Musical instrument Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⣄⢤⠀⡀⠀⠀⣀
⠀⠀⠀⠀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠉⠈⠙⠆⠀⠀⠀⠀⠢⠄⢀⠺⠭⢭⢌⡓⠐⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠠⣾⠀⠀⢀⠀⢀⠔⠁⠀⠀⡆⢰⠀⠰⠀⠆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡐⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⢔⠀⠀⢀⡠⠟⠁⠀⠠⠁⠀⠂⠀⠀⠘⠀⠀⠌⠀⠀⠆⠈⠄
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡱⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⢄⠠⣀⢄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠐⠙⠒⠐⠤⢄⠀⢀⡠
⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⢰⠞⢆⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⢳⡀⠀⢠⡇⢸⡄⠀⢸⠀⠈⢳⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⡴⢄⡠⡀⣠
⠀⠀⠀⠀⠀⠀⠀⢷⠀⣼⠁⠀⢻⡀⣿⠀⠀⠀⠹⣄⠀⠀⠀⠇⠀⠀⠀⠀⢀⡀⠄⠀⠠⠀⢀⠤⠄⠬⠁⣉⢀⠑⠂⡀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡟⠀⠀⠀⢳⡟⠀⠀⠀⠀⠘⠇⠀⠀⠀⡀⠀⣠⠖⠁⠀⠀⠀⠀⠀⡁⢀⠀⣀⠀⡀⠀⠁⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠸⠇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠢⡉⠃⠀⠀⠀⠁⠈⠊⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠑⠘⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠘⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⣾⢿⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⢸⡌⣬⣤⠀⢠⣤⡄⣅
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠉⠀⠈⠀⠀⠀⠀⢱⠄⠠⠤⠀⠀⠀⡀⠀⠀⠀⠀⠛⠻⠀⠸⠇⠟⠻⠀⠸⠻⠇⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⡀⣀⣠⣀⠀⣀⣠⠇
⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠰⠄⡀⠀⠀⢀⠀⠰⠧⡀⠀⡆⠀⢿⠂⠀⠈⠁⠈⡀⠀⠀⡀⠄⠀⠀⠀⢠⠀⢰⣶⠀⣦⠀⡀⠄
⠀⠀⠀⠀⠀⡇⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⠀⠀⢸⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠲⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠼⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠄
⠀⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠁⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⡈⠀⠀⠀⣘⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⢉⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡞⠀⠀⠀⠀⡏
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⡇⠀⢂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠛⠿⠀⠀⠀⠸⡇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠐⠂⠄⠄⠀⠀⢀⠀⠀⠒⠆⠀⠀⠀⠀⠘⠉⠀⠀⠀⠒⠆⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠠⠀⠀⠀⠒⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⠠⠖⠀⠁⠀⡒⠿⠛⣓⡶⠀⠀⠀⡅⢀⣀⠀⠉⠉⠀⣤⡤⢴⡶⠶⠶⠒⠛⣛⠛
⠀⠉⠐⠫⡡⠐⠐⣀⠤⠄⠉⡠⠔⠊⠁⠀⠀⠀⠀⠜⠉⠉⠀⢀
⠀⠀⠀⠀⠐⠾⣗⢀⠠⠒⠁⠀⠀⠀⠊⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⢀⠀⠐⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠖⠀⠀⠠⠀⠀⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⢠⢾⡝⠋⡅⣿⠀⣀⠀⠀⠀⠀⠀⠢
⠀⠚⠀⠀⠀⠐⡀⢀⠀⠈⡀⠀⠀⠀⡙⢯⠉⠉⢿⠀⢻⣤⣾⣿⡄⢐⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣆⣀⡷
⠀⠀⠀⠀⠀⠀⠸⣍⠀⠠⠞⠀⠀⠸⡈⠄⣣⠀⠈⣧⠀⢿⣿⣿⡇⠈⠀⠀⠴⠀⠀⠀⠀⢄
⠀⠀⠀⠆⠀⠀⠀⢻⣤⠀⢀⠀⠀⠀⠱⡌⢘⢧⠀⠘⣧⠘⣿⠟⠋⠀⡠⠀⠀⠀⠀⠀⠰⡾
⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠊⠀⠈⠀⠀⠘⡄⢩⠗⠀⠹⠖⠁⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⣇⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢀⠁⠀⠀⢸⣇⠀⠀⠁
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣯⠐⣥⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠐⠀⠘⠁⠹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠈⣧
⠀⠐⡄⠀⠀⣤⣀⢀⡀⢀⠀⠀⢁⠀⠀⢐⣗⣁⠤⠔⠂⣁⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢴⠒⠤⠀⢸⡇
⠀⠀⡄⠀⠀⣸⣿⡌⠀⢨⡀⠀⠈⠀⠀⠀⣽⠻⠿⠿⠟⠚⡅⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠓⠀⠀⠐⠚⠀⠀⠀⠆⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠚⠁⠀⠀⠀⠂⠀⠀⠀⠀⠤⢤⣤⡤⠶⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⡤⢤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡐⣃⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣇⣛⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⠀⢸⠀⠀⠚⠚⠓⠒⠚⠆⠀⠀⠀⣈⣍⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⢿⣮⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⣾⠡⡆⣳⢸⠀⠀⠉⠀⢰⠉⠁⠁⠀⠃⢰⠋⡴⢹⡆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇⠘⠳⠖⠃⢸⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠓⠶⠛⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠶⠶⠾⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠲⠖⠲⠶⠲⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠀⠀⠀⠀⠀⠀⡄⡀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠇⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠃⡰⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠇⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⡏⢸⡟⢠⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣴⡿⢠⠄⠀⠀⠀⠀⠁⢿⠇⠀⠀⠀⠀⠀⠀⣿⢰⠇⣼⢀⠃⢀⠂⢠⠁
⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⠀⠀⠈⠀⣠⣴⠟⡠⠂⡠⠀⠀⠀⠀⠀⠃⣼⠆⠀⠀⠀⠀⠀⠀⣿⢸⢠⡇⠄⠀⠂⢀⠇
⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠴⡾⢂⡅⢊⠄⠺⣇⠀⠀⠀⠀⠀⠥⢹⠁⠀⠀⠀⠀⠀⠀⣿⡟⣼⡇⠀⠌⢀⠾⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠀⣄⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⡤⠶⢦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠋⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⣰⢫⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣔⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣟⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠶⣦⣤⣤⣤⣤⡶⠾⣿⠁⢸
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⣀⡙⠶⠞⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⢸⡇⠀⠀⢸⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣸⡇⠀⢸⡇⠀⠀⢾⠀⠀⣿⠠⠊
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⠇⠀⠠⠾⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠘⢠⠐⢚⢻⣛⡷⣄⣀⠀⠀⠀⢀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⣻⡟⡓⠂⡄⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⡏⠒⠡⢮⣹⣿⣞⣀⣱⠍⢢⢀⠎⠀⠟⠉⣷⢦⣄⠀⠀⠀⠀⠀⠀⣀⣤⠴⣶⣚⣿⡍⢹⣊⣁⣻⣿⣟⡱⠬⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣟⠀⠀⠀⠀⢀⣽⠈⠉⠁⠉⢡⠂⠀⠀⠀⠀⠁⠠⠏⢱⠆⠀⠀⠀⠸⡁⠛⠀⢿⣷⠠⣾⡛⡃⠉⠈⣽⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⡇⠀⠀⠀⣠⡾⠋⠀⠀⠀⢠⣃⣴⠄⢀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣡⡀⠀⣻⣿⠀⣿⣧⢱⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢽⠇⢀⡴⣾⠋⠀⠀⠀⠀⠀⠈⠛⢝⡲⢿⡀⣤⠀⣎⠤⠷⢿⡽⢾⣽⠾⠦⡨⢦⡈⢹⣶⣾⣷⣤⡆⠀⠀⠀⠑⣷⢦⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣏⣼⡀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠩⢷⡴⠁⠀⠀⢸⠃⠀⡇⠀⠀⢡⡼⠛⠍⣷⣿⠈⠁⠀⠀⠀⠀⢀⣈⣻⢑⢟⡣⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣜⣫⣼⣳⣤⣄⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢻⣿⣿⣸⠾⠷⢕⣶⠶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⢸⡆⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⢀⣠⡾⠟⠛⠉⠉⠉⠉⠙⠻⢷⣦⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣻⠉⣿⡏⠉
