢈⣥⣤⣀⡀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠼⠄⠀⠀⠀⠀⢠⡈⠛⠀⡠⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠽⠚⠁⠉⠀⠀⠐⠉⠍⠉⠉⠙⣛⠓⠚⠣⠦⣄⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⢀⠀⠀⠀⠨⢆
⠀⠀⠀⠀⠀⠀⡰⡷⠁⠀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠑⠫⣢⡀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠈⠀⡀⠀⠅⢪⡀
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠠⠀⠤⠉⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠅⠀⠀⣀⠊⠀⢈⡹⣷⣌⠂⠄⠀⢁⠀⠀⠆⠄⠆⠀⢁⡨⠀⠀⠀⠀⣿⣓⣒⡀⡀
⠀⠀⠀⠀⢀⣀⣴⠿⠿⣦⣄⣈⡀⠀⠀⠀⠄⠠⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠻⣦⠀⡀⢂⡴⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⣴⡋⠐⠂⠠⠀⢀⡀
⠀⢀⣴⡾⠛⠉⠉⠉⠨⠉⣉⠉⠈⠛⠀⠛⠷⢶⢤⢬⣀⡀⠁⠀⠀⠠⠀⠐⠂⠀⠀⡀⢂⠂⠠⢳⡧⠐⠃⠀⠀⠐⠀⠂⠀⠀⢀⢀⡨⠞⢁⣀⠀⠐⠀⠀⠉
⢠⣨⠁⠀⡀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠅⢀⠀⠀⠨⠍⠐⠛⠿⢶⣤⡀⠀⠀⢀⠀⠀⠀⡩⠂⣾⠷⠔⠐⠶⠳⠶⠾⠶⣶⣷⣶⣾⣿⣶⣶⠶⣶⣶⣶⣷⣶⠖⠂
⢺⠉⠙⠳⢦⣤⣐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⠀⢛⢶⡀⠈⠡⠀⠀⢀⣴⡽⠲⠲⠒⢒⠳⠶⠖⠛⠛⠻⠿⠏⢻⣿⣿⣿⣿⣿⠟⠋⠉
⠈⠉⠁⠶⢄⡀⠉⠛⠶⢤⣀⠀⠁⠀⠐⡀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠄⢳⣿⡻⣷⠖⣞⣿⢫⠾⠟⠛⠛⠿⠏⣛⣛⠛⠛⠛⠒⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠒⠲⣄⠈⠉⠓⠶⣠⡀⠀⠀⠀⠀⠀⠀⠆⠈⠤⠀⣀⣎⣼⠤⠩⠀⠀⠉⠑⠒⠒⠢⠥⠒⠒⠠⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣤⣀⣙⠣⠗⠶⠒⢒⣲⣖⣼⡿⡛⣡⡮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⠶⠤⢴⣂⣲⣧⣴⠟⠛⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⢻⡉⠀⠀⠀⠀⡏⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⡔⣿⣿⣿⣿⣿⢸⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢧⠀⠀⠀⠀⠱⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣦⢻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡽⠋⠉⠳⣤⠇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⡿⠂⠀⠀⠈⠛⠃
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⠟⠁
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣹⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⡏⠀⠀⠉⠓⠲⠤⢤⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣭⣛⡻⠿⠿⠟⠁
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⡏⠉⠉⠉⢉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣴⡆
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⡄



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠊⠁⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⢀⠠⠔⠒⠋⢉⣩⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⡤⡊⠁⣀⠤⠒⠉⠁⠀⠈⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢐⡵⣞⠕⠋⠀⠀⠀⣀⡠⠤⠚⢀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠞⡩⠊⠁⠀⣠⠔⠚⡍⢠⡀⣄⣀⠈⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠐⢉⡵⠊⢀⡠⠒⡉⠀⡴⢺⣧⡿⠉⠁⣉⡠⠤⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣠⠊⢀⠔⠋⣰⣃⣻⢧⡇⢀⡠⠔⠊⠉⢀⣀⡠⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡜⢁⠔⣡⠦⠼⠝⠋⢉⡠⠚⠉⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠎⣠⠋⠀⠉⠀⠉⢀⠔⠁⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢠⠂⣰⠃⢀⣠⡄⠈⡴⠁⢀⡼⠋⠀⠀⠀⠀⠀⠀⢀⡠⠖⣋⣭⣴⣖⡾⠷⢲⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠃⢠⡧⠞⣻⠟⢠⠎⠀⣠⠊⠀⠀⠀⠀⠀⢀⡠⢞⣭⡶⠉⢂⡭⠐⢊⢉⣩⡉⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡰⠃⠀⠈⠀⡴⠋⡠⠂⢀⠞⠀⠀⠀⠀⠀⢀⣴⣿⡾⠛⢁⡤⣚⣡⣄⠺⣿⣿⣷⠀⢄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣠⠞⠁⠔⠁⡰⠋⠀⠀⠀⠀⣠⣾⢏⠑⠁⣠⡔⣭⣥⣝⠿⠻⣟⣃⣉⣉⣀⡀⠃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢢⠤⣔⠁⠀⠀⠀⠘⠡⢀⠈⠀⡴⠁⠀⠀⢀⣠⠞⢛⠟⠁⡠⠊⣶⠛⢚⡩⠔⠊⠉⠀⣀⢠⣤⣤⣈⡷⠁
⠀⠀⢠⠤⠠⠄⡠⠁⠀⠀⠐⣀⣀⠾⣡⠋⠀⠀⠀⢀⠔⠛⠁⠠⠊⠀⠀⢀⢔⡿⣿⠖⢁⠔⠈⠠⠛⡠⠐⠁⠀⣀⠔⠊⠉
