Plant Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠐⢀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣄⠀⠉⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢫⠀⡤⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⡄⠶⠇⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠋⠚⡃⢀⡀⠈⠃⠀⠀⡀⠀⠐⠃⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠙⢎⠁⣿⠁⡀⠀⠁⠉⠀⠀⡄⠉⣭⡀⠀⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠷⠰⠋⠑⢧⡀⠋⠀⠀⠀⠀⢠⣄⢰⣶⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠂⠀⡀⠀⢀⠄⠀⠘⠢⠤⠀⠁⢦⠀⠀⠀⠐⣯⡉⣿⣴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠦⠈⡃⠀⠸⠃⢠⡓⠀⠀⠆⠀⢀⡃⠀⣻⡄⠈⣧⠉⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢠⡤⠁⠀⠈⣁⠀⡟⠆⠀⠛⠀⠀⢻⠃⠈⠛⢿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠉⣙⠀⠀⠰⠎⠁⠘⠋⠁⠴⢀⡙⠀⠶⠀⢻⠤⣀⡀⢠⡤⠴⠆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠂⠀⠀⠠⠠⠆⠐⢀⠀⠠⠙⠰⠆⣀⣼⠀⠉⠷⠀⠀⠀⠀⡠⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣀⠰⣌⣀⣧⡄⠀⠀⠀⠁⠈⠱⠋⠀⠀⠀⠈⢻⣆⡀⠶⠛⠚
⠀⠀⠀⠀⠀⠀⠈⠁⠋⠙⠿⢁⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡏⠠⠆⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠒⣰⠃⣠⣄⠀⠀⠀⠀⠐⡃⠀⠀⢸⣬⡅⠈⠓⢀⠀⢰⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠛⢀⡀⠶⣧⣄⣻⠀⠀⢠⡶⠀⠈⠁⠀⠀⣸⠉⠀⢮⠁⣄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⡏⠶⠚⡻⠀⠀⠀⠀⠀⢠⡜⠀⠀⠀⠁⠸⠐⢶⣋
⠀⠀⠀⠀⠀⠀⠀⠈⠰⠁⠶⢄⠶⣀⠤⢨⠗⠀⠀⠀⡄⠀⠀⣿⠀⠀⠀⠀⠀⣿⠛⢁⡀
⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠃⠒⠀⠀⠟⠀⠀⠀⠹⠥⡶⠄⢀⣖⣠⠟⠛⠁
⠀⠀⠰⣿⡃⠀⠀⠀⠀⠀⠀⢒⡀⠠⡐⠆⠀⡀⣾⠃⠀⠠⠀⠲⠀⠀⠠⠈⢙⣁⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆
⠀⠀⠀⠘⢣⡄⠀⠀⠀⠀⠀⠀⠀⢂⣤⠘⠢⣤⠀⠀⠀⠄⠀⢀⠀⠀⠲⡶⠆⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃
⠀⠀⠀⢀⣄⠙⠀⠀⠀⠀⠀⠀⠐⣿⣿⢀⣤⠘⣀⠰⠂⡄⠀⣼⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠐⢶⠀⢠⣦⠀⠠⣌⠛⣤⡿⣀⡽⢃⡀⠀⢰⠇⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣅⠀⠀⠙⠻⣿⣾⡏⠀⠁⢄⠀⡜⠀⠘⠀⠀⠀⠀⠀⠀⠀⠰⠀⣴⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣤⣠⡀⠘⡿⠀⠈⠀⠀⠰⡇⢀⠃⠀⠀⠀⣀⣦⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢺⣷⠀⠀⠀⠀⢰⣦⠀⠠⠐⠚⠛⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣴⠀⠀⠀⢈⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠘⠻⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠈⢰⡞⠀⠀⠀⠐⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢄⢸⡇⢀⣾⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡆⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢡⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⢾⣋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⣲⢤⡀⠹⣿⣧⣿⣿⢃⣤⡖⣲⣶⣔⣦⣄⡀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣾⣷⣤⣿⣆⣿⡦⡈⠻⠛⢡⣾⣻⣷⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⠁⣸⣿⣧⣤⣴⣶⣒⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠓⢦⣤⣝⠙⡻⣿⣿⣷⠀⠂⢸⣾⡟⣡⠇⠀⠀⠀⠀⠀⠀⠐⡄⢀⡆⢾⣧⣴⠛⠋⠀⠙⠻⠿⠿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠷⠤⠽⢿⠀⡔⠐⡯⠖⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⡴⠏⠓⠀⠀⠀⠀⠀⢀⣠⠆⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⢀⣀⠀⠀⠀⣀⢈⣡⣶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⣄⣀⣀⡀⠀⢄⠀⠀⢀⠂⠀⠀⢀⣸⢉⣉⣠⣼⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣲⣦⣽⣦⡐⣤⣄⣠⣤⣄⠀⠀⠀⠈⣷⡿⣿⣿⣿⣷⡶⠦⢱⣦⣼⣿⣍⣶⡾⢿⣿⣿⣿⣗⣾⠗⠲⣤⡀
⠀⠀⠀⠀⠀⢀⢐⣿⠟⠩⠤⠤⠈⣉⡛⢿⣼⣿⣿⣿⣿⣿⣆⡀⠀⣼⣿⠟⠻⣿⣿⣧⡀⡟⠓⡛⢉⣠⣤⣴⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣦⡤⠄
⠀⠀⠀⠠⠖⠋⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡉⠋⢀⣰⣾⣼⠏⠀⠀⠉⢹⣿⣾⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠑⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠛⠉⠉⠁⠀⠀⠈⢹⣽⠏⠁⠀⠀⠀⠀⠀⢻⡿⠟⠋⠋⠩⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠷⣄⠀⠀⠢⢤⣬⣵⣏⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣄⣀⠉⠉⢉⢉⣁⣀⣹⣧⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⠙⠿⡿⢻⡿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⣠⣿⣿⡇⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢸⡷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣱⣶⣿⣿⣿⣿⡇⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡠⠀⣀⢀⣀⠀⣀⣠⠔⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠛⠿⣿⣿⣿⣿⣇⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⡿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⡅⢶⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⣇⠀⠀⠟⠁⣸⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣿⣿⣿⠀⣿⠀⣆⣀⡤⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⢿⣿⣧⢰⠦⠟⢿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⠆⢸⣿⣧⠈⣠⠚⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⡟⣋⣨⡽⠿⠛⣿⣿⠗⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣏⣻⠟⣿⠀⠶⠂⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠈⢿⣷⡶⡄⣄⠒⣘⣋⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣸⣏⣤⣤⢰⣂⣭⣿⣿⣿⣷⠶
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠏⠀⠈⠙⠋⠛⠛⠋⠉⠁
⢀⠙⠉⣠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⡀⠀⣿⣰⣿⠄⠀⠀⢀
⠀⢱⡶⢼⡧⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣦⢙⣟⣁⡤⠂⣠⡎
⠀⠈⠃⡤⠛⠀⠈⠁⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⡘⢿⣿⣿⡿⠛⠁⡤⣨⠏
⠀⠀⠀⠀⠀⣤⡄⢳⢀⡟⠀⠀⠀⠀⠀⠀⢠⡌⢻⣄⠙⣿⣿⣧⡾⠟⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡈⠃⠎⠀⢠⠀⠀⠀⠀⠀⣿⣿⣄⢿⠀⡞⠉⠀⣀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⡞⠀⠀⠀⠀⠘⣿⣿⣿⣧⣷⢁⣶⠈⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠁⠀⢀⡰⣤⡀⣿⡿⠙⢿⡿⠈⣳⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡄⣠⠛⢱⡍⢿⣾⠃⡀⠀⢀⡾⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡆⣿⣀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣯⣄⠀⣤⡈⣿⡀⢲⠀⢸⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣄⠀⠀⢿⡍⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣉⢈⡉⠀⠘⠿⠻⣷⢸⣦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢿⣿⣦⡀⠀⢿⣿⠋⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣧⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡇⢸⠟⣿⣿⠇⠀⡏⣀⢃⡼⠃⠀⠀⠀⠠⣀⠀⠀⠀⠐⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠊⠀⠈⠻⠀⠆⠘⣿⠚⠁⠀⠀⠀⠀⠀⠙⢷⡌⠀⠰⡀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⢠⡇⠀⢺⣇⠀⠉⠀⠀⠀⠀⠀⠀⢀⣿⣤⣹⣦⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠁⠀⠀⣿⡄⠄⠀⠀⠀⠀⠀⠀⠈⢻⡉⣿⣿⣀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢰⠀⢠⡆⢸⣇⠀⠀⠀⠀⠀⢀⡴⠀⢾⣇⣡⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢲⣤⣄⡀⠀⠙⠷⣦⠸⡇⠘⡟⠀⠀⢀⡦⢀⠈⠁⠀⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣌⡳⢦⡄⠀⠘⠇⠀⠀⠀⢐⣈⢰⣷⠐⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠻⢿⣿⣷⡆⢰⡇⠀⠀⣴⠿⣿⠀⢻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠙⢿⣇⣘⡁⢉⡼⢁⣤⣿⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⢀⠙⢿⠁⢩⡄⢸⣏⢉⢡⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠈⡀⣼⡇⢸⣿⡤⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⢘⣷⠘⡇⢠⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⢀⡟⠀⠀⠀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⣿⡆⠘⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢎⣿⡄⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⢀⣿⡄⠀⠀⠐⣄
⠀⠀⠀⠄⡀⠀⠀⠂⣤⡀⠘⣿⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠫⢝⣶⣄⠀⠀⠀⠀⠀⡖⠀⢹⣿⠀⢠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⢀⡀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠙⣆⠀⢀⠀⣱⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠖⠀⠀⣠⠀⠀⠀⠀⠁⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⠀⠀⠀⠀⠙⠇⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠁⠀⣀⣤⣤⣀⡀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⠰⡀⠀⠀⠀⠀⠀⣠⢎⡕⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠳⡀⠀⠀⠀⡴⢡⠎⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠻⡲⢄⠀⠀⠀⡠⠜⠀⡿⠀⠀⠀⢱⠖⠑⠋⣰⠏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⠢⡱⣄⠀⡇⠀⠀⣇⠀⠀⠀⢘⠀⠀⣰⠏⢀⣄⠀⣙⠀⠀⠀⠀⣀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⢮⡑⠋⠳⠀⣿⠀⠀⣀⠜⠀⢀⡟⡰⡟⢠⠀⢧⠀⢀⢔⡫⠋⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠳⣄⠀⢇⢹⡀⢸⠀⠀⠀⣸⠏⡜⢀⡜⠀⡰⢟⡵⠋⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢦⣀⠀⠙⣆⠈⠛⠧⡀⣇⠀⢀⡏⡼⠀⡜⡔⠉⣴⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠻⡳⡄⠘⣧⠀⠀⢃⡸⠓⠊⡼⠁⠀⢧⣹⡾⠁⠀⠀⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⡀⠀⠀⠀⠘⢆⠘⢮⢢⣘⣧⠀⢘⡂⠀⣸⠃⠀⠀⣸⡟⠁⠀⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠛⢕⠢⣀⠀⣸⠀⠈⢳⡄⠈⣧⣿⠇⢀⡏⠀⠀⠀⢻⠀⠀⠰⣋⡠⢄⡶⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠙⢮⡉⠉⢄⠀⠀⠹⡄⠸⡉⠀⣸⠀⠀⠀⢀⡼⠄⠒⣋⡵⠚⢁⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠙⢦⡎⠀⠀⠀⠹⡄⠈⠱⡇⠀⠀⣰⠛⢁⡴⠞⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⢻⡖⢤⡀⠀⠹⡄⠀⡄⠀⠀⢱⣴⠋⠀⠀⠀⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⠆⠀⠀⠹⣤⡃⠀⠀⢳⣸⠃⢀⣴⠟⠁⠀⠀⡔⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠖⠒⠀⠛⠘⠒⠀⠘⠛⠚⠃⠛⠂⠐⠒⢖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡀⠀⠀⠀⢀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⢀⣠⣤⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠿⢶⣦⣄⠀⠀⠀⠀⠀⢹⣇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⠟⠛⠛⠛⠛⠛⠛⠛⠻⣶