⠀⠀⠀⠀⠀⠀⢠⡿⣾⠇⠀⠀⢸⡇⠨⠀⠸⠃⠀⠸⠃⠀⠸⠇⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⢸⣿⣇⠀⠀⠀⠀⠀⠀⢸⢻⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣟⣿⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡗⠛⣿⠚⢻⡗⠚⣿⠂⡟⢷⠆
⠀⠀⢀⣀⠀⡶⡿⠿⣿⣀⡴⢣⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⠤⢄⡀⠀⠀⠀⠀⠀⡆⡷⡇
⠀⠀⡇⣈⠙⣿⠛⠒⢧⠀⢠⠃⢸⡇⢠⣀⣸⣇⣀⣸⣇⣀⣸⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣿⣿⡇⠀⢹⣤⣼⣧⣤⣿⠄⣿⡇
⠀⠀⡇⠀⠀⠈⠉⠙⠋⡀⣾⠀⢸⡇⠈⠉⠉⠉⠉⢹⠋⠉⠉⠉⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣴⠝⠛⠻⣢⢸⠀⠀⠀⢸⣽⠀⣿⡇
⠀⡜⠁⠀⢀⣤⣀⣀⢀⡇⠸⡀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡼⠀⠀⢀⢧⠀⢣⠀⠀⢸⣻⠀⣿⡇
⡈⠀⠀⠀⠸⠦⣤⣼⡟⠀⣀⢣⣼⣇⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⣼⠏⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠀⠀⠀⠀⠀⠁⠀⠀⠱⡀⣸⢿⠀⣿⣇
⡇⠀⠀⠀⢤⣤⣀⡾⠠⣆⣛⢹⠋⠻⡆⠀⠀⠀⣸⢻⠻⣆⠀⣴⠏⠀⠀⠈⠙⠿⠷⣶⣶⣶⣶⠶⠿⠛⢹⠀⠀⣤⠀⢤⣀⡀⠰⠀⠀⣥⠟⠙⣿⠉⠹⣆
⠘⢦⡀⠀⠀⠀⠉⠀⠰⠆⣩⠏⠀⠀⠹⢄⠀⡼⠇⠀⠀⢹⡎⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠀⠀⠀⣠⡟⢀⠼⠉⡧⠀⠹⢆
⠀⠀⠈⠓⠢⣤⢤⠤⠖⠊⠉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⣀⣀⣠⡄⠊⠉⠁⠀⠉⠀⠉⠀⠀⠁
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⠶⡈⠁⠢⡀
⡸⠒⠘⡄⠀⢸⠄⣠⠤⡤
⠉⠲⠠⠧⠴⠋⠈⣩⣿⣜⠚
⡀⠂⢴⡀⠆⢀⠻⣿⣿⣿⣷⣤⡀
⠐⠠⡋⠐⡗⠉⠢⠽⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠉⠊⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢿⣿⣿⣿⣿⣷⣤⡴⠖⠛⠋⠉⠉⠉⠛⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⢿⡷⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠙⢾⡿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⠻⣿⣳⣝⢿⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣟⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⣝⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢿⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣝⣿⠿⡛⠢⠀⠀⠀⠀⠈⠳⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⡉⠢⡈⠢⡁⢠⣶⡐⠒⢦⡈⠳⣦⣀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣈⠶⠛⢋⠉⡇⢻⣆⠀⠉⠛⠛⠛⠛⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⣀⣠⣄⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⡶⠉⠀⣈⣤⡴⢇⠀⠹⣷⣀⠀⠾⣷⠄⠀⠀⠉⠻⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⢸⠋⠀⠈⠙⠶⣄⠀⠀⠘⡇⠘⠁⠀⠇⣰⠞⠉⢄⠀⢀⠑⢄⠈⠙⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⠶⠶⠤⣄⠘⢧⡀⠀⠹⣆⠀⠀⠘⠁⠀⠑⢄⠀⢄⠁⠤⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⣄⠹⡄⠀⠈⢷⡄⠀⠀⠀⠀⠀⠱⣢⡭⠖⠉⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠞⠀⠸⣇⡼⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠙⢦⡘⢦⡀⠀⠀⠀⠀⣠⠞⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠉⠙⠲⣄⠀⢳⠀⠙⣆⠀⣠⠞⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣷⡀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢧⡤⠾⢿⠁⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠳⣄⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠛⣧⠀⢸⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⠻⢶⣼⣧⣄⣀⣀⣀⣀⣠⣤⡶⠟⠋⠁⠀⣀⡼⢧⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⣀⣤⡤⠶⠛⠉
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠤⢤⠀⠀⠘⠛⠉⠠⢀⣠⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠃⠀⠀⠀⠀⠀⢐⡄⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡀⢀⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠆⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡅⢰⡅
⠀⠀⠀⠀⠀⢀⠀⠌⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠄⠻⠊⣾⡥
⠀⠀⠀⠀⠀⠸⠐⠂⣀⠀⠀⠀⢠⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⡿⠆
⠀⠀⠀⠀⠀⠰⠀⠅⢸⡆⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣰⠀⢠⣟⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⣷⠀⠀⠀⠠⠐⣎⠡⠐⠂⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠅⠉⠋⢸⣏
⠀⠀⠀⠀⠀⣸⠤⠜⠒⠉⠀⠀⠀⠀⠀⠡⣁⠤⠔⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⢧⠅⣾⠀⠀⢀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠘⡱⠇⢠⡀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡄⡀⠀⣅⠀⠐⠀⠀⠀⡀⠀⠐⢄
⠀⠀⠀⠀⠈⠄⠀⣤⣴⠈⠁⠀⠀⠐⠈⠁⠸⢰⠁⠀⠀⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⣀⢆⢠⣈⡁⢠⠈⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣹⠉⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡈⢙⠀⢠⣍⡁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠠⠄⠀⠀⠀⣨⠠⠤⠁⡤⠐⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠟⠧⠄⠀⠠⡇⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠁⠈⡅⠤⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠠⠀⠐⠱⠂⠀⠀⠀⠀⠀⠀⠀⡬⣾⡽⡴⠉⢢⣻⠇⠉⣦⠀⠄⠀⠉⠀⡌
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠞⠵⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣹⡇⠻⠤⢊⣍⠀⠀⡾⡐⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠊⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠖⠢⠨⠉⠂⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠾⢸⣄⠄⣥⡴⠂⢲⡀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠰⠠⡀⠀⠁⠀⢀⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠲⠂⢇⣀⢸⠀⢲⡠⠞⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣃⠰⠇⠒⠈⠁⠀⠁⠀⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣤⠀⠈⡅⠈⡔⠁⠙⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢄⠀⠀⠀⢀⠐⠀⠀⡆⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠉⠀⠀⣅⠀⠥⣀⣰⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⣀⠈⠀⠀⠁⠀⡃⠄⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⢸⡀⠈⠁⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠐

⡿⠉⠙⡟⢛⠛⠟⠟⠻⣟⠻⠟⠿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣻⣿⣿⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡏⠁⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠒⢤⡀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠒⠀⠈⠀⠀⣀⠤⠛⠈⡀⠄⠊⠁
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⣶⣦⠀⠙⢢⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢤⡀
⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠺⠿⠟⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡀⠘⠁⠀⠀⠙⠲⠤⢄⠠⠄
⠀⠀⠀⠘⡆⠀⠀⠀⠒⠀⠀⠀⠀⠐⠉⠁⠈⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⣀⣥⣴⢂⡆⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⢐⣤⣾⡙⣟⠝⠋