⠀⠀⠘⠂⠠⠄⢒⡠⣈⣲⣿⠿⢉⠀⠁⠀⠀⢀⠖⡋⠊⠀⠔⠁⠀⡀⣢⢕⠷⢋⡠⠞⠁⠀⢀⠔⠈⠀⣠⠔⠋
⠀⠀⠀⠀⠀⢄⠐⠊⢹⠟⡆⢨⠁⠀⠀⣠⣘⠊⠂⠀⠠⠁⠀⠄⡨⠾⠁⠁⠐⠁⠀⠀⠠⠂⡠⢂⠴⠊⠁
⠀⠀⠀⠀⠀⠈⠳⣶⠀⡘⠀⠸⢦⣤⡿⠑⣠⢀⡤⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⡠⠔⠁⠠⡨⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⢸⣾⢲⡉⡉⢛⠛⠒⠉⠁⣀⣀⠄⠒⠀⠠⠴⡂⠉⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⣬⣿⣯⣭⣁⠉⣉⣨⣅⠴⠄⠀⣀⠴⠊⣁⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠿⠛⠛⠋⠋⠀⠀⢂⣁⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣒⣒⣀⡤⠴⠒⠋⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣠⠄⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣼⡏⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢻⣧⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠻⣷⡀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢹⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⡼⠃⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠀⠒⠒⠂⠒⠒⠒⠒⠐⠒⠒⠒⠒⠐⠒⠀⠠⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡖⢉⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡍⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⣇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡰⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⠤⠊⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⣀⣀⠤⠐⠁
⠀⠀⠀⠀⡠⠄⠒⠒⢈⣉⣭⣤⣬⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣧⣤⣤⣤⣉⡁⠒⠒⠠⢄
⠀⠀⠀⠀⠢⢄⣀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⢤⡀⠭⠭⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠭⠭⢀⡤⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠂⠀⠤⠤⠤⠤⠤⠤⠀⠐⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠔⠓⢆⡀⢐⣦⣠⠼⠷⡖⠀⠀⢀⠠⡾⠀⣤⣤⣤⣭⣥⣀⣀⡀⠀⠀⠘⠿⠃
⠶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣮⣷⢶⡚⠙⢯⣀⣈⣶⣤⠀⠀⠀⠀⠀⢱⠀⢒⣒⣒⣿⣿⣿⠿⠇
⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣧⠟⢾⡉⠉⢳⣄⡈⠀⠀⠠⠄⠀⠀⠀⢴⠚⠛⠩⠉
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠺⠗⠀⠀⠀⠀⠀⣿⠶⠖⠛⠛⠩⡈⠀⠐⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣶⢆⣶⠁⢀⣀⠄
⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠰⠷⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⢸⠇⣴⣿⣿⣿⣦⢠⡀
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣾⡄⢿⣿⣿⣿⡿⢰⡿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⢿⣁⠀⠀⠙⠿⢦⣽⡿⣿⡁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⣤⣤⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⠀⣰⠛⠁⡠⠒⠒⠄⠀⠀⠀⠀⠀⠚⠋⠟⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢁⠠⠤⠀⠀⠀⠀⠀⢀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠁⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⠓⠂⢀⢘⡄⠀⡄⠀⢀⣤⠉⠦⣤⠴⠙⠀⡀
⠀⠀⠀⠘⠁⠐⠄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠂⠀⠢⠀⠋⠒⠒⠂⠈⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠒⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡐⠾⠃⡡⢤⣭⡝⠋⣀⠶⠶⡦⠀⣀⡀⠠
⠀⠀⠀⠠⠀⠄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢀⠀⠁⠛⠛⠻⠶⠄⠠⢾⣽⡻⢋⢀⡶⠾⠁⣀⠀⠀⠀⠀⠢⣀⣴⣐⣆
⠀⠀⠀⠀⠐⢀⣹⠛⠟⠛⠓⠈⠀⠀⠀⢤⡀⠀⠀⠈⣠⠀⠀⠀⠈⠳⠒⠒⠠⠄⠀⠀⡀⣀⣀⡀⠀⠀⠤⡀⠀⠁⠀⠀⠀⠁⠤⣼⡿⠽⠞
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠀⠋⠀⢂⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⢹⣿⣿⡄⠀⠉⠉⠉⠛⠻⠷⠀⠀⠀⠆⠀⠀⢠⠆⠌⠁⠉⣴⣎⣀⠀⠹
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠃⡢⠤⡀⠀⠀⠀⠨⣹⣿⣿⣷⣾⣿⣿⠃⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠠⢴⡄⠀⠀⠀⠈⠀⠠⠑⠌