⣤⣾⠋⢡⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠠⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⢀⣀⣤⣶⡶⠶⠞⣩⡿⠋
⠈⠉⠐⢦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠶⣶⣄⡀⠀⠀⡙⢿⣄⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⣰⣤⣴⣾⠿⠉⠉⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣤⣀⠀⢻⣆⠀⠀⠀⢿⣷⠀⠀⠀⣰⡿⠋⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⣶⣄⢻⡄⠀⠀⢸⣿⠀⠀⣼⠟⠀⠀⣠⣾⢛⣁⣀⡤⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⢸⣿⠀⣼⠏⠀⣰⣿⠟⠓⠉⠉⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠺⢿⣦⡀⢸⡇⢠⡟⢠⣾⠟⠁⠀⠀⠀⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣸⡇⠘⣷⣿⣃⣤⣴⣶⡶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣰⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⡶⠶⠶⢾⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠟⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢶⣦⣤⣀
⠀⠀⢀⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⡀
⠀⠀⢸⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢻⡇
⠀⠀⢸⡇⠉⠛⠻⠷⢶⣶⣤⣤⣤⣤⣴⣶⣾⣛⣛⣛⠛⠉⠉⠉⠉⠉⠉⢹⣏⣿⠉⠉⠉⠉⢛⣛⣛⣛⣻⣷⣶⣦⣤⣤⣶⣶⠾⠟⠋⠀⠀⢸⡇
⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠻⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠏
⠀⠀⠀⠀⠀⠉⠉⣿⠳⠶⢶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠶⠶⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⢠⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢶⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠀⠀⣤⣤⡤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠩⠖⠂⠀⠀⣚⡧⠄⠀⠀⠀⠀⠈⠀⠲⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣶⠦⢴⠀⠀⠀⠀⠀⠀⠈⢨⣖⡀⠀⠀⠠⠄⢀⠀⠤
⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⡀⠈⠡⠀⠀⠀⠀⠀⠈⠀⠀⡄⡄⣀⡠
⠀⠀⢧⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠈⢿⠀⢄⢢⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠤⡀⠀⠀⠒⢝⠄⠁
⠀⠀⠀⠸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢠⠀⠈⡀⠤⠀⡐⠀⠀⢀⠀⠈⡀⠈⢀⠀⡀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠈⢀⢂⠀⠃
⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠶⠀⣦⠀⠀⠀⠀⠀⠀⠾⣸⡜⣯⣗⢯⠵⡆⠀⠀⠀⠀⠠⠒⠤⡀⠀⠀⠀⠀⠀⠳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠁

⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢠⡄⣤⠡⣶⣦⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠼⣠⡎⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⢿⣿⣧⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⡁⢹⡂⡈⢀⠎⠀⠀⡁⠀⠂⠀⠐⠀⠀⠐⡘⡿⢰⠀⢀⠂⠀⠀⡄
⠀⠐⠲⣄⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠆⠀⡄⠀⠰⠁⠀⠀⠐⠀⠀⠀⢀⡙⢦⣾⡣⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⢳⡁⠀⠀⠀⠀⢈⡗⠈
⠀⠀⠀⠴⠆⠋⠀⠀⠀⠀⠀⠀⠄⠠⠀⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠡⠒⠻⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⡤
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰
⠀⠀⠀⠀⢰⡀⠃⣴⠀⠀⠀⠀⠀⠀⠏⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣥⠁⠀⠀⠀⠀⠀⠈⠓⠺⠃
⠀⠀⠀⠀⢸⢻⡾⠸⡠⢲⠃⠀⠀⣀⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣿⣿⠓
⠀⢀⠀⠀⠸⠂⡟⡺⠁⡏⠀⠀⠀⡆⠉⠱⡇⠀⢸⠀⡀⢰⠀⠀⠀⠀⠀⢸⣏⡙⢹⡆
⠀⠀⣷⢄⠀⢠⡇⠃⠞⠀⠀⠀⠀⠙⠀⠚⠀⠀⠀⣼⡇⣾⣧⠀⠀⠀⠀⠸⣏⠀⣨⠃
⠀⠀⠸⣌⢳⡀⢡⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡗⣿⣼⡶⢠
⠀⠀⠀⠈⠑⠀⡄⢰⣦⣀⡈⢇⠀⠀⠀⠀⠀⠀⠓⣆⣿⣾⣿⢇⢈
⠀⠀⡠⠒⢀⠐⡇⠁⠀⡨⠙⠾⠀⠀⠀⠀⠀⠀⠸⣯⣿⡻⣿⣷⡏⠀⠀⢀
⠀⠴⠁⣴⠏⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⣓⡻⣿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠻⡜⠁⠀⠈⣧⠏⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣧⢸⣅⡿⠀⠀⠸⣄⢀⠇⠀⠀⠀⠀⠀⠀⣆⣁
⠀⠀⠁⠀⣤⣴⡿⠦⢤⠀⠀⠀⠀⢂⡀⠐⠀⠀⠀⢀⢽⣿⣿⢧⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⢠⡄⣾⣿⣤⡀⠀⢀
⠀⠀⠀⠀⢿⠋⠀⠂⠒⠀⠀⠀⢠⠸⠷⢤⣄⠀⠀⠀⠀⠉⠉⢁⠀⠀⣠⣧⣤⡀⠀⠀⠀⠀⢸⡃⠀⠀⠈⠇⠀⠈⠃
⠀⠀⠀⠀⠸⣧⡀⣦⠆⠀⠀⠀⠸⣄⠀⣀⠌⠀⠀⠀⠀⠀⠀⠜⠀⠀⣿⣸⣽⠇⠀⠀⠀⠀⠈⢧⣀⣀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢔⡉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⠃⠀⠀⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⣠⡀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⣹⠀⠀⠀⠀⠀⢀⡄⠀⠀⠢⠀⠙⠀⠀⠀⠀⠀⠉⢴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢤⡔⠠⠤
⠀⠀⠻⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⢀⣀⠀⣀⣠⣀⢀⡘⠃⠀⠀⠀⠀⠈⣂⠀⠀⠀⠀⠀⢠⡄⠀⠁⠶⠂
⠀⠀⠸⡀⠀⢠⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⣿⣿⣿⠿⠿⠛⠻⢿⣷⣶⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠃⠠⠈
⣦⠀⠴⠆⠀⠈⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣾⠉⠙⠀⢠⣄⣀⠇⠀⠙⠋⠀⠀⠀⠀⢃⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⣿⠙⠒⢦⠀⡈⠀⠀⣶⠀⠈⠂⠀⠀⠠⠀⠀⠀⣀⠀⡁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠞⠧⠀⢀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⢜⢀⡔⠀⠆
⠻⢀⠀⠈⠀⠁⠀⠀⣿⠀⣦⡀⠀⠀⠀⠀⠀⠀⠽⣶⣿⣞⠁⠀⠀⠀⠀⠀⡠⠀⠀⠐⠀⠘⠀⠀⡀⠠⠀⠀⡤⠀⠀⠲⠶⢈⠁⡀
⠀⣿⣤⡀⠈⠀⠀⠠⣿⡀⠀⡤⠀⠀⠈⠀⠀⠀⠀⠘⣿⠛⢀⠴⡇⡄⠐⠭⠃⠀⢀⠠⡄⠀⣆⣰⢧⠀⠀⠀⠀⠶⡀⠼⢂⣰⡀⠉
⠉⠁⣀⠘⠆⠰⠅⠀⣻⣄⣽⠀⠀⠀⠀⠀⠀⠀⠦⣄⠙⡧⠃⠎⠁⠛⡀⠀⠀⣰⠛⡠⠓⠃⢸⣝⣤⠀⠀⠀⠀⠀⠘⢦⣌⠀⠀⠠⠦
⠀⣸⠏⢳⡀⠀⠇⢀⡽⠉⣿⣧⢀⡄⠠⠀⠀⠀⣀⠋⢀⠁⠐⠛⢁⣽⠁⣶⢦⣛⢉⣇⠐⡆⢾⡟⠈⠳⡄⠀⠀⠀⠀⠂⠘⠉⡈
⠀⠁⢀⡀⣷⣀⣾⠦⣯⢠⣏⣹⣯⠀⠀⠀⢀⢄⣿⠀⢿⠀⠀⠀⠥⢸⠋⠉⠢⣬⠐⢻⣤⡙⠢⠙⠀⠀⠈⠶⢠⠀⢀⡄⢤⡄⠀⠓⠘
⠼⢆⠀⠛⠚⡉⠖⣂⣞⠒⣉⠙⣟⠳⡄⠠⠀⢸⠏⠀⠎⢓⣦⣇⡄⢠⡀⡀⠀⠀⢰⣷⣾⣾⢤⡄⠐⢃⡤⠖⡴⢖⣘⠢⢂⠉⠀⠀⠰
⠀⢺⡶⣥⠤⡵⡟⠟⣿⠞⠁⠸⣏⠀⢿⠀⣾⢿⡷⢀⡆⠾⠴⢛⡍⢻⠐⠉⣀⡄⠀⢐⣿⡦⣈⠄⠀⣬⣄⢠⣷⣋⠉⡀⠀⠀⠐⢦
⠒⢈⣴⣤⣈⢿⣯⣭⣿⣄⠘⠰⢄⢠⠘⠚⢷⣏⠀⠸⠛⢋⡀⠀⠰⣏⡠⣶⠋⡳⢻⢰⠉⢛⢃⡾⢀⠙⠁⠀⠁⠘⠳⣼⢳⣠⣶⠄⠻
⠻⢧⣟⣿⣱⣮⣦⡜⣿⠫⠀⠀⠹⢀⡿⣿⣿⣿⣿⣷⠶⠆⠠⠰⢾⣋⣾⡛⣼⣯⣣⣬⣃⠉⠡⠇⣼⣀⠄⠀⣴⣀⡰⠏⢀⡗⠙⠺⠃
⣟⠻⣿⠽⠛⠃⢽⣿⢁⣀⣀⠴⠆⣼⡦⣷⠟⠛⣳⡏⠀⠙⠲⠐⢹⣿⠋⡡⠈⣻⣻⣿⠊⢁⣼⠉⣀⠡⣛⣠⣿⡟⣷⢶⣿⣿⣶⡄⢀
⠠⠻⠿⠵⠷⠄⠠⠴⠫⠿⠿⠟⠿⠹⠥⠀⠿⠿⠳⠯⠄⠾⠃⠴⠼⠯⠏⠄⠄⠁⠹⠌⠁⠇⠛⠀⠛⠳⠈⠛⠾⠡⠽⠿⠿⠯⠝⠃⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⣦⣆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠢⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢙⣧⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠰⣅⣩⣥⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠛⠙⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⣴⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡟⣀⢀⣄⣀⣀⠉⠛⠁⠀⣤⠀⠀⠀⣤⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⠟⠋⠙⠿⣦⠀⠀⠀⢼⣦⠀⣸⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣰⢴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢎⡄⠀⠀⠀⠀⠘⢿⡆⠀⠀⡹⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣄⣤⡿⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠈⠁⢀⣠⡴⠟⠀⠀⠓⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⠉⣴⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⡷⠆⠚⢍⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡤⣾⣷⡦⣶⠶⢿⡾⠿⢿⣦⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣾⠟⠋⠀⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⢦⡀⣀⡄⣠⠂⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡿⠒⠀⠀⠀⢡⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡀⠊⠀⢀⡤⢴⠕⢀⢀⡆⢠⡖⠊⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡈⠑⢦⠀⠘⢧⣄⠒⠉⠀⣸⣶⣾⣾⢧⡸⢗⣋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣀⠄⠀⠀⠳⡀⠀⡢⠟⠛⠉⠀⢠⣿⣏⢈⡤⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢢⡀⠀⠀⣯⠆⠀⠀⠀⠀⠀⣼⠟⠋⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣺⣟⣢⣴⣯⡀⣀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⣀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡿⠛⢿⣯⣤⡦⠦⣠⡀⠀⠚⣁⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣙⡀⠀⠠⡄⢰⠀⠀⠸⡇⢀⢄⣀⠀⢀⠄⠀⠀⠀⡸⠋⠀⠀⠀⠈⠙⠻⢶⢤⣄⣀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣑⠤⣀⣼⣧⣄⡀⢤⡵⠋⢫⠀⠀⡌⠀⠀⠀⠚⠁⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⠀⡀⠀⢠⡀⠤⣼⣒⢿⠙⣯⣿⠋⠙⣿⡟⠁⠀⠠⣠⡚⠀⠀⣰⠇⠀⠀⡀⣶⠂⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠙⡄⠀⢹⠀⠀⠸⠀⠀⢠⣿⠋⠁⠀⢠⠏⠀⠀⣼⠁⢻⡶⢤⠈⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠈⠒⠀⠀⣡⡐⣸⠀⠀⣸⣠⡔⠋⠀⠀⠀⠈⡏⠀⠀⠀⣿⢀⡾⡀⠀⠀⢰⡇
⠀⠀⠀⠀⢀⣠⠤⠴⠲⠻⠦⠤⠠⢀⣀⣉⣩⣿⠶⢾⡷⠦⠤⠤⠀⠀⠚⠛⠁⠀⠀⠀⠺⣿⣽⣗⣠⣖⡁⠀⠆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⠟⠉⠀⠀⠸⣷⡀⠀⠀⠀⠀⠠⠇⠀⠀⠰⠀⢸⡿⠉⠉⠛⠉⠤⠀⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⡼⠀⠀⠣⠀⢠⡟⢁⠀⣄⠀⠠⠀⢀⡀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢠⡇⠀⠀⠀⢰⡟⠁⠈⢡⡜⣶⠖⣤⣯⣤⣀⠀⡤⠄⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣼⠁⠄⠈⢠⡟⠀⠐⠠⠖⠾⡌⣽⣛⠋⢉⡀⠀⣄⣤⣄⡀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣆⠘⢦⢛⠀⣠⡅⠀⠀⠀⠀⠀⠉⠙⠦⠠⠀⠀⠀⠀⠉⠑⠢⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢹⡄⣸⠻⣅⡂⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢻⡏⠀⠈⠙⢲⣾⣧⣄⣀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠀⠐⢠⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⣇⠀⠀⠀⡾⠃⠀⠀⠉⠉⠉⠙⠓⠦⠤⢰⣦⣀⣦⡄⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡆⠈⡇⢀⡾⠁

⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠂⠀⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⠀⠐⠋⠋
⠀⠂⠀⠀⠀⢣⢀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠤⡉⡰⢀
⠀⠀⠀⠈⠀⠀⠸⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠤⢀⠞⢠
⠀⠀⠀⠀⢤⠂⠀⠆⠨⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠰⠃⢀