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠰⣺⣿⢟⡯⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡤⠤⠤⠤⠄⠤⠄⣀⡀⠀⠀⠀⠀⠠⠀⠀⠔⠀⣘⡯⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠓⠦⢤⣀⣠⠆⠀⠈⠉⠒⠤⠀⠀⠣⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠉⠟⠛⠛⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⡜⠀⠀⠀⠀⠴⢤⠀⠠⣴⡴⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠞⠇⢀⣠⣬⣅⠀⠐⠠⣀⠀⠀⠰⠸⠀⢢⡠⠖⠻⣟⠛⠐⡗⣠⣤⡶⠄⠀⠀⢰⢰⠄
⠀⠀⠀⠀⠀⠀⠀⣧⠏⠁⠀⠀⠭⠒⢢⠘⡣⠐⠚⠐⠒⠢⢥⡬⠥⠤⠤⢬⡇⠀⠀⠀⠀⠀⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠠⠐⠂⠀⠂⠀⠀⠡⣀⣀⣀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⡧⣄⣀⣀⡀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠡⡁⠀⠈⠹⠁⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠰⣧
⠀⠀⠀⠀⢀⠈⠀⠒⠏⢄⠈⠠⠀⠏⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣧⡄⢰⢷⠁⡀⠀⠀⠀⠀⠀⢸⡄⣀
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠂⠀⠌⠀⠀⠑⠤⣀⣀⣀⣀⡠⡴⠃⠴⠙⠦⢸⡽⠀⠈⠄⠀⠀⠣⠤⢬⣤⡼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡪⠛⠉⠁⠀⢰⡁⠀⠀⠀⠂⠲⠤⣤⣀⡀⠀⠀⠁⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠐⠁⠀⠀⠀⠀⠀⢸⣳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠶⢤⣀⠀⠀⠀⠉⣦⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣌⡁
⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣀⢀⣀⠀⠀⠰
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠄⠒⠖⠊⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠤⠤⠀⠤⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠆⠶⠂⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢠⠼⠦⠺⠛⠖⡀⠉⠄⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢀⣇⣀⡎⡦⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣎
⠀⠀⠀⠀⠘⠂⠀⠀⠈⠃⡰⠃⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢸⡀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⡉⢀⠉⠡
⠀⠀⠀⠀⠸⠦⢤⡤⠤⠟⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⢷⠂⠀⠀⠡⠀⠀⠀⠄⠀⠀⠀⢠⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠑⢄⠀⠀⠀⠀⠀⡠⠃⢀⢃⡌⠡⠘⠀⠀⢣⠀⠀⠀⢀⣠⠴⠦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠈⠉⠁⠀⠂⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠘

⠈⣀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠄⠀⢀⣤⢀⠉⠀⠀⠀⠀⠀⠀⠀⠸⣧⣥⣀⣤⣀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠉⠉⠁
⠷⣾⢠⠆⣠⡶⠶⠶⣤⠀⠀⠂⡤⠀⠀⠀⠀⠀⠀⣢⣤⠀⢀⡀⡠⠄⢀⠉⠈⠉⠛⣮⣤⠀⠀⠀⠀⠀⢀⣠⢾⠷⣾⡰⠆⣠⡶⠶⠶⣤⠠
⠋⠈⠉⢰⢿⠀⢀⠀⠘⡇⢀⣤⣧⠀⠀⠀⠉⠄⢠⠏⠙⠀⢩⡀⠀⠀⢸⣆⠀⠀⠀⠀⢀⣠⠤⠶⠿⠞⠒⠂⠞⠉⠈⠉⢈⣟⠀⢀⠀⠘⡇
⠀⠀⠀⠀⠻⣦⣤⣤⡾⠃⠐⠎⠀⡑⠦⠤⢤⠖⢟⣲⣶⠀⠈⢧⡀⠀⠈⠹⣧⠀⠀⢣⠀⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⡾⠃
⡶⠶⠤⢦⠀⠀⡀⠀⠀⠂⢄⣀⡀⠀⡈⠁⠂⠅⠀⣙⡏⠀⠀⠘⣿⡄⠀⠀⠘⣧⡀⠀⡆⠀⠀⢤⡴⠦⠿⠶⢶⡶⠦⡤⢦⠀⠀⡀⠀⠀⠒
⠛⠲⢦⡀⠀⡴⠃⠀⠀⠀⠫⣄⣈⡻⠻⢄⡀⠀⠀⠈⠀⠀⠄⠀⢸⡽⣆⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢦⡀⠀⠼⠁
⠀⠀⠀⠉⠠⢤⠀⠀⢲⡀⠀⠀⠹⡗⠆⢢⣎⣹⠔⠠⠀⠀⠀⠀⠘⢻⡿⣦⠀⠀⠈⢿⣄⠀⠀⠀⠀⠂⠀⠛⡄⠀⠀⠀⠉⠠⢤⠀⠀⠦
⠀⢠⣤⢤⣠⣠⣤⡀⠀⠑⠀⡀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠉⠑⠃⠀⠘⠃⠈⣿⡗⠀⠀⠀⠀⠀⠀⡇⠀⢠⡤⣤⣤⣠⣤⡀⠀⠃
⠂⢢⠠⢸⡿⠥⠤⢥⠤⣾⡍⠏⠉⠀⠀⠀⠠⡄⠀⠄⠀⢀⡠⠔⠒⠆⠤⠀⢰⡀⠀⢀⠀⣿⣿⣀⠀⡀⠀⢠⡷⠂⢢⠠⢸⡿⠥⢄⢧⠤⣾
⠦⣤⠒⠀⠓⠖⠨⠛⡓⢿⠁⡃⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⡄⠐⠆⠃⠘⠂⠀⠁⠀⠸⠀⠐⠋⠁⠠⠁⠀⠘⡷⠦⣤⠒⠐⠓⠖⠨⠚⡓⠿
⢀⠃⠀⠀⠀⠈⡁⠇⠄⣀⣀⣿⡀⠀⡀⢸⡄⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡧⢀⠃⠀⠀⠀⠈⡁⠇⠄⣀
⠈⠣⡀⠀⣀⡴⡟⠱⠖⠯⠐⠢⣱⠀⠀⠈⡇⠀⠠⣿⠀⠀⠀⠀⠀⠀⡾⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⡈⠁⠘⠣⡀⠀⣀⡔⡟⠱⠒⠯
⣀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠤⠀⠀⠀⡀⠀⢻⠀⠀⢹⠄⠀⠀⠀⠰⠶⠇⢹⣷⡚⠁⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⡠
⠈⠳⣄⠀⠀⠂⠀⠒⠈⠀⠀⢶⠀⠀⠀⠀⢸⣄⠀⢸⡇⠀⣾⡦⠀⠈⠀⠈⠈⠂⠀⡠⠈⠀⠀⠰⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠂⠀⠒⠈
⠚⠓⠺⠶⣦⣤⣄⣀⡀⠀⠀⠰⣧⡀⠀⠀⠘⠇⠀⢸⣷⠀⠈⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠀⡀⠀⠀⠀⠙⠛⠓⠺⠶⣦⣤⣄⣀⡀
⢀⠀⠀⠀⠈⠦⣄⡉⠓⠀⢠⠀⢻⠅⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠢⠤⡈⡀⠀⠀⠀⠒⠒⠂⢁⣀⠀⠀⠀⠰⠀⠀⠀⠈⠦⣄⠉⠓
⠐⠆⣀⡀⢀⠠⠈⠳⡀⠰⠋⠀⠈⣨⢧⡄⠀⠐⠋⠐⣿⣄⠀⠁⢠⢶⣦⣤⣄⡈⠁⠐⠂⢌⠀⠉⠁⠀⠀⠀⠀⠐⢆⣀⡀⠀⠠⠈⠳⠀⠰
⠀⡸⠻⠏⠍⠩⣹⠃⠈⠳⠀⠀⠀⠹⣼⣟⣠⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠏⠍⠉⣹⠃⠈⠣
⠀⣿⣿⣶⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠏⠤⠀⠀⠄⠀⢾⣽⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠂⠀⠀⠐⠀⠀⠀⢀⠀⡿⣿⣾⣷⣶⡶
⢰⡿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠚⠁⠃⣠⠂⠀⢀⠃⠀⢠⡀⡃⠀⠀⠀⠀⠔⠀⠀⠀⢼⢰⡿⡿⣿⣿⣿⡇
⠺⠛⠛⠻⠛⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠈⠀⢰⡶⠞⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠛⠛⠻⠛⢛⠅
⣀⣢⠀⡀⠀⣀⣀⣀⠀⠀⠋⡀⢀⠐⠋⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠛⠶⠻⠶⣦⣠⠀⠀⠃⠀⠀⠀⠀⢀⣀⣀⣢⢀⡀⠀⣀⣀⣀
⡭⠿⠾⢁⣾⠋⠉⠉⠻⡄⠀⠀⡏⠈⠀⠀⠤⠀⠀⡾⠿⠀⡔⠒⠈⠁⢰⡀⠀⠀⠀⠙⠛⠀⠀⣀⣤⣠⢰⡚⣽⠭⠻⠮⠡⡾⠋⠉⠉⢻⡌
⠀⠀⠀⠈⣽⡀⠰⠀⣠⡇⢐⡿⠋⢦⡀⠀⠀⣉⣼⢁⣀⠀⠸⡆⠀⠀⠘⢿⡄⠀⠀⡔⠐⠚⠉⢩⡉⠉⠀⠀⠀⠀⠀⠀⠰⣷⡀⠰⠀⣠⠇
⣀⣀⠀⡀⠈⠛⠛⠛⠋⣀⠀⠀⠀⠀⠩⠉⣙⠁⠘⢺⡿⠀⠀⢸⣦⠀⠀⠀⢻⣄⠀⠘⡄⠀⠀⠀⣈⣓⣤⣀⣀⣀⣀⢀⡀⠈⠛⠛⠛⠉⣀
⢯⣉⡉⠙⠀⢠⠆⠀⠀⠀⡴⠒⠢⣄⣦⠀⠀⠀⠐⠲⠂⠀⠀⠀⢻⢧⡀⠀⠀⢻⣆⠀⠃⠀⠀⠙⠋⠉⠉⠉⠙⢯⣉⡉⠙⠀⢠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢠⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣀
⠀⠀⠀⠘⠀⠀⣠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣛⣻⣭⠁⠀⠀⠀⠀⠀⣄⡔⢋⣽⠳⡄⣹⣿⣷⣄
⠀⠀⠀⣀⣰⣴⣷⣮⠔⠀⠀⠀⠀⠀⠀⠀⠒⢺⠛⣡⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣍⢿⢿⢋⣿⡿⠋
⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⠟⠋
⠀⠀⠀⠈⠛⠛⠋

⡀
⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢟⣯⡶⢊⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⣿⣻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠟⠛⠛⠛⠛⠃
⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣠⠴⠛⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⣠
⠀⠀⣀⡤⠖⠉⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⣿⣦⠈⠆
⠀⠛⠉⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢸⣿⣇⠺⢂⣿⣿⠀⡘
⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋
⠄⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠁

⣎⢹⣿⣿⣿⣷⡀⠀⠈⠐⠢⣀⣶⣟⠃⠀⠀⠀⠻⢿⣿⣿⣿⡿⠏⠀⠀⢀⣴⣟⣟⣿⣿⣿⡿⠀⠀⠹⣤⢿⣤
⢸⡿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠈⠁⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⣿⡷⠟⠛⠉⠀⠀⠀⠀⠸⣾⢿
⡵⠾⠋⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠙⢶⡀⠀⢠⠄⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⢦⣤⢤⡶⠀⠀⠙⠶
⠀⠀⠀⢀⣀⣠⣤⡶⠖⠛⠁⠀⠀⠀⠀⢀⡄⠀⢀⣴⡏⠀⠀⠈⠁⠀⢀⣀⣀⠀⠀⠀⢀⡾⠀⠈⣧⡀
⣤⣶⡿⠟⣛⣯⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⠛⠁⠀⠀⠀⠀⣴⠟⠽⠻⡇⠀⠀⣾⣇⣤⣤⣸⣧
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣤⣴⠃⠀⠀⠀⢠⣤⡶⠚⠁⠀⠀⠈⠢⠀⢀⢳⡄⠀⠻⣿⣿⣿⣿⠏
⠉⠉⠉⠉⠉⠉⠁⠀⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠁⠀⣀⡀⠀⠀⠀⠒⠟⢯⠓⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀
⣿⣶⣦⡄⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣠⡾⣛⢭⣉⣷⣄⠀⠀⠀⠈⢧⠀⠀⠀⢠⠔⢶⣾⣿⣿⣿
⣿⣿⡿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣴⣿⣻⢧⠊⠻⣿⢹⡷⣄⠀⠀⠘⣇⠀⠀⠘⡄⠈⢿⣿⣿⣿