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢒⣀⣄⡀⠈⠉⠀⠭⠋⠛⠁⠀⣼⣿⣿⣿⢿⣶⣔⣄⠀⠀⠀⢀⠀⠈⠀⠈⠙⠛⠃⠠⠀⠃⠎
⠀⠀⠀⠀⠀⢀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠠⠀⠂⠢⡀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣶⣶⣟⣻⡇⠀⠀⠈⡼⠎⢒⡀⢲⡄⠰⢼⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡁⠤⢠⡀⠀⠀⠀⠉⠉⠍⠩⠽⠛⠁⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠁⠀⠁
⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠐⠒⢓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠂⣄⡀⠀⠀⠀⠐⠠⠀⡈⠀⠀⠀⠀⠀⢀⠀⠂⠀⢠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠢⠀⡈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠄⠐⠁⠀⠀⠀⠄⠀⠀⠈⠚⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠁⠈⠁⠋⠠⠀⠀⠀⠀⣰⣶⣠⣤⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠈⠀⠀⠀⠀⠀⠰⠂⠠⠀⠀⠀⠈⠈⡁⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠖⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠄⠀⠁⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⣠⢈⡄⡤⠠⠆⠿⡄⠁⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠖⠒⠈⢁⡠⠶⠪⢤⠏⠄⠀⠀⠉⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⠂⠀⠀⠀⠀⠀⠐⠞⠉⠁⠁⠈


⣿⠿⠿⠿⡿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⢄⣠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠
⠀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠚⠻⢸⠾⢡⠻⢓⠀⠀⠀⢀⡀⠔⠒⠋⠱⠤⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⢠
⠀⠧⣄⣀⣀⣀⡠⠜⠀⠀⠀⠀⠀⠀⠘⠈⠈⠁⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠆⠀⠀⠀⡀⠞⠚⠁⣸⠜⠉⠀⡀⣴⠀⠠
⠀⠿⢦⣤⡄⠽⡤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠘⠚⠀⠈⠓
⠀⠀⠀⠬⠩⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢀⣀⠀⠠⠄⢀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣶⣿⠟⠳⠶⠦⢦⡄⠀⠀⠀⠀⠀⠁⠀⠀⠁
⡔⠀⠁⠄⠄⠀⠒⠀⠲⠂⠀⣈⠁⢂⡠⠀⠀⠀⠰⠒⠀⠲⠶⠛⠉⠉⠂⠀⠀⠀⠈⠉⠻⠥⢀⣀⢤⡤⠴⠂⠀⠀⠀⠀⠀⠄⡀
⠈⠲⠤⠤⢑⣁⣂⠀⡀⠈⠛⢀⠀⠀⠀⠔⠂⠀⠀⠴⢤⣄⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠿⠾⠶⠶⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂
⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⣤
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠐⠀⠀⠀⠀⠁⡀
⠀⠱⢬⣽⣿⣿⡫⠅⠀⠀⠀⠀⠁⠀⡇⢠⠀⡄⠁⠀⠀⠖⠄⠐⢠⠤⠀⡄⠀⠀⡄⡀⠀⠀⢏⠀⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠔⠁⠸⢄⠀⠀⠠⠀⠢⠀⠰⠘⠠⠃⠡⠠⠠⠁⠃⠀⠀⠈⣉⠃⠀⠀⢠⣷⡈⣧⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠾⠋⠁
⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠱⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⡀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠄⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠈⠂⣐⠂⠀⠀⠉⠓⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⣰⡁⢀⣀⣤⣴⣶⣾⣿⣿⠿⠿⠿⣿⣿⣿⢿⣿⣟⣛⣛⣛⠛⠻⣛⡿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⡉
⠀⠀⠀⠀⣦⠻⣿⣿⣿⠿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣷⣬⣉⣙⢻⣿⣷⣆⣴⢁⡼⢀⣠⡔⠂⠉⠀⠲⣄
⠀⠀⠀⠀⢻⡷⢈⣛⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣥⣾⣿⣿⣣⠴⠀⠀⠈⠙⣿⡄
⠀⠀⠀⠀⢈⠁⠀⠀⠁⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡛⠛⢋⢡⣴⣾⡯⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⠼⣿⣿⡯⢸⣿⡿⠟⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣻⣿⣧⣾⠇⠀⠀⠀⠀⠀⠀⠊⡀⠁
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⡏⠀⠀⠀⣀⠤⠚⣡⠜
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⡴⠒⢊⣁⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡞⣿⣿⡿⣛⣉⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠙⠟⠛⠛⠉⠁