⠀⠀⢀⠀⣦⠁⠃⡌⠐⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃
⠀⠠⠄⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⡂⠀⠐⢊⠤
⠀⠀⢳⠂⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠐⠀⠀⠈⠁⢰⠠⠀⠉⠀⠀⠀⠀⠀⡀⠐⠑⠂⠀⠀⠀⡀⠃
⠀⠀⢸⡀⠀⠀⠀⣸⡃⠀⠀⠀⠐⠒⠈⡀⠀⠀⢀⣀⡓⠘⢀⡄⠀⠂⠾⠃⠀⠀⠀⠀⠀⠀⠐⢌⠍
⠀⠀⢸⠀⠀⠠⡐⢕⣀⠀⠀⠐⠛⠆⠂⠀⡀⠀⠀⠀⠠⠄⠋⠀⢦⡀⣤⣄⡀⠈⠀⠀⢀⠈⠀⠤⠂
⠀⠀⡞⠀⠀⢤⣈⣩⠢⠂⠀⠢⣀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠉⠱⡆⢢⠀⡀⠀⠀⠀⠀⠀⠁⠲⠘⠋
⠀⠀⠀⠀⠀⠢⣭⣠⠶⠖⠂⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡄⠀⠀⡎⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠰⠆⢀⣄⠀⡀
⠀⠀⠀⠈⠁⢲⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⡀⠈⠉
⠀⠀⠀⠀⣶⢈⠀⠀⠀⣀⠀⠀⠀⡡⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣂⠀⠀⠀⠙⠁⠀⢂
⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠠⠀⠔
⠀⠀⠀⠀⠺⠒⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢴⡄⠀⠀⠀⢄⠀⠐⡃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⢂⠈⣡⢊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⢀⠄⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠊⠉⠀⠀⠀⠀⠀⠀⢐⠀⡀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⢾⠢⡒⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⡏⠀⠐⠀⠀⠄⠀⠀⢀⡔⡉⢙⠒⠃⠈⠀⠀⠀⠘⠿⠧
⠀⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢃⡀
⠀⠀⠀⢤⡀⠂⠀⠀⠂⠁⢄⣳⣤⠀⠀⠀⢀⣼⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠅⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠟⠀⠀⠀⠀⠺⠓⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢬⠶⠘⠀⠀⠀⠙
⠀⠂
⠀⠄

⠀⠀⠀⡄⠘⢣⠋⡀⡇⡀⠀⠀⠀⠀⠀⠠⢊⡥⠦⡄⠁⠠⢀⠀⠀⠀⠀⣠⠴⢄⡋⠙⣆⠤⣄⠀⠀⠀⠀⠀⢀⢄⠸⠑⠘⠂⣠⡄
⠀⠀⠓⣒⠌⣁⣄⡀⠡⢀⠤⠀⠀⠀⠄⠀⣸⣜⣱⣼⡡⡙⣆⠂⠀⠀⢀⡹⣄⣀⣣⣴⠃⣀⣼⡀⠀⠀⠀⠐⠍⠀⠱⣄⣤⠎⠁⠱⠄
⠀⠀⣫⠄⡀⢿⣼⡇⠨⠍⠒⠀⠀⠀⠀⡞⡩⢹⣿⣿⢶⡵⠋⡀⠀⠀⠸⣀⣀⠬⢯⣿⠯⣀⡀⣸⠀⠀⠐⣇⠀⠚⢻⣿⢿⡋⠐⢒⠦
⠀⠈⠁⡌⠴⡤⢠⠠⢙⡘⠃⠀⠀⠀⢁⡳⢬⠽⣏⢤⣦⠆⡀⠀⠀⠀⠀⢞⠁⢀⡎⠘⣆⠀⣹⠀⠀⠀⠀⠛⠀⡠⠀⢸⠀⠙⡀⠼
⠀⠀⠀⠀⠋⠀⠂⠱⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠈⠉⠁⠊⠀⠀⠀⠀⠀⠀⠉⠁⠣⠤⠇⠉⠁⠀⠀⠀⠀⠀⠀⠓⠳⠎⠒⠋⠁
⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢠⣾⣶⠻⣿⢷⣾⣲⠀⠀⠀⠀⠀⡖⡃⡆⠆⠆⡥⡓⡆⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⢆⠀⠀⠀⠀⠀⠀⠀⡏⢠⠙⡆⢀⣀
⠀⢀⣼⣏⣻⡶⡻⣾⣋⣽⣦⠀⠀⠀⡸⣰⠉⣞⣿⣿⣮⢐⡚⡇⠀⠀⠀⡾⠀⠀⢀⢤⠀⠀⠈⣧⠀⠀⠀⡎⣉⡒⢇⠉⣆⠗⣋⠍⡇
⠀⠘⠾⣟⣹⣿⣵⢿⣉⣻⠞⠁⠀⠀⢇⠼⡊⢿⣿⣿⡿⡒⢇⡇⠀⠀⠐⣗⠀⠀⠈⠚⠀⠀⠠⡟⠀⠀⠀⠑⠌⢙⢳⣶⣷⢚⡁⠔⠁
⠀⠀⠸⣿⡿⣴⣷⣬⣿⡿⠃⠀⠀⠀⠘⢪⣙⢰⢩⠱⣔⣩⠜⠀⠀⠀⠀⠘⢧⣄⣀⢀⢀⣤⠟⠁⠀⠀⠀⠀⢾⠠⠾⣻⡙⠳⢈⠆
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁
⠀⠀⠀⠀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⢞⠁⠈⡷⠁⠀⡱⠀⠀⠀⠀⠀⣾⠟⠻⡇⢠⡟⠻⣳⠀⠀⠀⠀⣯⡖⠓⣿⣴⣿⠚⣲⣽⠀⠀⠀⠠⣎⠙⢿⡄⢸⠟⠉⡦
⠀⢠⠞⠛⠃⣴⣶⡄⠚⠉⢳⠀⠀⠀⣴⡺⠳⠦⣽⣾⡴⠞⠻⣦⠀⠀⠀⠙⠯⣶⣳⢿⣜⣶⠿⠃⠀⠀⠀⡶⠛⠳⢬⣷⣯⠶⠛⠓⡄
⠀⠘⠧⣤⠖⠛⣿⠋⠲⡤⠞⠀⠀⠀⠘⣳⠖⠋⡿⢻⡙⠳⣶⠛⠀⠀⠀⣴⡿⠻⣟⣿⣹⠟⣿⣆⠀⠀⠀⠙⡶⠛⢋⡟⣯⠙⠶⡖⠃
⠀⠀⠀⢧⣀⡠⢻⣀⣠⠇⠀⠀⠀⠀⠀⠳⠷⠾⡇⡨⡷⠼⠞⠀⠀⠀⠀⣯⣳⣖⡿⠙⢿⣲⣞⡽⠀⠀⠀⠈⠳⠴⢻⡇⢸⠷⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀
⠀⠀⠠⠀⣘⠃⢠⠛⢂⠡⠄⠀⠀⠀⢀⡐⡏⠈⣦⠀⢈⠀⠦⡄⠀⠀⠀⠀⢶⠄⣀⠋⣀⠤⠖⠀⠀⠀⠀⠀⣶⣫⠽⠞⠶⣭⢳⡆
⠀⠠⠘⢁⠈⣦⣷⡔⠊⠝⢠⠀⠀⠀⣏⠀⠈⢢⣼⣶⡁⠀⣠⠃⠀⠀⠀⣀⠤⠷⣼⣶⣧⠤⠤⣀⠀⠀⠀⣼⢽⠃⢀⣤⡄⠈⢻⢽⡄
⠀⠀⢠⣄⡠⠝⡿⢇⠀⢐⠔⠀⠀⠀⣤⠀⠀⢹⠿⠿⢏⠠⠈⡧⠀⠀⠀⠈⢉⠝⢻⠿⢟⠫⠀⠀⠀⠀⠀⢿⡽⣄⠈⠛⠃⢀⣸⣹⠇
⠀⠀⠐⠀⢐⡠⠁⢄⠇⡔⠂⠀⠀⠀⠙⠦⢔⠁⠀⠄⠄⡡⠒⠁⠀⠀⠀⠀⠚⠀⠈⡀⠀⠁⠒⠀⠀⠀⠀⠈⠻⣽⣓⡶⣖⣯⡷⠋
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⢂⢰⣾⣿⣿⣶⠂
⠀⠀⠀⠀⠰⡀⠀⠀⠈⢿⡀⠈⠰⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠃⠀⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡔⠋⠉⠉⠉⠁
⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠈⢇⠀⠀⠀⠀⠈⠑⠒⠶⣦⡀⠀⠀⠀⠀⠀⢠⣤⠐⣦⣤⡀
⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠐⠀⢀⡀⢹⠗⠢⡄
⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠷⣄⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠁⡘⡄⠀⠁⠀⠀⡆⣴⡝⠁⠀⠈⠛⠷⠀⠀⠀⠀⠀⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡚⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢄⠀⣆⢠⠀⠀⠀⠀⠁⠞⠋
⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣶⣶⣄⡀⠀⠀⠀⢸⣶⠇⠀⠀⠀⠀⢰⣴⣫⣥⣠⡤⠀⠄
⠀⠀⠀⠀⠀⣀⠀⢿⣰⣿⣿⣿⣿⣷⣧⠀⠀⠀⠉⠀⠀⡀⠀⠀⠛⠻⠟⠉⡀
⠀⠀⠀⠀⠀⠈⠃⠘⢯⣿⣿⣿⣿⠿⣿⠆⠀⠀⠀⠀⠀⠝⠲⣦⠄⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠙⠑⠈⠛⠃⠀⠀⠀⠈⠀⠀⠠⠛⣷⠀⠀⠀⠀⢠⣶⢶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣵⡀
⠀⠀⠀⠀⠀⠀⠉⠴⢦⣀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⡀⠩⠀⠠⠀⠄⠈⠃⢉⣿⠿⡿⣻⣇
⠀⠀⠀⠀⠀⠈⠀⠀⠬⣿⡏⠻⣤⠀⠙⣿⣦⣄⠀⠀⠀⣠⠾⠛⢠⠳⠀⣀⠰⠂⠀⢀⣁⢘⡃⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠊⠀⠉⠀⠀⠉⠈⢿⣎⠠⠀⠀⠁⢀⢈⠀⠀⠉⠳⠀⠀⠠⠀⠈⠉⠲⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠈⣿⠂⠀⠐⠚⠉⠛⢻⡆⠀⣀⣤⡄⠸⣤⡴⡤⣠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨⠛⣦⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣍⣬⣯⣠⣍⣽⣍⣽⣫⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⣀⣤⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣈⡻⠿⠟⠛⠃⠀⠀⠠⠶⢶⣶⠄⢸⣿⣿⣿⣿⠇⣀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣷⣤⣀⣀⣀⠀⠈⠹⣿⣿⣿⡿⠁
⠀⠀⣴⡾⠿⠛⣿⣿⣿⣆⠀⠀⠀⢀⣤⡄⠀⣿⡄⠘⠛⠛⣛⣁⠀⠙⣧⡀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠈⠛⠋⠉⠈⢉⡛⠛⠛⠷⠆⣩⣷⣦
⠀⠀⢿⡇⠀⢰⣿⣿⠁⢻⡷⠾⠛⠈⠉⠁⠀⣿⡇⠀⠀⠀⣿⣿⣠⣾⠟⠁⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠻⠿⠶⣤⣄⣰⣿⣿⣿⡆
⠀⠀⣼⡆⠀⣿⢿⠇⠀⠀⠀⠀⠀⠀⣠⠆⠀⣿⡇⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠷⠶⢾⣷⠀⠀⠀⠀⠈⠉⠛⠉⣿⣿⣷
⠀⠀⠙⠁⢸⣿⠿⠿⠿⠿⢿⣿⠀⠰⠃⠄⠀⣿⡇⢀⣴⡾⣿⣿⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀⠙⣿⣿⣷⣶⠶⢶⣦⣄⡀⠀⣰⡄⠀⠀⣹⣿⣿⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⢀⣿⣷⡿⠋⠁⣿⣿⠀⠀⠀⠰⢿⣿⣿⣿⣿⡷⠀⠈⢿⣇⠀⠀⠀⠀⠉⠙⠿⠟⠀⢀⣼⡿⠁⢹⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠛⠓⠀⢀⣴⣿⡝⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⠿⠿⢟⣁⠀⠀⠈⢿⣆⠀⠀⠠⡄⠀⠀⠀⣴⡿⠋⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠸⣿⠀⠀⠀⣠⣶⣶⣦⣾⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣤⣦⣄⠀⠘⣿⣿⡇⠀⠀⠘⣿⡄⠀⠐⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠰⣿⣦⡀⢰⣿⣿⣿⣿⡿⠹⣷⡀⠀⠀⠀⠀⠀⢨⣯⠀⠀⠸⣿⣿⡿⠶⣤⣽⣿⣿⠀⠀⠀⠈⣵⣄⣀⣄⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠿⠇⠀⠈⠛⠷⠶⠶⣆⠈⠉⠉⢀⡀⠀⠈⠉⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠘⠛⠉⠀⠀⠶⠶⠿⠇⠀⠀⠀⠀⠶⢾⣿
⠀⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⣀⣀⠰⠾⠂⠀⠀⠘⣷⣤⣴⡶⠾⠿⠷⣶⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⢿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢠⣈⡏⠀⣠⣾⣿⣿⣿⣆⠀⠀⠀⠀⠉⠀⠀⣀⣀⡀⠀⠀⠀⢹⣿⠀⢿⣿⣿⣿⣿⠟⠀⠀⣀⣠⣴⣿⣿⣿⠇
⠀⠈⠙⠛⣻⡁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⣿⣿⣿⣿⠟⠀⢸⣆⡀⠀⢠⣾⣿⣿⣿⣦⡄⠀⢸⣿⠀⠈⢹⣿⡟⣣⣴⡶⠟⠛⠁⠁⠈⠉⣁⣤⣀
⠀⠀⢸⣿⣿⣷⡄⢠⣾⣿⣷⣤⣤⣤⣤⣤⣬⣭⣯⣭⠀⠀⠘⠃⠓⠀⠘⢿⣿⣿⣿⠏⠁⠀⢸⣿⠀⠀⢸⣿⡏⠉⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣷
⠀⠀⢸⡏⢻⣿⣿⣌⠻⠿⠟⠉⠉⠉⠉⠉⠉⠉⣿⣿⣧⠀⠀⠀⢠⣤⣤⣤⣭⣭⡅⠀⠀⠀⠸⣿⠀⠀⢸⣿⡇⠀⠀⢀⣀⡀⠀⠀⠉⢿⣿⣿⣿⠟
⠀⠀⢸⡇⠀⠹⣿⣿⣆⣤⣶⠿⢷⣦⡀⠀⠀⠀⠸⣿⣿⡆⠀⠀⢸⣿⠁⠀⢹⣿⡇⠀⠀⠀⢰⣿⠀⠀⢸⣿⣧⣶⡾⠿⠛⣷⡄⠀⠀⠀⢨⣿⣧
⠀⠀⢸⡇⠀⠀⠩⣿⡟⠋⠁⠀⠀⠙⠻⣢⣀⣼⠃⢿⣿⣿⡀⠀⠸⣿⠀⠀⢸⣿⡇⠀⠘⠛⠛⠛⠀⠀⢸⣿⠋⠁⠀⠀⠀⠈⢿⣆⠀⣠⣸⣿⣿
⠀⠀⠘⠇⠀⠀⠀⢹⣿⡀⠀⡇⠀⠀⠀⠈⠻⠃⣠⣾⠿⢿⣧⠀⠀⠋⠀⠀⢸⣿⣇⡀⣀⣀⠀⠀⠀⠀⢸⣿⠀⠀⠘⢧⡀⠀⠀⠻⠟⠉⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠉⠀⠀⠀⣀⣴⡿⠛⠁⠀⠘⣿⡀⠀⠀⠀⠀⢸⣿⠛⠛⠻⣿⡇⠀⠀⣀⣼⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣸⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⢸⡟⠉⣀⣀⣤⣤⡀⢻⣇⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠇⠀⢠⣟⣥⡄⠐⣦⣀⡀⣠⣴⣶⠾⠟⠛⠉⢨⣯
⠀⠀⠀⠀⠀⠀⢠⣾⠉⠀⠀⠀⠀⠀⢸⡇⠀⣽⣿⣿⣿⣿⡄⠻⣷⡀⠀⠀⢸⣿⠀⠀⠀⠿⠷⠦⠈⠛⠁⣠⡤⠹⠛⠃⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⣀⣼⡇⠀⠹⣿⣿⣿⡿⠁⠀⢈⣿⣦⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⢀⣤⡄⠀⠀⠀⣿⠀⠀⢸⣿
⠀⠀⠀⠸⣆⠀⢀⣾⣦⣄⡀⠀⠈⠉⠉⠁⢠⣶⣶⣦⣶⣦⠀⠈⠉⠉⠉⠁⢸⣿⣦⡀⠀⠀⠀⠀⢀⣼⠟⢀⣠⣶⠟⠋⠀⠀⠀⠀⠙⠀⠀⢸⣟
⠀⠀⢰⡆⠹⠷⠾⠟⠉⠛⢿⣶⣤⣀⣀⣠⣿⣿⡟⠀⢸⣿⠀⠀⢰⡄⠀⠀⠀⣰⣾⣿⣷⣦⠀⣀⣾⣏⣴⣿⣋⣀⣀⣀⣀⣀⣀⣤⣄⢠⣾⡟⠛
⠀⠀⢸⣷⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠏⠀⠀⢸⡟⠀⠀⠘⠃⠀⠀⢠⣿⣿⣿⣿⣿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣾⣿⣦⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡆⠉⠻⢷⣄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⢋⣽⢿⣻⣿⠟⠛⣿⠿⢿⣄⣄⠀⠈⣷⡄⠀⠀⠀⠀⢹⣷⣀⠀⠀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⢯⣿⣿⣿⢿⣿⡉⠉⠁⠀⢻⣷⢫⠶⣧⡀⠈⢻⡀⠀⠀⠀⠀⠘⣿⣶⢾⣯⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢐⣮⡙⣏⣧⣦⣼⣧⡀⠀⠀⢸⡿⠃⠀⣿⣿⡀⠈⣀⣀⣄⡀⠀⠀⢹⣿⣿⣿⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣾⣿⣿⣿⣿⡿⣧⡀⣠⣿⡀⠀⠀⣸⠟⠀⠀⢸⣿⡿⠁⢠⠀⠀⠙⠿⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣴⣿⣿⣿⣿⣄⠹⡿⣿⢿⣷⠿⣷⣿⠜⠁⠀⠀⢀⣰⠇⠀⠈⡿⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠃⠀⠀⠙⣿⢱⣿⣿⣿⣷⣿⣤⡾⢛⣷⢿⡿⠀⣰⡆⠀⣿⡏⠀⠀⣼⠅⠀⣸⠅
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢹⣿⢋⣈⡙⣿⣿⣍⣿⣯⣵⣿⣧⣼⠏⠀⣠⣿⣷⣤⣶⠟⠀⢰⣿⣴⡀⢘⠂⠀⠁
⠀⠀⠀⠀⠀⢀⣀⠀⢠⣤⣀⠀⠀⡉⠈⢻⠿⠷⣟⡻⣟⠋⠙⣿⣿⡏⣵⣾⣿⣿⠉⠁⠀⠀⠀⠀⣸⣿⣿⣿⡋
⠀⠀⠀⠀⡖⢀⣭⡆⢈⡛⢝⠀⠀⠀⠀⠉⠙⠻⣮⡟⠿⢿⡛⠉⣩⡶⡟⠉⠿⢿⡄⠀⢀⠀⢀⠴⠛⢿⣿⣿⠛⠓
⠀⠀⠀⠘⢇⠘⠾⠛⢀⠃⠀⠐⠄⠀⠀⠈⠛⠀⢸⣿⠷⠢⠷⠾⠿⠒⠀⠀⠀⠸⡦⢤⣴⡟⠁⠀⠀⢸⣿⣿⡇⢰⠀⢀⡠⠀⢀
⠀⠀⠀⠐⠚⠃⢰⣴⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⠀⠀⠀⣍⠛⣦⡸⠀⣉⠳⣔⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡟⠀⠀⠀⠀⢠⣾⣿⣤⣿⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⠀⠁⠀⢸⣁⣷⠔⠀⢈⡤⣼⡙⡿⠿
⠀⠀⠀⠀⠀⠀⠀⡀⠙⢻⠏⠀⠀⡀⠄⠰⢿⣿⡀⠉⠉⢻⣿⣶⡀⠀⠀⠀⠀⢠⣾⣻⣾⡉⠀⠀⠀⠀⠞⠋⠛⠳⠀⠲⠄⠀⠁⠁
⠀⠀⠀⠀⠀⠊⠠⠍⣈⣧⠀⠀⣄⠀⢀⡠⢀⠉⠁⠀⠀⣀⠀⠉⣿⠀⠀⠀⠀⡺⠛⠃⠛⠁⠀⠀⠀⠀⠀⡇⠈⡻⠁⠠⠄⢠⣄⢛⣿
⠀⠀⠀⠀⠐⢀⡀⠀⠿⠟⠀⢰⡷⡀⠀⣤⣷⡀⠀⠀⡜⠗⠀⣿⣿⣶⡜⣣⣠⡗⣶⣴⡟⠀⠀⠀⠀⣤⣶⣿⡋⠑⠄⠠⡦⠈⣻⠛⠛⢠⣤
⠀⠀⠀⠀⣾⡯⢴⣿⠶⠂⠀⠀⠛⢿⣿⠝⣧⣈⣿⣶⡷⠛⡤⢞⡹⠑⠄⢹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⣼⠦⠀⠀⠇⠠⢠⠈⠉
⠀⠀⠀⠠⠿⣷⠿⠿⠄⡀⠀⠀⠀⠀⡄⠀⠉⣿⠏⣯⣡⣿⡀⠌⢐⢀⣄⣼⡏⢀⡀⠘⣿⡆⠐⣦⡀⠀⠘⣾⣯⣀⣈⠳⠶⠂⠀⢠⡴