⣿⡿⠁⠀⠀⠀⠹⣿⣯⣹⣿⣿⡿⠁⠀⠀⢿⣿⣿⣿⣼⣄⣙⠒⣒⠟⠀⠈⠀⠀⠀⠸⠂⠀⠀⠘⡄⠈⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠙⠛⠿⠟⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⣀⣀⣤⡀⠀⠈⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⢀⣄⣤⠔⠂⠀⣠⢤⡀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⣀⡀
⣶⣤⣀⣴⣶⣾⠿⣋⣀⠀⠀⠀⣰⣿⣿⣿⣄⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⢀⣠⣄⠀⠀⠀⠀⠙⠿⣷
⡿⣏⣯⣻⣿⣿⣄⡉⠉⠀⠀⠀⠻⣿⣯⣟⡻⣷⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⢷⣴⢿⣿⣿⡄⠀⠀⠀⠀⣀⣤
⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⡞⢣⡴⠛⣙⡎⣷⠀⢸⣿⣿⣿⣿⠆⠀⠀⠀⠈⢻⣷⣝⣿⣷⡀⠀⠀⠀⢿⣿
⣿⣿⣿⣿⣿⠇⢀⣤⡄⠀⠀⠀⠳⣌⢲⢿⣿⣰⠃⠀⠀⠉⠉⠉⠉⠀⠀⢠⡀⠀⠀⠙⢿⣿⣿⠇⠀⠀⣠⢘⠛
⠙⠿⠿⠟⠋⠄⠀⠀⠁⠀⠀⠀⠀⢈⡳⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢶⣤⣤⣤⡶⠀⠈⣇⠀⠀⠀⠀⠙⡲⣴⡖⠠⡀⣀
⣶⣶⣶⣤⠀⠀⢴⣶⠖⠋⠁⠀⠙⢦⣀⠀⠀⠀⠀⣼⠃⠀⠸⣇⠀⠀⠈⠀⠀⣰⠂⠀⠙⠧⣄⠀⡠⣺⡇⠀⢀
⠿⠿⠿⠋⠀⠀⠀⠀⢠⣶⣶⣆⠀⠀⠿⠇⠀⠀⣼⡿⢀⣀⡀⣿⣧⠀⠀⠠⣾⡇⢀⣤⣤⡀⠈⠻⠿⠟
⣦⣀⣠⣤⣀⣀⣀⣀⣿⣓⣁⣈⣳⣄⣀⣀⣀⣀⣿⣷⣼⣿⣧⣿⣿⣀⣀⣀⣁⣰⣿⣿⣻⣿⣆⣀⣀⣀⣀⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡄⠀⠀⠀⠐⡆⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣾⡄⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠈⣩⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠰⢳⡀⠀⠀⢰⠔⠉⣩⡄⠀⠀⠀⣀⣀⡀⡐⠠⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢈⠢
⠀⠀⠀⠀⠈⡝⣇⠀⠀⠀⠲⠞⠃⡄⠀⠀⠀⠀⠀⠀⢀⠀⠼⠀⠀⠀⠀⠑⠂⠀⠙⢄
⠀⠀⠀⠀⠀⠩⢼⣄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠰⡭⢿⠉⠑⢈⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠰
⠀⠀⠀⠀⠄⠀⢸⠽⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⠁⡛⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣦⠷⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡌⣈⠃⠀⠀⠀⡀⠈⡛⢧⠀⠀⠈⠭⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠘⠁⣠⡜⠀⠈⠣⡀⠀⠀⠀⠀⠀⠄⢠⠁⠀⠀⠂⠀⠀⠘⢄⡆⠀⠀⠂⠀⠀⢧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠤⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⡧⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⢀⠀⠀⠀⠇⠤⠶⠀⢠⡀⡀⠀⠐⠀⠀⠀⠀⠀⡆⠀⠀⠀⢄⠠⠇
⠀⠀⠀⠀⠠⡀⠀⠈⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠔⠛⠀⡟⠂
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠲⠤⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁
⠀⠀⠀⢠⡔⠁⡴⠄⠀⠀⠀⣘⡳⢤⡀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠑⠚⠁⠆⠀⠀⠀⠈⠀⠀⠂⠩⠐⢒⠒⢒⠒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠒⠒⠀⠒⠁⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⢀⠔⣠⠖⠀⠀⠀⢰⡔⠓⠢⣔⡿⢯⣄⡤⠄⢀⣀⣀⠀⢀⠰⣿⡋⠁⠀⠀⠀⠘⠓⠒⠒⠒⠂⠾⠾⠛⠿⠛⠃⠀⠀⠛⢋⠑⠒⠈⠀⣰⣿⣿⡄
⠀⠀⠀⢰⣾⣿⡧⠀⢀⠀⣸⣾⠀⠀⣻⣿⡿⣶⣭⣙⣟⠲⢦⣤⡌⣾⣉⣡⣀⣴⡇⠰⠾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⡆⣶⢰⣿⣿⣿⡧
⠀⠀⠀⣶⣿⣿⣗⠀⡠⠀⢼⡽⡄⠀⠑⢿⢿⣷⢾⣿⢸⠀⠀⠈⠃⢿⣀⣿⣿⣿⠃⢀⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⣤⣤⣄⣀⣼⣿⠏⠁
⠀⠀⠀⢫⣿⣿⡧⠀⢌⠀⣹⣿⠁⠀⠀⠀⠉⠉⠉⠓⠊⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠘⣿⡄⠀⢤⣤⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠙⠛⠁
⠀⢀⣀⣴⣿⣿⣋⠀⡑⠀⢺⣿⣀⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠉⠉⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠉⠙⣷⠆⠀⢀⠴⠚⠋⠹⠿⠏⠙⠓⠦⡀
⠀⠸⢿⡿⣿⣿⣇⣀⣈⣀⣸⡿⡾⠇⠠⡶⠒⠒⢒⢒⢂⣒⣐⣶⣶⣶⣖⡀⠀⠈⠉⠉⠀⣿⠀⠀⠀⠀⠀⢠⡿⡃⠀⢐⠀⢀⣐⠂⠁⠀⣐⡀⢀⡂
⠀⠀⠸⡇⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠻⠿⡿⠛⠓⠒⠊⠀⠀⢀⣽⡇⠀⠀⠀⠀⢸⣿⡸⡀⢸⣿⣷⣿⣶⣵⣶⣿⣾⣿⡇
⠀⠀⢰⠁⠘⣿⣿⣿⣿⣿⠟⢈⡈⢀⣀⣤⣤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⢾⣿⠄⡀⠀⠀⢸⣿⣫⠳⠀⠉⠛⠿⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠱⣦⡈⠉⠍⠉⢉⣠⠔⢁⣀⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣦⠀⢸⣿⠀⣾⠃⠀⢸⣿⠀⠐⠀⠀⢸⣿⠿⣧⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠉⠙⡇⡟⠉⠁⠀⠻⢿⣿⣿⣿⣿⡿⢿⣿⣿⣻⣿⣿⣿⠀⢸⠁⠈⢿⣄⠀⠸⣿⡇⠐⠀⠀⢸⣿⣽⣿⠲⣆⣌⠀⢠⣾⡟⠉⠀⠉⢦⣀
⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⠿⡄⠈⠀⠀⠀⣿⠀⡇⣻⣿⠇⠀⠀⢹⢹⠒⡿⣸⡟⡟⠀⣾⡟⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⢀⣀⣠⡇⡇⠀⠀⠀⠀⠀⠀⢹⠀⠀⠘⣿⠁⠀⢨⣿⠍⠀⡇⠀⠀⢰⡾⠋⠀⠃⢹⣿⠒⠑⡀⠸⣿⣛⡅⣿⠽⠁⠀⣿⡇⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠉⠉⠛⠻⠗⠆⠀⠀⠈⠀⠄⠀⠘⠀⠀⣴⣿⣀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡿⠀⠀⡇⠀⣻⣩⡅⣿⣿⠀⠀⢳⣶⣦⣄⣀⣨⣾⣿⡇
⠀⠘⢶⣤⣄⣀⣀⣀⣻⣿⣶⣤⣶⠇⠀⠀⠀⠀⠈⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⡇⠀⠘⠀⠐⣻⢢⣵⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣼⡿⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⠂⢄
⠀⠀⠀⠀⠀⠊⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠈⠂
⠀⠀⠀⠀⠰⣄⠀⠁⠢⠀⡀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⠁⢀⡴
⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠈⠁⠀⠒⠀⢠⣿⠇⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠂⡟⠁
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠁⢠⠶⣾⡟⠀⢰⡿⠀⠤⡤⠤⠀⠀⠀⠀⠀⣲⢦⠀⠉⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡴⠃⢰⣿⡀⢀⣿⠃⠀⡼⠹⡄⠀⠀⠀⠀⢰⠃⠀⠳⣄⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠘⣀⠀⢹⡀⠀⣠⠋⠀⢀⣾⠃⢳⣼⡏⠀⡼⠁⠀⠹⡄⠀⠀⣠⠃⠀⠀⠀⠈⠳⡀⠀⣰⠃⢀⡐
⠀⠀⠀⠀⠀⠀⠎⠐⠂⠷⢞⡁⠀⠀⣸⡏⠀⢠⣿⡁⣸⠁⠀⠀⠀⠱⡀⣰⠃⠀⠀⠀⠀⠀⠀⢙⣶⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣿⠃⠀⣾⠏⠿⠧⠄⠀⠀⠠⠤⠿⠇⠀⠀⠀⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣾⠇⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡠⢰⣿⠁⣼⡏⠀⣿⠃⠠⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⡟⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣼⡇⠀⣿⡇⢸⣿⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⠠⢠⣿⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡄⠐⠁⠀⠀⢿⡇⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⢀⣼⡏⠀⢸⡿⠁⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⢀⠉⠀⠀⠀⠔⠀⠀⠀⠀⠀⢸⣧⠀⣿⣇⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢴⡿⠀⢀⣿⠃⠀⠒⠂⠀⠀⠀⠀⡀⠤⠤⢴⡆⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠸⣿⡀⢸⣿⡀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢉⣾⡟⠀⠀⠀⠀⢤⠦⠴⠶⢖⣒⣶⢿⡞⠛⠋⠉⠁⣀⠀⠀⠨⠄⠀⠢⠀⠀⠀⢻⣧⠀⢻⣧⠀⢻⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢠⣾⣿⡇⠀⠀⠀⠀⠰⢖⠊⠉⠥⠄⠀⠒⠋⠀⠉⠁⠀⠀⠀⠀⠀⠈⠢⠀⠱⠄⡀⠀⢻⣧⡀⠻⣧⡀⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠓⠀⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡊⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⠉⠀⢀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡃⢀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣷⡽⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣯⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣻⣿⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠂⠀⣤⣿⣷⡛⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⣼⡻⢿⣕⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣰⢿⣿⡿⣷⠏⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠐⠁⠀⢀⡠⠀⡠⣿⣷⣽⡿⠁⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠊⢀⣴⣭⣶⠝⡅⠀⠀⠀⠀⠀⢟
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⣤⢿⣿⡯⠋⢀⠃⠀⠀⠀⢀⠎⠄
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⣾⣽⣷⠿⠤⠔⠁⠀⢀⠄⢊⠡⠊
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠞⡳⣿⣻⡿⠁⠀⠀⠀⠀⠀⢨⡌⠁
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠪⢝⡦⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⢀⠀⠀⠀⠀⠀⠀⡠⠔⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠥⠀⠀⠉⠥⠐⠈

⣿⡯⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣉⡬⠦⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⢀⠞⠀⠀⠀⠙⢦⡀⠀⠀⠀⣀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡔⠊⠁⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠙⠲⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠊⠀⠀⠠⢤
⠀⠀⠀⠀⡇⠀⠀⠀⠠⠀⠀⠀⠘⣿⡿⠃⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠎⠀⠀⠀⠘⠲⠦⠤⣀⣀⡄
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⡔⠒⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢨⣀⡢⠒⡄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⣠⠶⣿⡿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⣠⣴⣿⡿⢗⡽⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⢐⣥⡿⢟⡩⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢠⡶⠒⠒⠒⠒⠒⠢⠤⢄⣀⡀⠀⠀⠀⠀⠀⡆⠀⠠⠊⠀⣈⡭⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠓⠦⢤⣈⡀⣰⠆⠀⠀⠉⠑⠒⢤⠀⠀⠸⣄⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⠑⠒⣲⠶⠲⠶⢞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢠⠁⠀⠀⠀⠀⢀⡐⠀⠀⠀⢠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣯⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⣸⠋⢋⠁⠀⣀⣤⣤⣤⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠋⢈⢀⣴⠶⠶⠷⢄⡀⠈⠑⢦⡀⠀⠈⣁⠉⠀⠸⣴⠋⣁⡸⠖⠲⠶⣾⠶⠶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠀⠀⠐⠒⠒⠊⠓⠲⢊⠥⠒⠈⠁⠈⠉⠒⠤⡶⠶⠒⠒⠒⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⡠⠔⠒⠀⠀⠀⠀⠀⠈⢄⡀⡀⣀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠍⡇⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡸⠉⠉⠛⠲⠒⢒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠊⢀⢹⠄⠀⠠⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⢀⠌⢹⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠀⢢⠀⠈⠀⡜⠁⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠈⣷⠥⠨⢭⡇⠐⠄⠀⠀⠀⢀⠄⠀⢸⡗⠠⣄
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠑⠀⠜⠀⠀⠀⠉⠲⢤⣄⣀⣀⣤⡴⠾⠉⠠⠎⠈⠖⠨⠷⠃⠀⠈⠂⠀⠀⠈⠒⠶⠶⠶⠾⠟⠃

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

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⢈⡆
⠀⠀⡉⠒⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣀⣀⠀⣀⠀⠴⠋
⠀⠀⠀⠁⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠀⠈⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠦⠤⠤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⢠⡀⠀⠀⠀⠠⠤
⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠦⡀⠀⠈⠂
⠈⠀⠄⠀⠀⠀⠴⠤⠀⠀⠁⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠙⠂
⠀⡂⣂⠀⠀⠀⠀⠑⢸⠄⠀⠀⢀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⣶⠄
⠀⠸⢀⠡⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠘⠐⠀⠀⠀⡆⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠁⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢀⡤⠚⢀⠀⠀⠈⠊
⠇⡀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠋⠉⠉⣀⠴⠚⠂
⠰⠂⠀⠈⠀⠀⠀⠠⠀⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⠍⠉⠄⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠈⠁⠠

⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⡀⠀⠀⠀⠄⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⡀⠤⣤⣄
⠀⠀⠀⣀⣴⡇⠀⠀⠀⣦⠉⠙⣿⣿⣿⡶⣶⣀⣀⠀⠠⢀⡿⠇⠀⢀⠀⣀⣉⣉⠉⠉⠉⠉⠉⠉⣉⣀⣀⣈⣱⠀⠀⠀⢰⣿⣿⡆
⠀⠀⢀⣿⣿⡏⠀⠀⢐⣿⡂⠀⢝⣿⣿⣻⣷⢯⠉⠙⠿⢿⠃⣾⣾⣿⠀⠉⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⣛⠉⠋⢻⣿⡿⠇
⠀⠀⠸⣿⣿⣗⠀⠀⠐⣿⠇⠀⠀⠙⠛⠚⠿⠔⠀⠀⠀⠈⠋⠉⣻⠃⠀⣿⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠶⠚⠛⠉⠛⠻⠿⠋
⠀⢀⣀⣿⣿⣗⠁⠀⠨⣿⣅⡀⠠⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠁⠀⠀⠘⣇⠀⠈⠉⠉⠛⢷⠄⠀⢠⠴⠒⠲⣶⠒⠒⠤⡀
⠀⠸⣿⣿⣿⣇⣀⣁⣨⣿⣿⠇⢠⠖⠒⢲⢒⢀⣆⣰⣾⣶⣶⡉⠁⠘⠙⠀⢿⠀⠀⠀⠀⠀⣼⡀⠀⣂⠀⣀⡂⠀⣀⡂⠀⡀
⠀⠀⢻⢸⣿⣿⣿⣿⣿⡏⢿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠿⠉⠉⠉⠁⠀⠀⢼⡇⠀⠀⠀⠀⣿⣅⡀⢿⣿⣿⣶⣶⣶⣿⣿⠇
⠀⠀⢠⡀⠻⠿⣿⠿⠟⢀⠄⠠⣴⣶⣶⣶⣿⣷⠀⠀⠀⠀⠀⢠⡄⢀⡴⠀⢸⣿⠀⠀⠀⠀⣿⢧⡁⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠙⠲⢦⡥⡴⠖⠋⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠇⢸⡇⠀⢸⣿⠀⠀⠀⠀⣿⠭⣇⣄⠀⠀⠀⣠⡶⠗⠲⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣀⠐⠀⠈⢹⡆⠆⣿⣷⠀⠀⢰⢻⢥⡏⣾⢿⠃⣸⡟⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⢀⣀⡇⡄⠀⠀⠀⠀⠀⣟⠀⠀⣿⠉⠉⢻⣟⠁⡟⠀⠀⣤⠟⢁⠇⢻⡿⠔⠂⠘⣿⣺⢱⣿⡀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠈⠉⠙⠻⠗⡆⠀⠀⠀⠀⠀⠃⠀⢠⣿⣀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠠⠀⣺⢩⣰⣿⡇⠀⢱⣶⣦⣤⣀⣼⣿⡀
⠀⠘⠶⣦⣤⣤⣤⣿⣿⣶⠾⠃⠀⠀⠀⠀⠈⠁⠀⠸⡇⠀⠀⠀⠀⠘⠆⠀⠀⢻⠀⠀⠁⠈⠹⢠⣽⡿⠁⠀⠸⣿⣿⣿⣿⣿⡿⠃

⢐⢢⠀⠢
⠢⣆⣆⠠⠓⣻⣗⠠
⠐⢺⡄⠢⠺⣿⣿⣷⣄
⠀⠁⠴⠀⠀⠘⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣦⡀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡻⣿⣿⣿⣷⣏⠉⠀⠀⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠚⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠘⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠱⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠛⠁⠀⠀⣀⡘⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠢⣄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡽⠖⢪⢳⡌⠓⠶⠤⠴⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠑⣤⠤⣄⡀⠀⠀⢠⢤⡀⠰⠉⣠⠤⠚⠀⠻⢦⣐⣲⠆⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣇⣀⣀⡙⢦⡀⠸⣄⠀⠰⠊⠁⠀⢀⠀⣠⣄⠈⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⢢⡱⡄⠈⢧⡀⠀⠀⠀⢠⡥⠚⠁⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⢠⣌⡇⠀⠀⠀⠈⠢⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣄⠀⠉⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⢣⡀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⣆⠀⠀⠀⠀⠀⡠⠖⠒⠓⠒⠦⡀⢳⠙⢦⢀⡠⠊⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣦⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠘⣆⣷⠚⢋⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠳⢦⣸⣄⡀⠀⢀⣀⣤⡴⠞⠋⢈⣧⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡈⠉⠉⠉⠉⠉⠀⣀⡴⠚⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠘⡀⠀⠀⠀⠀⠀⡘⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⡌⠑⠀⠀⠀⠀⠈⠃⠰⠀⠀⠀⠀⠀⢻⡪⡃⠈⣙⠒⠤⣤⣀⣀⣀⡀⠀⠀⢀⡀⡕
⠀⠀⢀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⠦⠀⠀⠉⠪⢅⠪⢅⣐⠲⠈⢠⣍⡉⣉⣩⠉⢼⠃
⠀⠀⠀⠸⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠑⠲⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠨⠇⠴⢶⣶⠄⠀⠶⠞⠀⠀⠀⢀