⠀⠀⠀⢠⣴⣿⣿⣠⠎⣰⠀⣴⣷⣬⣁⢸⠏⡟⠠⢃⣽⣿⣧⣴⣾⣿⣿⣿⣷⣿⣿⣦⡉⠓⠸⠉⠿⠶⠿⠿⢿⣿⣷⣄⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠉⠉⠁⠘⠃⠘⠿⠏⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡶⠿⠿⠿⠿⠿⠛⡿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢠⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⠃⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢰⡇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣸⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡀⠀⢀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⠟⠛⠛⠛⠛⢿⠉⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⡇⠀⢀⡏⠀⠀⠀⠀⠀⢸⡄⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⣷⡶⠾⠃⠀⠀⠀⠀⠀⢸⣇⠀⢸⣷⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛⢿⡟⢻⣇
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣸⣿
⠀⠀⠀⠀⠀⢸⣿⣶⣤⣤⣤⣤⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⣿⠉⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣶⣶⣶⠶⢶⣿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣕⣯⣭⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠹⡀
⠀⠀⠀⢾⠓⠦⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢷⠀⠀⡠⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢆⠀⠈⠳⡀⠀⢀⡎⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡼⠀⡜⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢳⠀⠀⢀⡴⠒⠉⣹⠃
⠀⠀⠀⠀⠈⠳⣄⡀⢳⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⢹⣸⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⡰⠋⠀⢀⡴⠁
⠀⠀⢠⡤⠖⠒⠲⠭⢟⣦⣿⠀⣸⠁⡠⢦⠀⠀⠀⠀⠀⢇⠀⠑⢆⢸⡇⣠⠋⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢳⠀⢸⣰⠧⠴⠚⠁
⠀⠀⠀⠉⠓⠦⠤⠤⠤⠬⢿⡰⠃⡼⠁⢸⠀⠀⠀⠀⠀⠈⢦⡀⠈⢿⡛⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⢱⡀⠘⣆⣾⠓⠚⠉⠉⠙⠒⣢⠄
⠀⠀⠀⠀⠀⢞⡉⠉⠙⠒⢬⣇⢸⠁⢀⡞⠀⠀⠀⠀⠀⠀⣀⡈⠓⠺⡇⣠⠖⢻⡆⠀⠀⠀⠀⢸⡀⠀⣇⢀⠞⣀⣉⣓⣒⡒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠶⠺⣟⡠⠊⠀⠀⠀⠀⠀⠀⠀⡇⠙⢆⠀⡷⠁⠀⡼⠀⠀⠀⠀⠀⠀⢣⠀⢸⣾⣉⣀⣀⣀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⣦⡇⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢱⡏⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢃⣤⡀
⠀⠀⠀⠀⠀⢸⢰⠞⠁⠁⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠈⣣⣼⡉⣠⠄⠄⠀⣀⠀⠠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⢸⡤
⠀⠀⠀⠘⠦⠀⠿⠂⠘⠃⠀⠀⠀⢆⠰⠀⠀⢀⢰⡆⠀⠀⣩⣷⠀⠀⠀⠀⣤⡀⣄⢃⣨⡶⠗⠀⠉⠁⠀⢀⠈⠳⠄⢀⠀⣀⠀⠀⠠⢀⠀⠘⠟⠁
⠀⠀⠄⡀⠠⡿⠤⠤⠔⠂⠀⢶⠄⠈⢶⡀⠐⠁⡘⠀⠀⠀⠉⢹⠀⠀⠀⠀⠈⠛⣤⣏⡏⠒⣧⠔⠀⠀⠀⠀⠁⠤⢮⢠⣤⡄⠀⠈⠦⠐⢂⡴⠆
⣀⠀⠑⠼⣶⠆⠀⣀⡰⠀⠀⠀⠀⡀⠘⣧⡔⠀⠀⠀⠀⠀⠘⠝⡇⠴⠀⠀⠀⠀⠀⢸⣽⠻⠃⣤⠀⠀⠀⠙⢦⡀⠈⣥⡅⠀⠀⠐⠶⠂⠾⠆⠀⢀⡀
⠀⠀⢠⣤⠅⠀⢀⡴⠀⠀⠀⠀⠠⡈⣤⡼⠀⠐⠒⢰⠇⠀⢀⢠⣧⠤⡄⠀⠀⢰⡟⠂⢸⠀⣀⡰⠆⠀⠀⠀⠀⠐⠄⠘⡁⠀⠀⡀⢠⡀⢀⠀⠀⠘⠊
⠀⠀⢰⠉⢁⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⣸⣀⣁⠠⠂⠀⠀⠘⠈⡁⠀⠀⠀⠀⠀⠘⠟⣛⣯⡌⠁⠀⠀⡶⠀⠀⠀⠈⣿⠀⠀⠀⠙⠛⣁⢨⠦⡤⢀⠬
⠀⠀⠀⠀⠻⠀⣀⠀⠀⠀⠁⠀⢢⠀⠀⠉⠀⠀⠤⢺⠃⠀⠀⠻⠟⠀⠃⠀⢀⠀⠀⣀⠈⢃⠀⡠⢪⡞⠁⠀⠀⠀⠀⠘⠀⠀⠠⣠⠀⠻⠂⣤⠀⠾⠆
⠀⠀⠃⣀⠀⠀⠀⠑⢄⠀⠈⣦⠀⠁⢀⡄⣃⠠⢀⠂⠀⠀⠸⠽⣷⡰⠀⠀⠈⠙⠦⠬⠽⢶⣔⡤⠊⠀⠀⢠⠎⡆⠀⠰⠀⠀⢠⠼⠦⠀⠀⠉⣀⡀
⠀⠀⠀⡌⠀⠂⠀⠀⠀⢢⠀⠈⠳⣇⣸⠁⠉⢀⠁⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠁⢃⡅⣀⠀⠀⠀⠈⠚⠁⡤⣄⢠⠉⠋
⠀⠀⠀⠆⠀⠩⡀⠀⠀⠀⡆⠀⠀⠈⠏⠁⠀⠁⠀⠀⠀⠀⠑⠊⠋⠀⠀⠀⠀⡤⠄⠀⠀⠘⠀⠀⠈⢇⠀⡆⢸⠃⡋⢀⠀⠀⠀⠐⣀⣿⠁⠀⡤⢌⡆
⠀⠀⠀⠘⡀⠀⢧⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢐⠀⠀⠐⠀⡀⠀⠀⢰⠀⠀⠀⡀⠀⠲⣆⢠⠀⠉⠂⠀⠀⠀⠠⠈⠀⢹⠁⡤⡑
⠀⠀⠀⠀⠀⠦⠘⠦⠀⢀⠃⠀⠀⠀⡆⠀⠀⠀⢈⣋⠀⠀⠀⠀⠀⠈⠄⢁⢰⠀⠀⠀⠀⠈⠀⠀⠈⠙⠁⠀⡹⠊⢀⠀⠁⢠⠞⡇⠀⠀⠀⠌⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠁⠀⢀⠀⠀⠐⠀⢀⡀⠉⠉⠰⢄⠀⠰⡄⣄⠈⢠⡌⠀⢸⠇⠀⠠⠀⠀⠀⠑⢵⣀⢻⠀⢂⠀⠠⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢑⠀⠀⠀⠈⠳⠀⠀⠑⢬⡃⠀⠀⠫⡁⡀⢣⡀⠂⠃⠀⠀⠀⠀⠰⣄⠀⠙⢢⡦⠂⠀⡡⠀⢠⠊⠇
⠀⠀⠀⠀⠀⡀⠰⣆⠀⢀⠀⠀⠘⢆⣴⡄⠀⠳⠇⠀⠀⠀⠀⠀⢀⡀⠀⠳⣘⢁⣅⡀⠐⡦⠀⠀⠰⡈⢆⢂⠀⠡⡀⣸⠃⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠐⡀⢈⣆⠈⠀⠀⠰⠻⢀⡀⢠⠶⢀⠀⠀⠀⠀⡀⠀⠆⠐⠦⢜⡆⣑⣀⠄⠀⠀⠀⠀⠈⠒⠶⣄⠀⠡⠀⠀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠋⠀⠈⢆⠱⣅⠀⠀⡸⠁⠀⠀⠄⠠⠘⡗⠁⠀⠀⠀⠀⢀⠀⠀⢀⡀⠈⠀⠢⣇⠀⠋⢀⡶
⠀⠀⠀⠀⠀⠀⠃⠈⡒⢷⠀⠀⠾⠀⠀⠀⠦⠀⠑⢾⠇⠈⢀⡀⠀⠀⢆⢀⠁⠀⠰⣠⠁⠠⠀⠉⠀⠀⠈⠫⣆⡃⠀⠘⡀⢀⣨⠌
⠀⠀⠀⠀⠀⠀⣤⠀⡀⠹⡇⣀⠆⠀⠀⠀⠈⢌⠄⢸⡆⠀⠘⠁⠀⠀⢀⠑⣤⡔⡐⢡⡎⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠀⡟⠉⠁⠀⣤
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡟⠡⢂⠏⠀⠀⠀⠀⠙⢾⡇⡴⠰⡄⠀⠇⠈⠃⢸⢪⡴⠊⠁⢀⡄⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⡧
⠀⠀⠀⠀⠀⠀⠀⣤⠈⡘⢿⠔⣃⠀⠀⠀⢂⠀⠀⢸⡟⢁⡠⠁⠀⠛⠷⣷⠀⡼⠀⠀⡄⠘⠀⠀⠀⠀⢊⡁⠀⠀⠀⠀⠀⠀⠐⠠⠀⢱⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⡇⠀⠁⠀⠀⠀⠈⠢⡀⢄⣧⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢰⠀⡠⠁⠀⠠⠀⡤⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠘⢢⡀
⠀⠀⠀⠀⠀⠈⠣⡀⠀⣀⡅⢐⠂⠀⠀⠀⠀⠄⢈⡀⡟⠠⠐⠹⠁⠀⠀⢰⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⢈⠁⠀⠀⠐⠃⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠓⠻⠃⠍⣀⠀⠀⠀⠀⠀⠀⠈⢟⠐⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠃⠀⠀⠀⡤⡄⡠⠀⠨⠀⠀⠀⠤⠀⠀⠀⠀⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢇⢰⣿⣠⠍⠀⠀⠠⢀⠤⠀⠀⡏⠀⠀⠀⠴⡄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠐⠼⠧⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⡠⢀⢍⠜⠀⠀⠀⠀⠀⠓⠀⠀⠀⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⢶⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠶⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄

⠀⠀⠀⠀⠀⠀⢠⣾⣷⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⠖
⠀⠀⠀⠀⢀⣥⠼⢻⡿⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡄⠀⠀⠀⠐⢻⣿⠟⠉⠉
⠀⠀⠀⠘⠆⠟⢠⣾⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡀⠀⠀⠄⠀⠀⠀⢹⡫⢿⣿⡇⢀⣴⠏⠀⠀⠁
⠀⠀⠀⠰⡐⡦⠀⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⢃⣾⣿⣷⣼⣿⣄⣠⣄⣀⠠
⠀⠀⠀⠀⢋⣀⣤⣤⠀⡀⠀⠀⠀⠀⠀⢀⠀⠶⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠛⡿⢏⡉⠉⠉⠉⠚⠛⠀⢠
⠀⠀⠀⠀⠆⠈⢳⠉⠶⠃⠀⠀⠀⠄⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⢤⡀⠀⠀⠀⠀⠃⣤⣹⣤⣠⡄⠰⠆⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⢲⡀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⣰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣶⡀⠀⠀⠀⠀⢀⡞⠁⠀⠸⠀⠂⠀⣀⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠁⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠉⣿⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠘⠃⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄⠀⢠⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣦⠀⣰⣶
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⢸⡇⠀⠀⢀⣠⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠆⠈⢡⡶⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠀⠸⣿⣿⣷⡄⡀⠃⠀⠀⠘⢿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠹⢿⣦⡀⠀⠀⠀⠀⣠⡴⠃⠀⠀⣸⡶⠃⠙⠇
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢻⣿⣿⢹⣿⣿⡇⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⠄⠀⠀⠀⠉⠐⢦⡄⡀⢈⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⢠⣼⡿⢹⠀⠐⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠂⠁⢀⠈⢁⡀⢉⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⢿⡇⠀⠀⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢿⣵⠿⠂⠤⠿⠟⠉⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣷⠀⠀⣶⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⠀⠈⠠⠖⠈⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠰⢾⡷⠀⡈⠁⠛
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠄⠘⠀⠀⠀⡄⠀⣾⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠄⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠎⢹⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⡇⠀⢹⠀⢀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠲⠶⠛⣉⠁⢀⡀
⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠘⠀⠼⠄⣸⠆⠈⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣸⠀⠀⠘⠄⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡚⢛⣿⣿⠟
⠀⠀⠀⠀⢠⡯⠙⠁⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⠀⠈⠉⠿⠉⣠⡤
⠀⠀⠀⠀⠼⠖⠂⠀⠀⠀⠀⢠⣠⡄⢸⠀⢸⠀⠀⠀⣷⠈⢳⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⣲⠆⠘⠀⠀⢀⡀⠀⣩⣴
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢾⠀⣿⣧⣸⠀⡆⠀⠀⠀⢩⠀⠈⠀⠀⠀⠀⡟⠀⠀⠀⢘⡇⠀⠀⠀⠀⣶⣶⣤⣄⠀⠀⠀⠀⠀⠈⣿⠿⠆⠀⠀⠀⠀⠙⣾⠟⡁
⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⢠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡿⣿⣷⢂⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢹⣿⣿⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢣⡘⠁⠀⠀⠀⠀⠀⢸⠟⠻⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠇⠀⠀⠀⡀⠸⠇⡀⠀⠀⠀⠀⠀⠀⠛⠖⡉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠠⠄⠷⣤⠀⡀⠀⠰⠀⠀⠀⢸⠀⠀⠁⠀⡄⠀⠀⠀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⣀⢠⣶⣏⠉⠃⠀⠀⠀⠀⠀⢨⡇⢰⠀⠈⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢾⠿⡏⢰⣷⣷⣔⣀⠀⠀⠀⠀⠀⢺⡇⠘⠀⠀⠀⠀⠀⠀⢀⡛⢗⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠛⠾⠟⢻⣿⣯⣀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⣀⠈⢱⣎⣹⣇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⡟⠉⡄⠉⣶⣦⡀⡿⠁⠜⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⣹⡆⠰⢃⠀⠠⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠘⠂⠀⠀⠀⠀⠃⠀⠁⠸⢿⣈⣄⣷⠞⠛⠀⠀⠀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠷⠒⠞⠳⠶⣦⡀
⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣄⣀⣏⢈⣀⠀⠚⠀⠀⠀⠀⣿⠀⠀⠀⣀⢠⣴⣾⣷⠒⢠⣄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠉⠉⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙⣏⠛⠃⣴⠆⠀⠀⠀⡟⠀⠀⠀⢫⣶⣯⣽⡏⠐⢀⡽⠻⡇⣸⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠃⠀⠀⠀⠀⠀⠄⠀⢀⠀⠄⠀⣀⠄⠀⠀⠀⠀⠀⠘⢶⡸⠇⠀⠀⠀⠀⠃⠀⠀⠀⢣⣾⡿⡏⢙⠀⠹⠀⠀⠀⢉⠀⠀⠀⠀⠀⠠⠿⡿⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠃⣴⠃⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⠀⡰