⠀⠀⠀⠀⢈⠑⠀⡀⠀⠀⣀⣠⠔⠡⠑⠀⢁⡴⠍⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠂⢀⡁⠀⠀⠐⠛⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠈⡤⠗⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣣⡇⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢐⡵⠒⠛⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠈⠃
⠌⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣠⠔⣹⠆⠀⠀⠀⣀⠤⠀⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢎
⠋⠁⢈⡆⠀⠀⠀⠀⠀⠀⠀⠠⢔⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠫⡔⣊⡠⠀⠀⠀⣞⡉⠀⠀⠰⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⣯
⠤⢒⠭⠛⠀⠀⠀⠀⠀⠀⠈⠃⢄⠑⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠱
⠉⠤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⡀⠀⢰⠄⠀⠐⣄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠁⠀⠒⠄⠰⠄
⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣈⢦⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠰⠶⢄⠦⠈⠀⠈⠎⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⡠⡤⣀
⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠑⠐⠠⢄⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠑⠀⠀⣿⢉⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢔⠁⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⡿⠘⢸⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠑⢤⠂⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢠⠇⡖⡈
⠀⢈⡀⠀⠀⠀⠀⠀⠀⢀⣁⠐⢠⠷⣄⠀⠀⠀⠀⠀⠢⡀⠀⠀⡱⢄⡀⠢⡀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⡟⢀⢡⢁⠂
⠀⠨⣹⡀⠀⠀⠀⠀⠀⠛⢌⡠⠺⢤⠀⠉⠢⠀⠀⠀⠀⠈⠁⠉⠀⠀⠙⢦⡈⢦⡀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠘⠀⠀⠀⠀⢀⡼⠁⠋⡌⠎
⠠⠉⠉⠙⢄⡀⠀⠀⠀⠄⠂⠉⣕⡢⣁⠀⠀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡙⢆⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣰⠟⢠⠃⣼⠌
⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠈⠙⢦⡢⢄⠈⢢⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢯⣆⡀⠀⠀⠀⠀⠀⢿⠀⢀⡴⢋⠔⢀⠾⠋
⢀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠁⠀⠈⠁⠮⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠼⠁⠀⠀⠀⠀⠀⠀⠉⠻⠲⣠⡴⠕⠁⠀⠀⠀⠀⣠
⠀⠡⡀⠀⢀⠀⠀⣠⡄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⢠⠀⠀⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠟⠀⠈⠁⢰⡖⠀⠠⠀⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒
⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠲⠇⠀⠀⠀⠀⢀⡀⠈⠁⠈⠐⠃⠀⠶⠀⠀⡂
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⠀⡠⠃⠐
⠠⠤⣶⠆⠀⠀⠀⡀⠤⠀⠒⠒⠂⠄⠀⠀⠀⠀⠈⢉⠦⠀⠀⠀⠀⠀⣀⠀⢤⡤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠁⠀⠀⢀⠄⠁⠀⠐⠂⠁⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠉⠀⠉⠀⠀⠈⠉⠛⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⢠⡄
⠀⠀⠀⣰⣴⡏⠀⠀⠀⣷⠉⠙⣿⣿⣿⡶⣶⣄⣠⠤⠠⢀⡿⠇⠀⢀⠀⠀⠀⣈⣁⣐⣀⣀⣀⡀⡠⢄⣘⣛⣿⣦⡤⠤⠤⠠⡤⢤
⠀⠀⢀⣿⣿⡏⠀⠀⢐⣿⡂⠀⢿⣿⣿⣻⣷⣯⠉⠙⢿⢿⠓⣾⣶⣿⠀⠀⠸⠋⠁⠀⠸⣤⢀⣶⣷⣾⣿⣿⣿⣿⣷⣄⣀⡀
⠀⠀⠸⣿⣿⣗⠀⠀⠐⣿⠇⠀⠀⠙⠻⠛⠿⠜⠀⠀⠀⠈⠋⠙⣻⠃⠀⣿⡀⢀⣀⡀⠀⠀⠈⠉⠉⠉⠙⠿⠻⠉
⠀⢀⣀⣿⣿⣗⠐⠀⠪⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠀⠀⠘⣧⠀⠈⠉⠙⠛⣷⠄⠀⢠⠴⠒⡲⣶⠒⠒⠦⡀
⠀⠸⣿⣿⣿⣇⣀⣈⣨⣿⣿⠇⠀⣲⣖⣒⣒⣒⣒⣒⣡⣬⣦⣤⣤⣤⣄⠀⢿⡀⠀⠀⠀⠀⣼⡂⠀⣂⠀⣀⡂⠁⣀⣂⠀⡂
⠀⠀⢻⢹⣿⣿⣿⣿⣿⡏⢿⠀⠀⠀⠀⠁⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢼⡇⠀⠀⠀⠀⣿⣇⡀⢿⣿⣿⣶⣶⣶⣿⣿⠇
⠀⠀⢣⡀⠻⠿⣿⡿⠟⢀⡌⠠⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⢠⡄⢀⣴⠀⢹⣿⠢⡀⠀⠀⣿⣧⡁⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠙⠲⢦⣥⡴⠞⠋⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⠇⢸⡇⠀⢸⣿⡀⠀⠀⠀⣿⢭⣇⣀⠀⠀⠀⣠⡶⠗⠲⣄
⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠉⠛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣀⠘⠀⠈⢻⡆⡂⣿⣷⠀⠀⢰⢿⣽⡟⣼⢿⠃⣸⡿⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⢀⣀⡇⡇⠀⠀⠀⠀⠀⣿⠀⠀⣿⠋⠉⢻⣟⠁⡿⠀⠀⣠⠞⢃⠇⢻⡿⠔⠆⠘⣿⣺⣱⣿⡆⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠂⠉⠛⠻⠗⡆⠀⠀⠀⠀⠀⠃⠀⣠⣿⣀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠸⠀⣻⣩⣴⣿⡇⠀⢹⣴⣦⣤⣀⣾⣿⡁
⠀⠘⠶⣦⣤⣤⣴⣿⣿⣷⠾⠃⠀⠀⠀⠀⠈⠁⠀⠸⡇⠀⠀⠀⠀⠘⠆⠀⠀⢻⠁⠀⠁⠈⢹⢢⣿⡿⠃⠀⠸⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⣉⣧⣠⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠈⠙⢦⡀⠀⡀⠀⠀⠀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠈⠉⠒⠀⠊⠀⠀⠀⢀⡠⠔⠋⠁⢀⡤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠹⢦⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠈⠀⠀⡀
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡇⠀⠀⠠⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⢁⡴⠋⠀⠀⠠⣄⣉⠁
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠰⡀⠀⠀⠁⠛⠛⠁⠀⣀⣀⠈⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢀⢆⢸⡀⠀⠀⠀⠀⠀⠉⠉⠑⡖⠚⠃
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣠⣦⣶⡍⢩⠆⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠐⣠⣴⣞⢻⡿⣫⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⣀⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠐⢀⢤⣾⣿⡿⢛⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⡠⠔⣵⡿⢛⡭⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣶⡛⠛⠛⠛⠓⠒⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠘⡄⠀⠴⠃⠀⣀⡵⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⣴⠂⠀⠀⠀⠉⠓⠢⣄⠀⠀⠱⣄⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠋⠑⠒⢲⠶⠶⠶⢶⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⡁⠂⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⣸⠚⠎⠉⠀⠀⣀⣀⣀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁
⠀⠀⠀⠀⠀⠀⠀⣰⠋⡃⠀⣠⣤⣤⣧⣀⠉⠐⠲⢤⡀⠀⠀⠸⠆⠛⠀⠸⣤⠶⠛⠩⣯⠉⠉⠈⡫⠉⣵⣶⠶⠆⠀⠀⠀⢀⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⡞⠉⠀⠤⠤⠬⠙⠶⢤⡤⠟⣡⠤⠒⠃⠒⠢⠤⣉⣀⣌⣭⣥⣠⣄⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⢀⣀⡀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠑⠀⠸⡖⣶⡒⠒⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⠤⢤⣄⣀⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠱⣜⠀⠀⠈⠈⡇⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠤⣼⢂⠀⠘⠀⡀⠀⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⢀⠔⢤⣯⡓⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠳⡀⠀⠀⡜⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡼⡇⠂⣪⠾⠀⠈⢆⠀⠀⠀⢀⡖⠀⠀⠿⠈⢳⣤
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠉⠓⠦⠤⢤⡤⠴⠖⠻⠁⠀⠊⠀⠙⠑⠚⠚⠁⠀⠀⠃⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡁⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠲⣄⠀⠀⠀⠀⡀⠔⠊⠉⠉
⠀⠀⠀⠀⡔⠀⠀⠀⠉⠀⠀⠀⠀⢠⠒⠉⡀⠀⠂⠁
⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⣾⣿⠀⠈⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⣀⠢