⠀⠀⠀⠀⠀⠀⠉⠀⠐⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠜⠓⠠⠰⠇⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⡀⣀⣀⡀⢀⣀⣀⣀⡀⣀⠀⢀⡀⠀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⣀⠀⢀⣀⢀⣀⢀⣀⣀⣀⣀⡀⢀⣀⠀⣀
⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣜⣋⣻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠠⠀⢀⡀⠀⡀
⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠠⠋⠀⠀⢠⡀⠀⠉⠀⠀⠀⠀⢀⡄⠀⠀⠉⠀⠊⠀⠀⠀⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⣗⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁
⠀⠠⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠘⠻⡉⠀⣸
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⡄⠀⠄⠀⠀⠀⠀⠀⠁⠂⠀⠀⢶⠃⠀⡇⠀⢀⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠐⢀⢐⠀⠀⠀⣴⡦⠀⠀⠸⠂⠀⠇⠀⠈⠀⠀⠀⢈⣁⠄⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡸⢬⠂⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠾⣿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⢀⡀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣿⡇⣽⣿⣆⣿⡇⢸⣧⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡟⠓
⠀⠀⠀⠀⠀⠀⣿⡇⣿⡏⠻⣿⡇⢸⡟⢻⣦⡀⣤⡄
⠀⠀⠀⠀⠀⠀⣨⣤⣈⣥⢄⣨⡄⣨⢀⣤⠍⣤⢨⡄
⠀⠀⠀⠀⠀⠀⢿⡼⠛⣿⡀⢽⠷⠿⠻⣴⠷⠿⠻⠇
⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠘⢿⣿⠟
⠀⠀⠀⠀⠀⠈⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⢀⣠⡄
⣶⣶⣿⣿⣿⣶⣦⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⣈⠙⠟⢋⡴⠞⠉
⣿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣆⠀⠀⠀⠀⢀⡴⠃⣀⣴⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⡜⠉⢳⡄⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣦⡀⢀⣤⠟⣡⠞⠉⠀⠈⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⢧⣀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠙⣧⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠉⠉⢀⣈⣤⣤⣤⣄⣀⠀⠀⠘⢧⠀⠀⠀⠀⢀⣤⣾⡿⠻⢷⡝⢷⣶⣶⡶⠟⢃⡔⠀⣠⣤⣄⠀⠀⠈⣿⣿⣿
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢈⣤⣤⣤⣈⠉⠻⢿⣿⣦⡀⠀⠣⣄⣠⡴⢫⡾⠉⠀⠀⠀⠙⠆⡀⠀⠰⠖⣉⣴⣾⣿⣿⣿⣷⣄⠀⢻⣿⣿
⠀⠈⠻⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠹⣿⣿⣦⠠⠈⠅⣴⠟⠀⠀⠀⠀⠀⠀⠀⢏⡛⠚⠛⠛⠻⠿⣿⣿⣿⣿⣿⣧⡜⠉⠉
⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⠀⠘⢧⠀⠘⠻⠿⠷⠖⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠃
⠻⣦⣀⠀⠀⠀⠀⢀⣠⠐⠋⠀⠀⠉⠙⠿⣿⣷⣄⠀⠈⢷⡀⠀⢀⡴⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⡀⢈⡻⢿⣶⣶⡾⠟⠁⠴⠛⠛⠳⣦⡀⠀⠈⠛⢿⣷⣄⠈⢷⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⣠⡴⠋⠀⠠⣄
⣬⣀⠙⠲⠤⠤⠒⠀⠞⢠⡀⠀⣄⠈⠻⣦⡀⠀⠀⠻⣿⣧⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⢉⡔⢫⣶⣦⣌
⢠⠞⣵⠖⠒⠈⠀⠀⠀⠈⢷⡀⠈⠳⣦⡈⠻⢦⡀⠀⠈⣉⠖⣠⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡂⢄⣉⣀⣠⠴⣋⠄⠁⠀⠀⠙
⢋⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠈⠻⢶⣄⣉⠛⠛⠁⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠶⣬⣡⠾⣭⡶⠞⠁
⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⣌⣉⣉⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡐⢦⣀⣀⣀⣠⣴⣿⣅⣀⡀⢠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠉⠉⠉⠉⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⣙⡋⠝⠂⠁⠀⠀⠈⠱⠄
⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠉⠀⢀⣤⣤⣤⣤⣀⡀⠹⠟⠻⠿⣿⣶⣶⣶⣶⣶⣶
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡠⢁⣠⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⢓⠒⢤⡙⠻⣿⣿⣿⣿
⢣⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠠⠤⠤⠤⠤⣀⠀⠉⠛⠿⠿⠿⠟⠋⠁⢠⠶⠓⠈⢻⣿⠟⠛⠉⠉⠉⠀⠀⠀⢰⣿⡉⠳⢬⡲⡈⠻⣿⣿
⣦⢣⡀⠀⠙⠛⠿⠿⠟⠛⠉⠀⢀⣤⡩⠅⠀⠩⢁⡈⠁⠐⠠⢀⣀⠀⣀⣤⠞⢁⣴⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠱⣌⠀⠈⠁
⡀⠑⠝⣦⡀⠀⠀⠀⠀⠀⠀⡰⠚⠙⢿⣶⣶⣶⣤⣌⠀⣤⣤⣈⣉⣉⣉⣤⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⢠⣄⠘⠆⠀⣠
⠛⠓⢀⣀⢭⣓⣦⣤⠴⠖⠋⣀⠀⠀⠀⠀⠀⠀⠈⠉⢷⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣧⡀⠀⠁
⣤⣴⠏⢀⣠⣤⣤⣤⣴⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢀⣀⣄⣀⣀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣷⣄⣡
⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⣿⣿⠀⠀⢸⡿⠻⠟⠋⠁
⠛⠛⠋⠉⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⠀⠀⣿⠁⠀⠀⢠⠾

⠀⠀⢀⠀⢠⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠠⣀⡄
⠀⠀⠸⡆⢸⡆⠀⠀⢠⡇⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈
⠀⠀⠀⢷⠸⡇⠑⠀⢸⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠰⠀⠄
⠀⠀⠀⠘⠀⠇⢀⡇⠈⢸⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣧⢲⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⢠⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⠳⣀⠃
⠀⠀⠀⠀⡰⠀⠀⢠⠀⠸⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠈⡇⠈⠠⡆
⠀⠀⠀⡀⢃⠀⢰⡸⡄⢻⠇⠈⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠲⡿⢀⣀⠄
⠀⠀⠀⠇⡞⢰⠀⠷⣧⠋⡆⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⣳⡀
⠀⠀⠀⢸⠃⠸⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠹⠉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠠⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡀⠀⠀⡿⠘⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣧⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⣤⡰⠦⠀⣙⡛⠀⠀⠀⠀⠋⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠖⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⣦⣃⡀
⠂⡐⠀⠈⠀⠀⠈⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⣿⡛⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢀⠀⡈
⠀⠀⠀⠀⠀⢤⢠⠄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⡞⠅
⠀⠀⠀⠀⠀⠈⢀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠇⢼
⠀⠀⠀⠀⠀⠢⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⣾⣉⣈⣆
⠀⠀⠀⠀⠀⢀⡀⠘⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢿⡾⠟
⠀⠀⠀⠀⠀⠈⠁⠀⢡⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠰⠆⠀⣿⣟
⠀⠀⠀⠀⠀⠀⠐⠢⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢾⣶⣤⢏⣶
⣤⣤⣤⣤⣤⣤⣤⣤⣴⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣬⣯⣤⣿⣬
⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠛⠿⣿⣦⡀⢀⣴⣿⠟⢛⣛⡉⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⢀⣾⣿⡿⠋⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢰⡇⠀⠀⠀⠀⠙⢿⣾⠟⣡⣾⡿⠋⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢸⣿⠟⢀⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⣿⡄⠀⠀⠀⠀⠈⠟⢰⣿⠟⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢸⣿⡟⣹⣿⡇⠘⣡⣴⣿⣿⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡈⠻⣿⣄⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⢸⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣦⣈⠻⢷⣦⣀⠀⢸⡏⠀⠀⠀⠀⢀⣴⣿⣧⣤⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢟⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠉⠛⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣭⣙⢿⣷⣄⠀⣼⣿⠿⠛⠉⣠⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠹⣧⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⡹⣿⣆⢉⣤⣴⣶⣿⣿⣿⣿⡟⠁
⠀⠀⢀⣀⣀⣠⣤⣄⣰⣿⣿⠁⢀⣀⣀⣠⣤⣴⣾⠿⠋⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⡆⠉⣹⣿⣿⣿⡿⣿⣿⡄
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣉⣛⠛⢛⣋⣡⣴⠂⠀⠀⠀⢸⣿⡄⢶⣤⣀⣀⣀⣀⣠⣴⣾⣿⠛⢉⣾⡿⢋⣥⡶⠀⠈⢻⣿
⠀⠀⠀⠈⠻⣿⣷⣦⣄⣉⡛⠿⠿⠛⠛⠛⠟⠛⢿⣿⠀⠀⠀⠀⢸⣿⡇⢸⡏⢻⣿⡿⠛⠛⠛⠛⠿⣷⣾⡿⢠⣿⡟⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣷⣶⣶⣤⡀⠸⣿⡆⠀⠀⠀⢸⣿⢃⣿⡇⢸⣿⡀⣤⠀⠀⠀⠀⠈⠙⡇⢸⡿⠁⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠟⠋⠉⣀⣤⠀⠹⣿⣆⡀⠀⠿⣋⣾⡟⠀⠈⢿⣇⢻⣷⣄⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣾⡿⢶⣶⣶⣤⣀
⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠉⢀⣀⣤⣴⣾⣿⠏⢀⡀⠈⠻⣿⣶⣾⡿⠋⠀⠀⠀⠀⠹⣦⡙⠿⣷⣦⣄⡀⠀⢸⡇⠀⣀⣤⣤⣶⣶⣶⣦⣍⡻⣿⣷⣄
⠀⣠⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡿⠋⣴⡿⠿⣷⣤⡈⠻⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⠷⠆⠈⠉⠛⠛⣿⣿⡟⠋⠉⠉⠉⠉⠉⠉⠉⠓⠘⣿⣿
⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⣼⡟⣱⠂⠀⠉⠻⣆⠀⠀⠀⢀⣀⠀⣴⣾⠟⠁⠀⠀⠀⠀⢀⣼⠏⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⢹⣧⡶⢛⣛⣛⣿⣿⠃⠀⠀⠀⠀⣠⣴⡿⠁⠀⠀⠈⣿⣦⠰⣤⣤⣤⣤⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣽⣇⢻⣷⠀⠀⠀⠘⣡⣾⡿⠟⠋⣿⣿⠀⣠⣤⣶⣿⠿⢋⣴⡆⠀⠀⠀⠘⣿⡆⢻⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠉⠀⠹⣧⠀⢀⣴⠟⠁⠀⠀⠀⢿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣇⠀⠀⠀⠀⢿⣿⢸⣿
⠀⠀⠀⠀⠸⣿⣿⣷⣶⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣿⣃⠀⠀⢀⣠⣴⡾⠋⠁⠀⢠⣄⡉⠙⠛⠿⣿⣦⡀⠀⠀⠼⢃⣿⡏
⠀⠀⠀⠀⠀⠹⣿⣮⡙⠿⣿⣿⣮⡻⠿⣷⣶⠶⠶⠟⠛⢹⡏⠉⠛⠷⣶⣬⡙⢷⣄⠀⠀⠘⣿⣿⣷⣶⣤⣌⡙⣿⣷⣦⣴⣿⡟
⠀⠀⠀⠀⠀⣀⣨⣿⣿⣷⣦⣬⡛⠿⢷⣶⣶⡞⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢿⡆⢿⡆⠀⢠⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢀⣠⣶⣿⣿⣿⣿⠿⠿⠿⠛⠛⠓⠀⢀⣿⠃⠀⠀⠀⣾⡇⣶⣄⠀⠀⠀⠀⠙⢸⣿⠀⣿⣷⠈⣿⣿⠙⠛⠻⠿⠿⠿⠿⠿⠿
⠰⣿⣿⣿⣿⣿⣷⣤⣤⣴⣶⣶⣾⠟⠀⠘⣿⡀⠀⠀⣼⡿⢁⣿⠻⢿⣶⣶⣶⣶⣿⣿⠀⢹⣿⣧⣽⣿
⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⢻⣷⣀⣘⣭⣴⡿⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠁⠀⡠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠙⠀⣰⠉⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⢀⠉⠙⣗⠉⢀⡆⢳⣤⣠⣌⡴⡀⠘⡿⠎⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⡀⢴⢦⣿⡀⢴⡇⠈⣿⣿⣿⢁⣧⠐⣹⡴⠈⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⢢⣿⣼⣏⠈⣻⣿⣷⡀⢘⣿⡟⣿⡯⡶⠉⢀⣾⣿⣦⠔⢐⡊⠀⠈⠣⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠨⣓⣚⣿⣿⣿⣶⣭⡿⣿⣷⢴⠿⢯⣿⣿⢁⣴⣿⣿⣿⣟⠛⠁⠀⠀⠀⢀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⢐⢤⡈⠉⠙⠻⢿⡿⡫⠚⠉⠈⠑⢌⢳⡿⡛⣹⡏⣙⣿⣿⡷⠄⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⡀⠪⠁⡀⣉⣶⣤⣄⣼⠕⠀⠐⠈⠀⢢⠀⣾⣿⣷⣿⣿⣉⣀⣹⣆⠘⣁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢺⡋⢀⣶⡾⢿⣿⣻⣿⣿⣥⠀⠓⡔⡤⠞⢀⣿⣏⠀⠈⠈⠉⠙⠻⠍⠈⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣼⠀⠀⠀⢻⣻⣿⣾⣿⡿⠛⢹⣷⡵⣲⣌⣠⣤⣿⣿⡿⣿⣿⣷⣿⢿⡿⠏
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⣀⠀⡀⠽⢿⣿⡿⠋⣀⣰⣯⣵⣾⣿⡇⠈⢿⣿⣷⠇⠽⣿⣿⣿⡙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠝⠒⣠⡞⠛⢩⢾⡿⣿⣿⣷⠀⢸⡟⠻⣿⣦⡼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠠⡟⠀⣁⣀⣼⣿⣿⣿⣿⣿⣦⣸⡿⣄⣸⣿⣍⠛⠃⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⢒⠀⢸⡇⢆⠈⢹⠋⠼⡻⠻⡟⣿⣿⠏⠁⠀⢤⠔⠙⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⡆⠁⣺⠄⠈⠛⠒⠀⠀⠀⠀⠀⠀⡅⠀⠃⠀⠀⠘⠖⠀⣀⠠⠳⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⣠⠊⠉⠒⠉⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡁⢘⣆⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⢀⣠⡤⣤⡀
⠀⠀⠀⢀⡴⠊⠉⢠⡰⢏⠃⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣘⣁⠙⣉⣏⠀⠀⠀⠀⠀⠀⠀⣀⣽⣷⣾⣿⢶⣤⠁
⠀⠀⠀⢺⢀⡷⠚⠃⠀⡜⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣍⢤⣩⣀⣯⠀⠀⠀⠀⠀⠀⢸⠟⠈⢲⡷⠊⠀⠘⠃
⠀⠀⠀⢸⠻⢥⣤⠤⠊⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⢲⠓⠂⠚⠀⠀⠀⠀⠀⠀⠼⠥⣌⣡⣨⢽⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚

⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⠀⠀⡄⡀⠀⢰⣀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⢀⣠⡴
⠀⠀⢀⢤⠀⡊⠀⢈⡀⡏⣷⠀⠀⠀⠀⠀⠀⢠⡀⠀⡰⠟⢠⠖⠁⠀⠀⢈⠙⣶⠂⣿⡃⢀⣞⣥⠾⠤⠀⠀⠀⠀⢹⣧⠀⢀⢔⡿⠉
⠀⠀⢸⣸⣦⣰⠀⢸⣾⢟⠟⠀⠀⠀⠀⣀⣈⢳⣿⣠⢶⣟⣿⣀⠀⠀⠀⠋⠉⠙⠫⡹⡴⠟⠛⠻⢯⠀⠀⠀⠀⠀⠀⣯⣇⢎⡞
⠀⠀⠈⠳⠥⡟⠀⢰⠏⠁⠀⠀⠀⠀⠀⠈⢎⠳⡽⢡⢻⡟⣥⠴⠀⠀⠀⠀⠀⠀⠀⢧⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⡏⣿⣼⡀
⠀⠀⠀⠀⠀⠱⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣇⣬⣬⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣇⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣆⣸⣿⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⠤⡄
⠀⠀⠠⠶⢤⡄⡾⢁⣤⡆⠠⠀⠀⠀⠀⠀⣴⣸⣿⣷⢟⣾⣶⡁⠀⠀⠀⠀⠀⢀⠮⠭⠥⠬⠭⢷⠀⠀⠀⢀⡴⠅⣤⢤⠒⠶⠻⣄⣄
⠀⠀⠀⠑⠂⠉⣧⠟⠭⠔⠀⠀⠀⠀⠀⠀⣿⣿⣾⡏⣼⣿⣹⣃⠀⠀⠀⠠⣦⠞⠀⠀⠀⢀⠀⢈⢣⣄⠀⢨⠧⡶⠿⢀⡀⢐⠶⠀⠘⢶⡄
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⡟⣾⡛⣿⢗⡿⡏⠁⠀⠀⠘⠓⠚⠙⢦⡜⠉⠑⠊⠀⠀⠀⠀⢱⠃⣠⠋⠉⠙⠋⠙⣦⠀⢣
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠟⠚⠃⠛⠂⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀
⠀⠀⠀⠀⡤⠢⡔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢟⣻⠒⢤⠀⡴⢫⠝⠋⠉⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⣀⣀⣃⢀⣀⡸⠊⠉⢿⠀⠀⠀⠀⠀⠠⡀⠀⡆⢀⡠⠔⠂⠀⠀⠀⠀⣀⠤⡤⡭⣿⣿⣧⡀⣲⢦⡀⠀⠀⠀⢀⠞⠁⠀⠀⠙⡄
⠀⠘⠢⡤⠈⣿⢉⡷⠠⢤⠚⠀⠀⠀⢀⣀⣀⡈⢦⣷⢞⣡⡤⠤⠀⠀⢠⣮⢴⠎⣰⠇⠈⠘⡆⢷⠈⠉⠁⠀⠀⠀⠸⠀⣄⠀⠀⢀⢱
⠀⠀⠘⠤⠚⢈⡉⡧⣸⠞⠀⠀⠀⠀⠉⠀⠀⠉⠻⣷⠋⠁⠀⠀⠀⠀⠈⠀⠈⡼⠀⠀⡇⡆⠙⣾⠀⠀⠀⠀⠀⠀⠘⠚⢻⠒⢲⠛⠋
⠀⠀⠀⠀⠑⠊⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠉⠛⠿⠿⢿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠋⠀⠀⡀⠀⠀⢀⡀⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢿⠀⠀⢈⣍⠁⠀⢉⡍⠀⠀⣿⠻⣏⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⡄⠀⠀⠁⢀⡀⠈⠁⠀⢠⣟⣠⠏⠀⠀⠀⠀⠀⣿⣿⡇⠠⠄⠀⠘⣁⠀⠈⠛⠻⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⣈⣡⡀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠘⠻⣇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⢀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣥⢤⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⡴⢛⡏⠁⠀⢹⡗⠳⣄⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⡙⢶⣄⣈⣋⣀⡴⠛⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⠴⠞⢛⡿⠀⠈⣥⠀⠀⢈⣥⠀⢹⡟⠳⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⡧⣿⠉⠁⢀⣤⠞⠉⢿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⡿⠋⠙⠿⢿⣿⣿⣿⣿⢻⡏⠀⠀⠀⠸⡧⠶⠦⠌⢛⡶⠋⠤⠶⠤⠗⠀⢸⣏⢩⣽⠃⡈⠛⣋⠙⢿⢋⡴⣧⣀⡴⠏⠀⠀⠀⠀⢹⡿
⠀⠀⠀⢹⣿⣿⠋⠀⠖⠂⠀⠀⠖⠌⠙⢿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠃⠀⠂⠀⠐⠀⢸⠟⠀⢠⠟⠁⠄⠀⠀⠀⠀⣎⣧
⠀⠀⠀⠸⣇⢻⡀⠀⠈⠁⣠⠀⠉⠀⠀⣾⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠆⠀⠀⠀⠀⠀⠀⠈⠛⢳⣄⠰⢶⠆⣠⡏⠀⣰⠋⠄⠁⠄⣽⠁⠀⠀⣿⣿
⠀⠀⠀⠀⠈⠙⢷⣄⠀⠻⣉⡽⠀⢀⣼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠻⠿⢿⣿⠀⢠⠏⡀⣀⡁⢠⡇⠀⠀⠀⡿⣼
⠀⠀⠀⠀⠀⠀⠀⣉⣿⠒⠀⠒⢺⣻⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢾⢀⡀⠀⠀⡤⠤⠤⢴⢀⡏⠀⣄⠀⠀⠻⣿⢀⡟⣾⠙⠉⢹⣼⠃⠀⠀⢀⡏⣿
⠀⠀⢀⡴⠶⠚⠋⠉⢧⣄⣀⣀⣬⡍⠛⠛⠲⢾⡄⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⠀⠀⢧⡀⢀⡾⠛⢧⡘⢧⠀⢀⣠⣿⣸⠟⠁⣠⡴⠛⣽⠀⠀⠀⢠⡇⡿
⠀⢠⣾⠑⠀⠀⠀⠀⠀⠈⠉⠉⠀⡀⠂⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠙⣇⠈⢿⡛⠈⠻⣏⠀⠈⠁⣠⠞⢃⣠⡞⡉⠀⠀⠀⢸⢳⡇
⢀⡾⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣿⢠⠄⠀⠀⠀⠀⠀⢹⣄⡀⢙⣳⠶⢞⣛⣶⠿⠛⠛⠋⡀⠀⡀⠀⠀⠀⡾⢸⠁
⣼⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⠿⣥⢼⡉⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⠞⠁⣾
⠙⢳⡶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣾⠛⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠀⠈⣧⠀⠀⠀⠀⣀⣠⣤⠶⠛⠋⠀⠀⢠⡏
⠀⣼⠀⠀⡏⠠⠀⠀⠀⠀⠀⠀⠄⠀⠄⠁⢸⡇⠀⢻⡄⠀⠀⠀⠀⠀⣿⠐⠂⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⠋⣿⠦⢶⢲⣋⣩⣤⣼⠷⠀⠀⠀⠀⠈⡇
⠀⡏⠀⢠⡏⠠⠀⠀⠀⠀⠀⠀⠄⠁⠄⠁⠨⡇⠀⢸⡇⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣿⠠⠉⠉⠄⠁⠄⠁⠄⠀⠀⠀⢿
⠸⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠄⠁⠄⠁⠀⣇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠿⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠸⠆

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⢖⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢿⠸⣠⠇⠀⠀⠸⣆⠈⣩⡆⠀⠀⠀⠀⢀⠄⠀⠀⠀⣿⠀⢛⡛⠁⠀⠀⠀⠀⠀⠀⢀⡤⠘⢁⡀
⠀⠀⢈⠐⢋⡶⠀⠀⠀⠈⢈⡵⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡈⠚⡏⠀⠀⠀⠀⡀⠀⠀⠀⠈⢿⠴⠛⠁
⠀⠀⠸⣦⡈⢠⢴⡆⠛⣩⠃⣞⣴⠃⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⠇⠀⠀⠀⠀⠁⠀⠀⠸⣷⡄⣰⡦
⠀⠀⠰⣄⠙⣠⠶⠀⢤⣘⠧⢁⣴⠇⠀⠀⠐⠀⠀⠀⠀⣄⡻⠄⣀⡶⠀⠀⠁⠀⠀⠀⠀⣤⣽⣡⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠚⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡶⢀⣤⣄⠀⠀⠀⠀⠀⠀⡀⠀⡀⢠⠆⠀⠀⠀⡈⠗⠾⠇
⠀⠀⠰⡆⢚⡋⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⠰⠈⠛⠋⠀⠀⠀⠀⠀⠊⠸⣀⠁⢋⣠⠄⠀⠀⣻⢇⢴⣦
⠀⠀⢀⠐⢋⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⣠⡄⠀⠀⠀⠀⠀⢀⠀⠈⠁⠋⢡⠆⠀⢀⡹⠀⢰⠇
⠀⠀⠘⠇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⡾⠍⡉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣗⡏⢠⡶⠘⣛⠁⢉⡙⠁
⠀⠀⠰⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣈⣹⣏⣤⠀⠙⠳⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠒⠀⠀⣠⣴⣾⠿⠿⠿⣶⡄⠀⠐⠀⠀⠀⣤⠀⠀⣠⡶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠈⣿⠠⠶⠶⠶⢶⡿⠾⠛⢫⣶⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⣿⡇⠀⠀⠀⢀⡀⢠⡏⢠⣾⠀⢀⣿⠃⠀⠀⣀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠻⣿⣄⠀⠀⠸⠷⠏⠀⣤⠁⠀⣼⡟⠀⠀⣼⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢟⣡⢀⣠⣤⣀⠈⠻⣷⣄⠀⠀⠀⣸⡏⠀⢰⣿⠃⠀⣼⣿⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⢠⡟⣵⡟⠉⠀⣹⠀⣀⡈⢻⣧⠀⢰⡿⠁⡰⢹⡟⠀⣰⣿⡇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠰⡟⠀⠀⣠⠏⣾⠋⠀⠀⣿⠀⢸⣇⡴⠁⠸⣧⠞⠁⢿⣇⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠙⠷⣤⡤⠞⠁⠀⠙⢧⣤⠾⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠆⠀⣀⣤⣤⣀⠀⠀⠀⢀⣤⡀⢀⠀⣦⣰⣦⣿⣠⡷⢀⡆⠀⠀⠉⢀⣾⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢶⡀⢠⣾⠟⠉⠉⠙⣷⡀⠀⢈⡛⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⣠⡴⠋⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⣇⠀⠀⠀⠀⢹⡇⢀⣾⡇⠀⠛⢻⣿⣿⣿⣿⠿⠏⠀⠙⠛⠁⠀⢠⣿⡇⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠻⣦⣀⠀⢀⣸⡗⣹⣿⠀⠀⢠⠀⣿⣿⣿⣿⠀⠀⣤⡬⠊⠻⠿⢿⣿⣷⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⡇⠀⠀⠉⠉⠁⣿⠀⣿⡇⠀⢠⠃⠀⣿⣿⣿⡟⠀⢰⣧⠀⠀⠀⠀⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⠇⠀⢿⣇⡴⠁⠀⠀⣿⣿⣿⡇⠀⠈⢿⣄⣀⣀⣴⡿⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢿⡇⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⣀⠀⠉⠉⠉⠀⠀⢠⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢿⣦⡴⠋⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡶⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⢸⣿⡿⠛⣿⡀⢻⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠘⣧⠀⠀⠸⠟⠁⢀⣻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⣿⠀⢠⡄⠀⣠⡘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⠀⠀⢸⣿⣿⣿⠇⢀⡛⣤⣽⣷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⣿⣿⣿⠆⣿⠛⠉⠉⠿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡿⠀⢹⣿⣿⡄⠀⣠⠞⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⢿⣿⢳⠛⣬⣹⣷⣾⠛⣿⣶⣿⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡾⢷⣾⣟⣿⠉⣀⣤⠘⠋⠙⠁⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡟⠳⣾⣭⡉⣿⠠⠉⠁⠀⢀⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠹⣿⣿⠿⠦⠶⠌⠃⣈⣡⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⣠⣿⣁⣤⣠⠀⣴⠂⣠⣿⣿⣿⣿⣿⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠁⠉⠉⠛⠶⠿⠿⠿⠿⠛⠋⠉⠁
⠀⢲⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⢰⡆⢀⣼⠃
⠀⣄⠀⠀⢾⣷⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⢸⣧⣸⡿⠃⠀⠀⠀⢠⠄
⠀⠈⣿⡇⢾⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠈⣻⡏⣀⣤⠞⢁⣴⡟