⠀⠀⠀⢣⠀⠀⠀⢀⠀⠀⠛⠋⠀⡀⠈⠱⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠠⢈⣀⠀⠀⠈⠉⠙⠶⠐
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⢀⣠⣾⣿⡦⠃
⠀⠀⠀⠀⠈⠢⣀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⢠⣾⣿⢗⠽⠊
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠵⢟⡭⠚⠁
⠀⠀⠀⠘⠣⣄⣀⠀⠈⣉⠀⠒⠠⢄⡀⠀⠈⡄⢈⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⡲⠓⠂⣤⠤⠤⢔⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⠁⠀⠀⠀⣠⡀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⢀⠿⠀⢀⣀⣖⠀⠀⢀⡀⠀⠀⡄⠸⠉⡄⣠⠴⣶⣒⣂⣠⣀⣀⣠
⠀⠀⠀⠀⠀⠁⢸⡰⠋⠉⠉⠡⠦⢤⠼⡂⠄⠐⠐⠠⢌⣡⣴⡬⠤⣤⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠊⠠⠄⠀⠀⠀⠀⠈⢄⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⢸⢤⣀⣀⣀⡀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠈⢨⠀⠈⠉⠁⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠀⠀⠘⠠⡀⠀⠀⡜⠡⡀⠀⠀⠀⠀⠀⠀⠀⡼⢹⣴⠁⢚⠀⠄⠀⠀⠀⢀⠀⢸⠀⣀
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠢⠤⣄⣀⡤⠴⠊⠠⠂⠱⠠⠿⠀⠀⠂⠀⠀⠁⠶⠶⠶⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⢉⡠⢴⠟⠈⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠠⠀⠀⢐⠐⠋⠀⠀⠀⠀⠀⣳⢴⣷⠆⠄
⠀⠀⠀⠀⠀⠀⣞⣁⠔⠊⠁⡴⠋⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠂⣏⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⢀⣀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡇
⠀⠀⠀⠀⠀⠀⢀⡷⢌⡀⠀⠀⠀⠀⠀⣀⣠⡴⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡔⠁⢴⢧⠄⣤⡂⠀⠉⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠮⣸
⠀⠀⠀⠀⠀⠀⠈⣮⠀⠀⠹⡋⠋⠛⠙⡯⠁⠀⢸⡿⠀⠀⠀⠀⠠⠖⡀⠀⠀⢸⢀⡆⡸⣰⢠⠱⢸⠘⠠⣼⠀⠀⠀⠀⠀⡌⠀⠀⢀⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠅⠀⠀⠀⣭⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠘⠛⠄⡗⡷⢾⢭⣩⡧⢠⠁⡀⠀⠀⠀⢀⠅⠀⠀⠌⢈⠇⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠹⢛⣿⣿⠏⠀⡰⠋⡔⠀⠀⠀⠀⠈⢀⠀⠐⠄⠼⠀⠀⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠓⠀⠈⠀⠊⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⠀⢠⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢛⡵⣣⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡞⡩⢊⡴⣁⢊⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⡔⠀⠀⠀⠇
⠀⠀⢲⡀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠠⣴⢾⠋⢽⠤⠿⣜⠕⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠐⢀⠆⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⡄⠌⠀⠀⠀⠀⡆
⠀⠀⠘⢶⣢⠉⠀⠀⠀⠀⠀⠀⡠⠖⠩⢀⣽⣳⠆⣀⡼⠂⠀⠀⠀⠀⠀⢀⡜⠁⢄⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠈⡙⡀⠀⠀⠀⢀⠀⠜⢗⠔⠠⠏⠁⠠⠒⠟⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠛⠁
⠀⠀⠀⠀⠁⢡⠀⡀⠐⠈⠀⠜⠁⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠆
⠀⠀⠀⠀⠀⠐⠀⠐⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⡂⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡼⠶⡦⠀⠀⠀⠀⢒⡡⢒⠛⢋⡀⢀⣠⣄⠀⠀⠀⠠⠏⠀⠀⢠⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠀⠀⠀⠀⢂⡖⠒⠛⠂⠀⠀⠒⠂⢴⠋⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⣄⡇⠠⢁
⠀⠀⠀⠀⠀⠀⠀⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢯⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⣠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢉⣇⢀⠂
⠀⠀⠀⠀⠀⡴⠊⠀⠙⣆⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢴⠀⠊⠀⠀⠀⠀⠀⣀⡀⣠⠾⠋⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠣
⠀⠀⠀⠀⠀⠻⠇⢶⢚⣃⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠒⠲⠶⠈⠉⢋⠓⠚⠉⠁⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢉⣁⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠘⠁⠀⢀
⠀⠀⠀⠀⠀⢠⠃⠀⢻⣵⣶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠨⠿⠗⠂⢀⠠⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠇⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠲⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠬⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠊

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠖⠒⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠻⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠟⠀⠀⠈⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⣾
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣰⠃
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣡⠁⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠉
⠀⠀⠈⠊⣄⡆⠄⠀⠀⠀⠀⡀⡖⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠁⠀⠀⠀⢐⠉⡇⠁⠀⣄⠀⠤⠧
⠀⠀⠀⠀⠂⠁⠄⠀⠀⠀⠀⠘⠁⢤⢘⡝⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠅⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠠⠐⣆⠀⠐⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡠⠂⠀⠀⠀⠐⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⢀
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠆⠀⠈⠂⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚
⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠀⠃⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠄⠀⠀⠈⠀⠠⡀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡀⠀⢠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠂⠀⠈⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡄⠘⠁⢀⣠⣤⠶⠂⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡶⠤⢌⢄⠖⠀⠈⣉⡉⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⣤⠀⠠⣄⠀⠀⠀⠁⠀⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠂⠀⠀⣶⠀⠀⠉⠀⠀⠀⠀⢀⡄⠂⠑⠁⠒
⠀⠀⠰⠽⠀⠀⢧⠀⠀⠈⠀⠀⡠⠃⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⣰⠄⠀⠀⠀⠀⠀⠈⠀⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠇⠈
⠀⠀⠀⠔⠂⠉⠁⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠚⢀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣆⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⡸⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠈⠁⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣟⡷⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡟⠁⠀⣀⢶⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣛⡮⣄⢠⣮⣻⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢮⣪⡪⡪⣳⠟⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣕⢝⣷⣕⢜⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣮⡪⡻⣮⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢷⣷⣝⢿⣯⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡻⣿⡪⡻⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠉⠀⠀⠉⢑⣶⢝⢟⢾⣈⢻⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⣠⣮⡻⡻⣷⣑⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⢼⣿⣾⢿⣾⡮⠋⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠁⠀⠀⢀⡠⢄⣸⣷⣵⣝⢷⠟⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⢀⠞⠁⢀⢞⠮⣻⣿⠛⠃⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⣅⣑⢕⠝⠁⡇⠀⠀⠀⠀⠀⡸⠹