⠀⠀⠛⠃⣀⠻⠂⠀⠘⠃⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠟⠉⢀⡤⣉⠎⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⢄⠈⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣆⠙⢿⣿⡿⢦⣐⣴⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠲⠾⢧⡼⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠈⣿⡆⠈⠿⣿⡿⠟⠋⠉⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠺⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣿⣿⣧⡸⣧⠀⣿⠀⠀⢀⣄⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣸⣾⠃⣰⡆⠛⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠈⠁⠀⠀⠀⣄⡀⠀⢸⣿⣿⠛⢿⣿⣟⠸⠿⣄⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣿⣍⠻⣷⣌⣿⡏⠀⠈⠹⠉⢀⣶⢟⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣅⣴⠀⠀⢸⡆⠹⣿⣿⠀⠶⠀⠀⣠⣟⣵⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣀⠀⣤⡄⢹⣿⡀⢸⡆⠀⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠸⣿⡎⠉⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⢋⠉⠉⠉⠀⠘⢿⣮⣿⣧⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⣶⣤⣬⡀⠀⠁⢨⣿⣦⣿⠇⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢀⡎⣀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠙⢿⣿⣿⣦⣄⠀⠙⣿⠇⢀⡄⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣾⠀⣿⠛⢿⣿⣿⠸⠀⣿⢠⡌⢡⣾⠋⠀⠀⠀⠀⠀⢠⣄⠀⠀⣀⠀⠀⢻⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠆⠁⠀⠀⠻⠇⠸⡆⠈⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠛⣷⣆⠁⠀⢰⡄⠀⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⠀⢀⡆⠀⠀⣴⡆⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠙⣄⠀⣧⣼⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣸⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣷⣿⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢻⡏⠀⠀⠀⠘⣿⣧⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⢸⠿⣿⣤⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⠀⢰⡄⠀⣼⡆⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⣿⢧⣈⣴⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠙⢷⣎⣡⠀⣿⡇⠸⣿⠂⠀⠀⠀⣠⡄⠀⠘⠋⠀⠀⣘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠰⣌⡹⠁⠈⠁⢠⣯⠀⠀⠀⠈⠉⡀⠔⢀⣤⠀⢀⠋⢀⣤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣍⣳⣷⠀⠀⢀⡏⠀⠀⠀⠀⢀⣤⣤⠸⣿⣆⣨⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡋⠻⣿⣿⣿⣿⡇⠀⡇⠀⡀⠀⣸⡿⢿⣿⠀⠹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠈⠙⢿⣿⡁⠐⡇⠘⢃⡼⠋⣀⣰⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠙⢿⣿⡇⠰⠟⠁⢰⣿⠛⠛⠆⢀⣠⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠆⠀⢹⠁⠀⣼⡇⢰⣿⡇⠰⢼⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⣇⢰⣿⡇⠸⣿⡿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⡀⠀⠀⣿⠀⢹⡇⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⠀⣿⠀⠈⠁⠀⣱⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢿⣿⣟⠛⢰⣿⠀⢠⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢻⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣹⣿⡄⢹⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣟⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⡠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡼⠈⢣⣸⠁⢸⡄⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢤⣘⡌⠳⡇⠀⡎⡇⠀⠀⡷⠃⡼⢀⡤⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⢳⡀⠘⣴⡁⢰⠀⢸⠃⢠⠟⠉⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⢦⡀⠙⣄⠘⣇⢸⣀⡎⡰⠃⠀⣠⡮⠤⠴⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡶⡎⠙⠢⣄⣀⠙⠢⣌⣶⣿⣿⣿⣿⣷⡴⠊⠁⣀⣤⣾⢥⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⡀⡞⠀⢷⠚⠉⢉⣭⢿⠶⣾⣿⣿⣿⣿⣿⣿⣿⡂⠉⠁⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⢶⠲⢤⡤⣄⣇⠀⢿⠃⠀⢀⣤⡞⠋⢀⡾⢴⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡉⠛⠛⠲⠤⣀
⠀⠀⢠⡤⠤⣌⣧⡀⠙⢦⣻⡄⠘⡆⠀⣼⠏⢀⡠⠞⠉⢁⣠⡾⢿⣿⣿⣿⡟⢧⡈⠑⢯⡙⠳⢞⡋⠉
⠀⠀⠀⠳⢄⡀⠈⠙⠦⡀⠙⣿⣶⣷⣶⣿⣴⠋⢀⣠⣴⡫⠵⠷⢾⣼⡇⢹⡟⢆⠈⠢⣄⠈⢢⡤⠽⠂
⠀⠀⠀⠀⠀⠙⢲⣤⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⢀⣠⣴⢋⡟⡇⠀⡿⣌⠳⣄⠈⠳⣤⣹⡄
⠀⠀⣀⡤⠖⠛⠛⠉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣉⠉⠉⠉⢉⣙⣷⠀⡇⠘⢆⠈⢳⠦⢼⣆⠁
⠀⠈⠙⠒⢲⡶⠖⠋⢁⡤⠚⣻⣿⣿⣿⣿⢟⠓⢄⡙⠪⣽⢿⢉⢯⢹⠻⣄⡇⠀⠀⠳⣼
⠀⠀⢀⣴⣋⣠⣤⠞⠁⢀⠜⠁⡌⠀⡇⠘⡌⢦⡀⠙⣤⣈⠙⢿⡚⠛⠀⠛
⠀⠀⠀⠀⠀⣴⢃⣠⠴⡏⠀⣼⠀⠀⡇⠀⢹⡄⠙⢦⡘⡏⢻⡉⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⣇⠜⣿⠀⢠⣇⠀⢸⠙⢦⡀⠙⡟⠶⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠏⢹⡄⡾⠀⠀⠙⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⢀⡽⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⢹⡤⡶⠿⡗⣦⢸⢰⢓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢤⡀⠀⠀⠀⠀⠀⠀⠓⠙⠚⠃⠘⢸⠈⠉
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⣰⣿⣷⣀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢄⡀⡀⠀⠀⠀⠀⠀⠀⣠⢀⣿⣿⣯⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠂⠀⠀⠀⣦⣾⣿⣿⣿⣿⣿⣿⣿⣏⡔⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠛⠻⠿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣤⡗⣠⡴⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠸⡏⠠⣀⢐⡀⠘⣿⠄⠀⠀⠀⢸⡟⡾⣛⣿⠿⣶⣏⣽⣮
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡞⠁⠌⠁⠀⠀⠀⠀⠘⠠⠀⠀⠉⠰⠋⠀⠠⢆⠀⠀⠉⠀⠉⣻⡇⣼⢾⣾⠅
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⢡⡠⣆⣴⢂⡖⢄⠀⠀⠀⠘⠆⠀⠋⠀⠀⠐⢠⣬⢸⣷⡄⠀⣼⢏⣾⠳⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡘⣿⣿⣟⢻⣙⣿⣻⢶⡆⠀⠈⠂⠀⠀⠀⠣⡀⢄⢰⡨⢟⣻⣿⣤⢫⣾⣿⢲⡏
⠀⠀⠀⠀⠀⠀⠰⣿⡀⣤⣿⣿⡎⣿⣿⣿⢰⡇⠀⠀⠀⠀⠀⠐⠀⠘⠀⠁⠹⢿⣿⣿⡀⣴⣿⣿⠘⠃
⠀⠀⠀⠀⠀⠀⢲⡿⢻⡝⠋⣾⣦⣡⣨⣯⢾⣇⢀⠀⠐⠂⠀⠀⢀⣠⠀⠀⠀⢀⣈⡉⠙⢟⣋⠑
⠀⠀⠀⠀⠀⠀⡈⣼⣿⣧⠿⣿⣷⠛⣿⣿⢽⣯⣤⣴⡦⠀⠈⣠⣿⣿⣧⣤⣶⣿⣿⣿⣤⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⣾⡋⢉⣿⣷⣸⣿⣿⢼⣿⣿⠈⣇⣹⣿⣵⣾⣿⠿⠟⡋⠉⠀⠀⠙⠛⠛⠹⠁⠘⠻⠋
⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⠿⢝⠋⠋⠻⠟⠀⠈⠀⠉⠈⢃⠠
⠀⠀⠀⠀⠀⠙⠏⠁⠉⠂⠀⠀⢀⢴⣖⢶⣄⠀⠀⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⣧⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⣾⣿⢯⠟⠃⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣄⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠓⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡿⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠘⠿⠷⠀⠀⠀⠀⠀⠀⣠⡤⣾⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⢦⠀⠰⢄⣀⡀⠀⠀⠂⠸⡆⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠇⠀⢿⡑⡈⠁⢒⢨⣿⠃⠀⠘⠫⣼⣭⣭⡻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣶⡾⠇⠀⠀⠁⠙⢻⠋⠋⠀⠀⠀⢠⣶⣯⣿⣿⡄
⠀⠀⠀⠀⠀⢺⠤⢄⡀⠈⠈⠀⠂⠀⠀⠀⠀⢰⡆⠀⢰⣧⡀⠀⠉⠙⡏⠛⠁⠀⡤⠓⠀⠀⠀⠀⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠐⠀⣜⡳⣶⣤⢀⠀⠀⠀⠀⠀⠀⡇⢀⣺⣾⣧⡄⠀⠠⠀⠀⢤⠒⠻⣀⣀⣻⠿⢟⠟⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢥⠈⠙⠿⣧⠀⣄⠀⠀⠆⢳⠀⠈⠇⣷⣆⠀⣈⠰⡖⠻⢇⣴⠌⣋⡵⣂⠱⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠐⡮⣷⣝⠿⠁⠀⢻⣦⡄⠈⠿⣗⣠⡟⠉⣡⣾⣿⣿⠯⠅⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠔⠀⠛⠀⠿⢿⣦⢻⡧⠀⢚⣿⣿⣴⠿⠿⡙⣭⣿⡶⣯⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⡀⠀⠠⢂⣀⣶⣮⣝⣿⡂⢨⡿⢟⣾⣭⡎⠄⠩⠜⠙⠀⠙⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣈⣍⠉⣲⣿⣿⡏⠃⠀⣿⣿⣿⣿⣿⠾⠶⠶⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠙⠛⠓⠛⠛⠋⠙⠛⠃⠈⠁

⢠⣤⡀⠀⣠⣤⣄⡀⠀⢀⣄⠀⠀⢠⠀⠀⠐⢊⣍⠶⠀⠀⡂⠀⠀⠀⢀⣀⠀⠀⢠⣦⡀⠀⣠⣤⣤⡀⠀⢀⣀⠀⠀⢠⠀⠀⠰⢎⣍⠶⠀⠀⡆⡀⠀⠀⢀⣀
⠈⠋⢀⡞⠁⢸⠀⠙⡆⠘⠛⠁⠀⠀⣶⣶⣶⣦⣤⣤⡄⠀⠘⠫⠀⣤⣿⡟⠀⠀⠈⠋⠀⡞⠁⢸⠀⠙⡆⠘⠛⠁⠀⠀⣶⣶⣶⣦⣤⣤⡄⠂⠜⠫⢀⣤⣿⡏
⣀⠀⠘⢧⡔⢻⠳⣤⠇⠀⠀⠀⠀⢸⣿⣯⣿⣿⣽⣿⠃⠀⣀⠀⠀⢹⣿⢿⡷⠆⣀⠀⠈⢧⡔⢻⠓⣤⠇⠠⠀⠀⡃⢰⣿⣯⣿⣿⣽⣿⠇⠀⣀⠀⠀⢩⣿⢿⡷
⣿⡗⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠈⣛⠛⠛⠛⠛⠛⠀⢠⣿⣿⣇⠀⢀⠀⠀⢲⣿⡗⠀⠈⠙⠛⠛⠁⠀⠀⠈⠀⠀⠈⣛⠛⠛⠛⠛⠛⠀⣠⣿⣿⣇⠀⢀⡀
⠀⢁⡴⠖⠢⢄⠀⢀⣶⣷⣄⣠⡀⠀⠉⢀⡶⣟⠛⠳⣄⠀⠘⠋⠁⠀⡾⣿⠃⠈⠁⢁⡴⠒⠦⣄⠀⢀⣶⣷⣄⣠⡀⠀⠙⢠⡴⣟⠛⠳⣄⠀⠛⠋⠉⠀⡾⣿⠃
⠀⡏⣴⠛⢷⡈⣇⠈⢿⣿⣿⣿⠇⠀⠀⣾⠀⢸⣶⠤⣽⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡏⣴⠛⢷⡈⡇⠀⢿⣿⣿⣿⠇⠀⠀⣿⠀⢹⣶⠤⣿⠀⠀⠀⠀⠀⠀⡀
⠀⢣⡙⠄⠚⣠⠏⠀⠈⠻⠛⠁⠀⠻⠃⠘⠷⣿⣼⡶⠋⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⢣⡙⠤⠚⣠⠇⠀⠈⠻⠛⠁⠀⠿⠃⠘⠷⣿⣬⡷⠋⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠉⠛⠛⠁⠀⠙⣀⣤⣴⠶⢿⡀⠀⠀⠀⠀⠀⣰⣧⣤⡀⠀⡶⠆⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠙⣀⣠⣴⠶⢿⡀⠀⠀⠀⠀⠀⣰⣷⣤⡀⠀⡶⠆
⠀⠀⠀⠀⠀⣶⠞⣛⣩⣥⣶⣲⠈⢷⠀⠀⠀⢀⠘⠻⢿⣯⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⢛⣭⣥⣶⣲⠀⢧⠀⠀⠀⢀⠘⠛⣿⣏⠀⠀⢠⣤⡀
⠀⠀⠀⠀⣠⠹⡄⠳⢟⣛⣭⣵⣾⠿⠃⣿⣷⣿⡇⠀⣀⢀⡀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⣠⢹⡄⠳⢞⣛⣭⣴⣶⠿⠂⣿⣷⣿⡇⠀⣀⢀⡀⠀⠻⠿⠟
⠀⠀⡠⠶⣄⠀⢳⡾⠟⠛⠋⠁⠀⢠⣷⠎⠙⠛⠀⢠⣽⣿⣷⣟⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⣄⠀⢿⡾⠿⠛⠋⠁⠀⢠⣷⠊⠙⠛⠀⢠⣽⣿⣷⣟⠀⠀⠀⠀⢀
⣠⡊⠀⢄⣈⠳⣄⡀⠠⠄⢰⣿⣇⣠⡀⠀⠀⢀⠂⠀⠘⠛⠟⠉⠀⠰⠷⠀⠉⠀⣠⡊⠀⣄⣈⠳⣄⠀⠠⠄⢰⣿⣇⣤⠀⠀⠀⢀⠀⠀⠘⠛⠟⠉⠀⠐⠿⠀⠉
⠙⢿⣦⡘⠻⡷⠈⠻⣦⠀⠘⣿⣿⠿⠃⠀⠀⠈⠄⠀⢀⡀⠀⣰⣦⠀⠀⠀⠲⠀⠙⠿⣦⡘⠻⡷⡌⠳⣤⠀⠘⣿⣿⠿⠁⠀⠀⠈⠀⠀⢀⡀⠀⣰⣦⠀⠀⠀⠲
⠀⣀⠈⠻⣦⡈⢀⡴⠋⣤⣤⡁⠀⣤⣤⡄⠀⠀⠀⠃⠙⢿⣿⣿⣇⠀⢀⣀⡄⠀⠀⢀⠉⠻⣦⡀⢀⡴⠃⣤⣤⡉⠀⣠⣤⡄⠀⠀⠀⠃⠸⢿⣿⣿⡇⠀⠠⣀⡄
⠀⠛⠁⠴⠈⠻⠋⠀⠘⠻⠿⠀⠀⠙⠛⠃⠐⠉⡉⠑⠀⠈⠛⠈⠁⠀⠁⠋⠓⠀⠀⠛⠁⠴⠈⠻⠋⠀⠘⠻⠿⠀⠀⠙⠛⠋⠐⠁⡏⠑⡀⠈⠛⠈⠁⠀⠁⠏⠛
⢠⣶⡀⠀⣠⣤⣤⡀⠀⢀⣄⠀⠀⢠⠄⠀⠐⠬⡍⠶⠀⠀⡀⡀⠀⠀⢀⣀⠀⠀⢠⣶⡀⠀⣠⣤⣤⡀⠀⢀⣀⠀⠀⢠⠄⠀⠐⠌⣍⠶⠀⠀⠂⡀⠀⠀⢀⣄
⠈⠉⢀⡞⠀⢸⠀⠙⡆⠘⠛⠀⠀⢀⣶⣶⣶⣦⣤⣤⡄⠀⢜⠃⢀⣤⣿⡟⠀⠀⠈⠉⠀⡞⠀⢸⠀⠙⡆⠘⠛⠀⠀⠀⣶⣶⣶⣦⣤⣤⡄⠂⠙⠫⠀⣤⣿⡏
⣀⠀⠈⢧⡞⢻⠓⣦⠇⠠⠀⠀⠁⢸⣿⣿⣿⣿⣽⣿⠁⠀⣀⠀⠀⢹⡿⠿⡷⠆⣀⠀⠀⢧⡖⢻⠓⣤⠇⠀⠀⠀⡃⢸⣿⣷⣿⣿⣽⣿⠃⠀⣀⠀⠀⢩⡿⠿⡷
⣿⡗⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠈⣉⠛⠛⠛⠛⠛⠀⣤⣿⣿⣇⠀⢀⡀⠀⢺⣿⡗⠀⠀⠙⠛⠋⠁⠀⠀⠈⠀⠁⠈⣉⠙⠛⠛⠛⠛⠀⢤⣿⣿⣇⠀⢀⡀
⠀⢁⡴⠒⠲⢄⠀⢀⣾⣷⣄⣤⡀⠀⠉⢠⠶⣏⠙⠳⣄⠀⠘⠋⠁⠀⠾⣿⠃⠈⠀⢁⠴⠒⠢⢄⠀⢠⣾⣿⣄⣤⡄⠀⠉⢠⡶⣟⠙⠳⣄⠀⠙⠋⠁⠀⠾⣿⠃
⠀⡏⣴⠛⢷⡈⡇⠈⢿⣿⣿⣿⠇⠀⠀⢿⠀⢸⣶⠦⣾⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡏⡴⠛⢷⡌⡇⠀⢿⣿⣿⣿⠇⠀⠀⣿⠀⢸⣶⠦⣾⠀⠀⠀⠀⠀⢀⣀
⠀⢣⡙⠠⠚⣠⠇⠀⠀⠛⠛⠁⠀⠻⠃⠈⠳⣿⣼⠷⠋⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⢣⡙⠀⠚⣠⠇⠀⠈⠻⠋⠁⠀⠻⠃⠈⠳⣿⣼⠷⠋⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠉⠛⠋⠁⠀⢉⣀⣤⡴⠶⢻⡄⠀⠀⠀⠀⠀⣴⣧⣤⡀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⢉⣀⣤⡴⠶⢿⡀⠀⠀⠀⠀⠀⣼⣧⣤⡀⠀⠿⠆