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⡪⡫⡺⠋⠀⡰⠁⠀⠀⠀⢀⠔⣡⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣔⣕⢝⢟⠾⠤⠐⠊⠀⠀⠀⡴⢊⡡⠔⠁
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢞⠳⣮⡫⡲⡳⠃⠀⠀⠀⠀⠀⠀⠸⡰⠁
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠙⠪⡙⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢖⠤⣀⣀⠀⠀⠀⢀⣀⠠⠒⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠬⠍⠉⠠⠤⠒⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢸⡁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣀⡻⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣣⠼⠋
⠀⠀⠀⠀⠀⢣⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡞⣩⢤⠨⢵⡽⣷⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢣⠀⠈⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣴⣶⡤⢣⡟⠀⠀⠀⠀⢸⣿⡿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠖⠛⠁⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠳⠿⠷⠶⠋⠀⠀⠀⠀⠀⠀⠙⢿⣾⡿⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠐⣦⣤⣤⣴⡆
⠀⠀⠀⠀⠀⢺⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢹⡄
⠀⠀⠀⠀⣤⡟⠙⠙⠋⠉⠙⠛⠛⠙⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠉⠛⡟⠛⣿⠛⠛⠛⠛⠛⠛⢿⠟⠋⠀⠀⠀⠀⠀⠀⣼⣿⣯⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⣿⣧⣿⣟
⠀⠀⠀⠀⠀⠀⡇⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡯⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁
⠀⠀⠀⠀⠈⠻⢷⣶⣶⣶⣄⣠⣶⣶⣾⢿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠞⠉
⠀⠀⠀⠀⠀⣀⣀⣹⡿⢿⣩⣍⣿⣿⣏⣀⠉⠉⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣿⣿⡇
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⠺⣻⣿⠇
⠀⠀⠀⠀⢀⠈⠿⠿⣿⣿⣿⣿⣿⣿⠇⠀⣀⡀⠀⠀⠀⠀⢿⣯⣹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⡻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠂⠀⡙⠿⣿⣿⡿⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣼⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⡀
⠀⠀⠀⠀⠀⠀⡴⢿⢹⣯⡄⠀⢶⡶⠀⠀⠀⠀⠀⠈⠉⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⢠⠲⣜⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢺⡇⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⠀⣤⢠⡄⣠⠀⣄⢠⣤⠀⣤⣄⢠⡄⣤⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠙⠿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⡏⠘⠂⡧⢸⡇⣿⢸⡇⣿⣇⣿⠀⣷⠸⣇⣼⠀⣷⡏⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣇⣰⠀⣇⢸⠇⣿⢸⡇⣿⠸⣿⠀⣟⢸⡇⢹⠀⢸⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠀⠈⠉⠁⠉⠀⠉⠀⠁⠈⠁⠈⠀⠈⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡮⣵⣦⣄⠀⠀⠀⠀⠤⣤⠄⡤⡤⢀⡠⠄⢰⢦⡤⢤⢰⠆⡄⡄⢠⡄⠀⠀⠀⠀⣠⣬⣉⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣼⣿⣿⠆⠀⠀⠀⠀⠀⠀⠂⠞⠊⠸⠆⠘⠈⠇⠸⠚⠆⠃⠇⠸⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠻⢿⣿⠀⠀⣀⡀⣠⣤⣤⣤⣶⣦⣶⣦⣤⣤⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡽⠿⣯⣼⡃
⠀⠀⠀⠀⠀⣴⡄⠀⠀⣾⣋⠀⠁⠈⠀⡙⣷⠀⣿⣷⢺⣛⡟⣖⣲⢲⣒⣖⣖⣲⣻⣛⣾⡿⠠⡄⠀⠀⠀⠀⢠⣟⡁⠈⠀⠁⢈⣳⡄⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⡸⠀⠀⠀⠀⠃⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣷⡆⠀⠀⠀⢻⡧⠇⠛⠚⠓⠸⣸⡇⠀⠀⠠⡇
⠀⠀⠀⠀⠀⢭⠀⠀⠀⠙⠷⣤⡆⢰⣤⡾⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⢦⣴⣷⣦⡴⠟⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⡞⣽⣿⣿⣿⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣀
⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢫⣧⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡏⠀⢹⣿⠁
⠀⠀⣾⣿⣯⣀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⡟⠙⠁⠀⠀⠀⠀⠀⠀⣠⡞⢹⡛⣛⣿⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣿⣿⣷⡀
⠀⢸⣿⣿⡿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⢻⣿⡇
⠀⠀⠿⣿⣿⣷⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡋⠙⣶⣶⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⡏⠈⣉⢹⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣼⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠊⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠐⠲⠦⠤⢀⢤⣄⡀⢀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠂⠀⠀⠀⣀⣴⣦⠳⠄⠀⠀⠀⠚⠓⠀⠀⠀⣰⣿⢋⠀⠀⠀⠠⠈⠒
⠀⠀⠀⠀⠀⠀⠙⠤⠄⡼⡶⠀⡄⠉⢻⠛⠻⣿⣿⠇⠀⠘⠛⠀⠀⣠⣴⠿⠛⢉⣀⣠⣤⣶⣶⣤⡀⠀⠀⠐⠶⠿⣡⠍⣿⢠⣄⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠒⠋⠀⠀⠈⠉⠀⠀⠀⢀⠀⠉⠁⢠⣖⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠈⠈⢃⣤⠞⠉⣤⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⢷⣄⠉⠻⣿⣿⣿⣿⣿⣿⣟⠻⣶⣄⡀⠀⠈⠉⠛⠁⠀⠉
⠀⠀⠀⠀⠀⢠⣖⣟⣋⣛⣛⡛⠋⠿⢩⠙⢷⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⣤⠀⠀⠀⠝⣡⣞⣀⣼⣿⣿⡇⠀⠀⠀⠀⠆⠚⣆⠀⠀⠙⢷⣄⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠹⣿⣷⡤⣴⣶⣶⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠙⢷⣄⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠉⠉⠉⠉⣩⠉⠛⠻⣿⣿⡿⠀⠀⠉⠀⠀⠀⠂⠐⠀⠀⠐⠂⠀⠙⣷⣄⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢉⣉⣤⣾⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠒⢄⠀⠡⠀⠀⠹⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠛⠉⠁⢠⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⡠⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡠⠎⠀⡀⠂⠀⠀⠒⠂⠀⠈⡠⣄⠀⠀⠀⠀⠀⠀⠀⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⡏⠁⠀⢤⠀⢑⡴⠆⠉⠀⠈⠅⠘⠂⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠉⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⣤⡀⣀⠀⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉
⠀⠀⠀⠀⠀⠀⣠⣶⣛⣩⣅⣀⡀⠀⠀⠀⠖⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡀
⠀⠀⠀⠀⣐⡾⠿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⢠⠒⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠛⠛⠻⠿⠷⢿⣯⣽⡉⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⠀⢀⡴⠠
⠀⠀⠀⠉⢻⡒⠶⢷⣖⣦⣤⡄⣸⡟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠁
⠀⠀⠀⠀⠸⠇⠀⠀⢸⠅⠉⠉⢸⡇⢀⡀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠠⡀⠀⣀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠸⢃⣜⠻⠖⠀⠀⠰⠀⠘⠀⠄⠀⠠⠄⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣯⢠⡿
⠀⠀⠀⠀⠀⠀⠰⢥⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡏⡤⣤⢈⣽⣏⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⡀⠠⠆⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠿⠓⠋⠻⠂⠰⣷⠆⠀⠀⢰⣿⣿⡟⠀⠀⠀⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠘⠿⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