⠀⠀⠀⠀⠀⣶⠞⢛⣭⣵⣶⣱⠈⢷⠀⠀⠀⢀⠘⠻⢿⠧⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⣛⣩⣵⣶⣹⠌⣧⠀⠀⠀⢀⠘⠛⢿⡧⠀⠀⣠⣤⡀
⠀⠀⠀⠀⣤⠸⡄⠁⢛⣋⣭⣴⣾⠿⠃⣿⣷⣿⡇⠀⣀⢀⡄⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⣠⠸⡄⠳⢛⣋⣭⣴⣶⠿⠃⢿⣷⣿⡇⠀⣀⢀⡄⠀⠻⠿⠟
⠀⠀⡠⠶⣄⠀⢳⡾⠟⠛⠉⠁⠀⢠⣷⠊⠙⠛⠀⢠⣽⣿⣷⣟⠀⠀⠀⠀⢀⠀⠀⠀⡰⠶⣄⠀⢳⡿⠟⠛⠉⠁⠀⢠⣷⠂⠙⠛⠀⢠⣽⣿⣷⣟⠀⠀⠀⠀⢀
⣠⡊⠀⢀⣈⠳⣤⡀⠰⠄⢸⣿⣧⣤⡀⠀⠀⢀⠀⠀⠘⠛⠟⠉⠀⠰⠿⠀⠉⠀⣠⡊⠀⢀⣈⠳⣦⡀⠰⠄⢸⣿⣧⣤⡀⠀⠀⢀⠀⠀⠘⠛⠟⠉⠀⠐⠿⠀⠉
⠙⠻⣦⡈⠻⡷⠈⠻⣦⠀⠘⣿⣿⠟⠁⠀⠀⠈⠔⠀⢀⡀⠀⣴⣦⠀⠀⠀⠺⠀⠙⠿⣦⡘⠻⡷⠌⠛⣦⠀⠘⣿⣿⠟⠁⠀⠀⠈⠄⠀⢀⣀⠀⣴⣦⠀⠀⠀⠲
⠀⣀⠈⠻⣦⡀⢀⠔⠁⣴⣤⠀⠀⣤⣦⡄⠀⠀⡐⠃⠘⢿⣿⣿⣇⠀⠰⢀⡤⠀⠀⣀⡈⠻⣦⣄⢀⡴⠁⣶⣤⡀⠀⣤⣦⡄⠀⠀⡐⠃⠘⢿⣿⣿⡇⠀⢐⢠⡄
⠀⠛⠁⠶⠈⠛⠋⠀⠘⠻⠟⠀⠀⠙⠛⠃⠐⠁⡍⠑⠀⠈⠛⠀⠁⠀⠀⠈⠓⠀⠀⠛⠁⠶⠈⠛⠋⠀⠘⠻⠟⠀⠀⠙⠛⠋⠔⠁⡇⠑⠄⠈⠛⠀⠁⠀⠁⠎⠛
⠀⠉⠁⠁
⠀⠐⠒⠃

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢠⠘⠃⠀⠀⠀⠀⠀⠀⡘⠆⠀⠀⠀⢀⣠⣼⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠒⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠱⡀⠀⠀⠃⠀⠀⠀⠀⠤⣙⡠⠀⠀⠀⠰⠵⢞⣯⠉⠃⠀⠀⠀⠀⠀⡇⠀⠀⠘⠃⣣⠀⠛⠁⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠰⠆
⠀⠀⠀⢓⡀⠀⢰⠃⠀⠀⠀⠶⠆⣮⡄⠀⠀⠐⣄⠀⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠉⢠⣐⡾⠶⠀⠀⠀⢠⣿⣿⡿⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⢀⣁⡋⠀⠀⠀⠸⡆⠘⠀⢠⠆⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⢄⠀⠾⠇⢸⠀⢿⠟⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⢰⠈⢅⣀⠀⠀⠀⢻⣄⢠⠃⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⠄⡀⠀⠀⠀⠙⣆⠀⢘⡶⠀⢀⡞
⠀⠀⠀⠀⠠⣼⠎⠀⠀⠀⠪⡛⡚⠀⢙⠦⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠈⣇⢸⠃⠀⠘
⠀⠀⠘⢃⠔⡻⠁⠀⠀⠀⠀⠁⠍⠡⠂⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣴⣾⣿⠒⠲⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠈⠸⠅⠀⠀⠀⠀⠀⠀⠀⢻⠘⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠘⠃⠀⠀⠀⠀⠀⢸⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡶⡀⠀⠸⣷⣿⠀⠀⠀⠀⠀⠲⠞⠂
⠀⠀⠀⣠⣤⣄⡀⠀⠀⠈⢲⣇⡂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⣾⣶⡄⠀⠀⠀⠀⠸⣛⣿⠏⠀⠀⣿⡏⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠼⠿⣿⣿⡇⠀⠀⠐⠀⠉⠵⠀⠀⠀⠠⣴⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠄⠛⡉⣶⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⢡
⠀⠃⠀⠀⠸⠻⠤⠀⠀⠀⣠⠁⠀⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠉⡀⠉⠀⠀⠈⠀⠀⠀⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⢀
⠀⠂⢠⡶⣶⡶⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠑⠤⠤⠀⠀⠀⢶⣧⠄⠀⠀⠀⠀⠀⠀⠤
⠀⡀⠘⣾⠿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠅
⠀⠄
⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⢱⣿⣿⣿⣧⡀⠉⠉⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⣿⡿⠀⠈⣿⡿⢀⣀⣀⡀⣿⣿⣿⣰⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠰⣿⠇⢸⣿⣿⣇⠛⠋⠁⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⣾⣿⣷⡸⠛⠉⢸⠁⢀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠿⠋⢹⡇⠀⣀⡘⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠸⠟⠉⣿⠀⢀⣘⢳⣾⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⢹⡇⠀⢀⠛⣶⣿⣧⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢳⣾⣿⠀⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠃⠘⠟⠿⠀⠻⠿⠗⠘⠿⠛⠃⠻⠿⠟





⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣴⣾⡇⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠠⠀⠀⢀⠀⠀⢀⣴⣿⣟⡁
⠀⠀⠤⣾⣿⡯⠅⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠨⡗⠀⠀⠀⠀⢄⠒⠀⠀⠀⣠⣿⣿⣿⣵⠦
⠀⠀⠚⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠐⠢⠀⠊⠀⠀⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢿⣿⠷⣒⣉⠥⠄
⠀⠀⣰⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣭⣿⡻⣿⣖⣒⠁
⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⣈⣻⣿⡽⠶⠖⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠀⠀⠀⠀⠀⢸⠀⠀⠙⠳⠂⠀⠀⠀⠤⠬⠜⣯⠭⠄
⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⢀⡀⠀⠀⢀⠀⠀⣀⡀⠀⠒⠒⠂
⠀⠀⠀⠀⢰⣿⠀⠀⢸⡆⠀⠀⠀⢈⠑⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⢹⠀⠀⢸⠀⠈⢻⡋⠀⠀⠀⡄
⠀⡀⠀⠀⠻⣿⠀⠀⢸⠀⠀⡀⠀⠀⠀⢐⠃⠀⢸⡄⠀⠀⣿⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⡁⠀⠀⠀⡇
⠀⠀⠃⠀⠀⠛⠀⠀⠸⠀⠰⠗⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠿⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠁⠀⠐⠇
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⣶⠀⠀⠀⠀⡴⠺⠓⠆
⠀⠠⡇⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠺⣀⡁
⠀⠀⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⢱⣶⣶⡾⢿⠷⢶⣶⣤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠐⠀⠐
⣆⠠⠤⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠋⢀⣄⣀⠀⠈⠛⠁⠀⠀⠐
⣯⠙⠲⡄⡈⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⢀⡄⡀⢀⠀⠀⠉⠀⠀⠀⠸⠓⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡔
⠙⡤⠀⠀⠀⠀⠀⡇⠰⠄⠀⠀⠀⠀⠀⠘⢿⡿⡇⠀⢀⠀⢀⢠⠂⠀⠀⠀⠘⠀⣠⠀⠀⠀⠂⠀⠈⡚⠀⠀⡄
⠄⠗⠓⡄⢀⡄⠈⡗⢠⡌⠂⠀⠀⠀⠀⠀⠀⢿⠁⢂⠏⢠⠀⠈⠀⣠⠄⢃⠄⠳⠟⠂⠀⠀⠀⠑⣌⠱⠚⠂⢀
⠀⣰⠲⡄⠀⡅⢀⡟⢾⣇⠀⠀⠀⠀⠀⠈⠒⠠⠃⠤⠆⢰⠂⣤⡰⠇⢸⠀⡄⣸⡞⠀⡀⠀⠀⠀⠀⠙⠖⠀⠈
⠀⠁⠀⢱⢀⣤⢨⡇⢸⢻⣎⠁⠀⠀⡄⣼⠆⡷⠀⠀⢌⢙⠂⠃⢍⡁⠻⣤⠳⠝⠃⠀⠑⣤⢀⠀⢀⠀⡀⠁⠆
⠔⠄⠈⠒⠋⢗⣠⡇⢂⠉⣿⠳⠀⠄⠀⡏⠀⠈⠳⣔⡀⢈⣀⡀⠀⠀⢾⣾⡧⢤⠀⠐⣤⠒⡖⣆⡓⠀⠈
⠀⢾⠾⠔⣶⣟⢙⡟⠋⡐⠿⠀⠇⢐⢟⡟⢠⣄⡒⠊⠭⣹⠀⠀⡴⢀⠈⣽⣦⡔⡀⢠⣤⢰⡿⣄⡁⡀⠀⠘⢣
⣥⢰⣿⡦⡰⠿⢾⣷⠄⠀⢣⠐⣌⣩⣿⣤⣜⣀⠀⠀⣀⡽⢒⣟⢠⣽⠈⡄⠤⢼⠃⠆⠀⠀⠀⠀⢳⠏⣔⣿⣠
⡤⢺⢿⣷⠟⠻⡖⠃⠀⢀⡈⢸⣫⣿⣿⣿⡿⠉⢄⡀⠹⡳⡷⠆⠻⣿⣿⠗⠂⡬⠜⢓⠠⢀⣯⣾⣁⣴⣣⣄⠈
⠁⢼⣗⣤⣄⢀⣥⣺⣶⡦⣦⣻⣉⢡⣶⠚⣗⣀⡴⠀⣤⣟⣆⡁⡘⠻⡞⠂⠀⢃⠰⢺⠐⠿⡝⣜⣧⢿⢷⠻⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⣿⢶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠈⢤⡟⠈⠉⢻⣤⡁⠀⠀⠀⠀⡀⠠⡞⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠗⠐⣿⡋⠀⣾⠀⠀⠀⠀⠈⠛⠲⢶⠁⡎⠀⣠⡟⢠⠁⠀⠀⠀⠀⠀⠀⣀⣤⡾⢋⡜⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡦⢴⠆⣠⡇⢰⡇⠀⢀⠰⣾⠇⣀⠀⣾⣄⠃⡰⠛⠁⠀⣀⠔⠁⠀⠀⢀⡰⠟⠁⢠⡏⠄⢀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠠⡿⠃⣸⣄⡛⢀⠸⠧⠐⢋⣴⠃⠀⠀⠀⠀⢻⡇⠠⠀⢀⡾⠁⠀⠀⠀⣴⡟⠁⣴⣂⡿⠋⠀⣘⠁
⠀⠀⠀⠀⠀⠀⠠⣩⣶⣷⣤⣉⣉⣡⣬⣤⣴⠶⠛⠁⠀⠀⠀⢠⣧⣠⣏⠀⢰⡟⠀⠀⠀⢠⠞⠀⠀⡀⢿⣿⠃⠀⠄⠛
⠀⠀⠀⠀⠀⠀⠇⣏⠘⠛⠛⢿⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠀⣼⠀⠀⠀⣀⠏⠀⠀⢸⣿⣼⣷⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢩⠖⢡⣶⡀⠹⣆⠀⠀⠀⠀⢰⣦⣤⣴⣿⣿⡿⢋⡄⠀⠁⠀⠀⠠⡯⠀⠀⢸⣾⣿⣿⣿⠁⠀⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡟
⠀⠀⠀⠀⠀⢀⣄⣁⠤⠃⠀⣧⡀⠛⣧⠀⠀⠀⠘⣿⣿⣿⣿⢟⣃⡼⠟⠓⢶⣄⠀⣴⠀⠀⠸⣿⣿⣿⣿⣏⡀⠈⠀⠠⡄⠀⢀⣀⠴⠞⠛⠛⠉⠀⣼⡇
⠀⠀⠀⠀⠈⠁⢀⠙⢄⠀⠀⠏⢑⡄⢻⠀⠀⠀⢻⣿⣿⣿⠿⣿⣿⣷⠆⠑⠆⠙⢦⠟⠃⠀⣴⣿⣿⣿⣿⠟⠀⠀⡀⢀⢀⠶⠋⠉⠀⠀⠀⣖⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠡⠾⠖⢁⣤⣾⡇⠸⠀⠀⢀⣨⣿⣿⣿⣆⠘⠿⣷⠶⠿⣆⠑⢊⢶⡜⢷⣿⣿⣿⣿⣿⣶⠆⠐⢀⡟⠻⠀⠀⠀⣰⡀⢠⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⣤⡴⠶⢬⣋⠁⠈⠻⠖⠶⠾⠛⠉⢉⣾⣿⣿⣷⠛⠙⠳⠀⠀⠈⠐⡙⢣⡄⢸⣿⣿⡏⣿⣟⠆⣠⠏⠀⠀⢰⣤⣶⣿⣶⣟⡱⠻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠂⠀⠀⠀⠀⠟⠋⡛⣼⡗⠀⠀⠀⠀⠈⢡⣄⠘⢷⡝⣦⣽⣿⣇⣿⣿⣶⣿⡇⢀⣰⣿⣋⣿⠟⢁⣸⡇⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⣇⠁⢸⠄⠀⠀⠀⠀⠀⢿⡇⢸⣟⢳⣽⣿⣿⢸⣿⣯⠀⠀⣼⣧⣼⠿⠓⣴⣿⣧⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏⠀⠀⠀⠀⠀⠿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢋⠀⢻⡈⢷⡿⣿⣿⣿⣯⠀⣶⣸⡿⣍⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢠⢴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠱⢄⣻⡘⣿⣿⢋⡀⣿⡿⢃⠼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣇⠈⠁⠜⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⢀⣤⣾⣽⣿⠉⠁⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⣴⣿⣿⣿⡋⢑⡎⡀⢧⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠊⢡⣿⣿⠋⠀⠀⠉⣿⣥⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢀⣾⣿⠁⠀⠀⠀⠀⠉⢠⡈⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠈⢱⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣿⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡝⢿⡇⠀⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢿⡀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠳⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣤⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠀⢲⡄⢸⡄⠀⠀⡟⢸⡇⠀⢸⠃⡀⠀⠀⢳⠀⢸⠃⣿⠀⢀⡄⠀⣿⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⣷⠀⣾⠁⢠⡇⠘⣧⡀⠸⡇⢸⡇⠀⣼⠀⣷⠀⠀⣿⠀⢿⠀⣿⠀⠀⢧⠀⢹⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣿⠀⠰⠃⠀⠈⠀⠉⠀⠀⠹⡇⠀⠉⠀⠑⠀⠈⠁⠘⢦⠼⠁⠀⠈⠁⠈⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡇⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠑⠒⠠⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠴⠒⠒⠋⠉⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣄⣀
⢀⣾⣷⣀⢠⣶⠖⡀⠀⠀⠀⠀⠀⣬⣣⣒⣻⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⢀⠰⠞⠁⢀⠀⠀⠀⠀⠀⠀⣿⣭⣧⠼⠿⢟⠃
⢹⢿⡿⣿⣵⣥⡩⠒⠀⠀⠀⠀⢓⣑⣢⣶⠗⠆⠀⠀⠀⠀⠶⠀⣀⠈⡲⢤⡆⠒⡀⠀⡤⠆⠀⠀⢠⣶⣿⡿⣿⣶⣷⣿⣿⣄
⠠⠉⢲⣿⣿⢬⡟⠛⠃⠀⠀⠀⣷⣾⣶⣶⣾⠆⠀⠀⠀⠀⠀⠀⠖⣠⣄⣁⣴⠖⠒⢤⣀⠀⠀⠀⠸⠟⢠⣾⣿⣿⡿⠉⠛⠁
⠀⢂⡾⠜⣿⣷⡽⠲⠢⠀⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿
⠀⠸⠁⢈⡿⠹⡗⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟
⠀⠀⢀⣶⠅⢺⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠀⠀⠀⠀⠀⣀⣤⣴⣴⣦⣤
⠀⠀⠚⣯⠀⣿⠇⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣸⣾⠟⠘⠁⠀⠀⠀⠀⠀⠀⠀⣦⡀⣦⢀⣴⠟⠀⠀⠀⠀⠀⣠⢿⣿⣿⣷⣽⣖
⠀⠀⠀⢀⣸⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⣇⣿⣿⣿⣥⣾⠃⠀⠀⠀⠀⠞⠋⣿⢻⡉⠙
⠀⠀⠀⠀⠱⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣼⣿⣿⡧⢾⣒⠀⠀⠀⠀⠀⠀⠀⣿⡄⠁
⠀⠀⠀⠀⠀⠃⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠼⢻⣽⣿⣿⣱⣆⠈⠁⠀⠀⠀⠀⠠⠶⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣤⣤⣤⣀⡲⠟⠀⣠⡶⣶⡄⠀⠀⣠⣶⡄⣾⣠⡾⠃
⠀⠀⠀⠀⣺⣼⠇⣶⣿⠟⠛⠉⣉⣀⣠⣬⣭⣉⣙⣛⡻⠿⣶⡿⠀⣿⠷⣶⣾⡟⣿⡇⠐⠫⠶⠿
⠀⠀⠀⠀⠉⠉⣴⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⢳⡆⢸⣟⣆⣛⣭⣾⣟⢷⣤⣴⡶⢿⣧
⠀⠀⠀⠀⠀⢸⣿⡇⠈⠿⠛⢿⣿⣿⠿⡻⡟⠰⣣⣿⡿⠓⢻⠁⣾⡏⢈⣿⠉⣿⣽⢘⡛⠋⣀⣢⣿⣤⣄
⠀⠀⣶⣄⢿⡘⣿⠇⢠⣦⡀⠘⢟⡅⠠⠿⣁⠀⢿⣿⡟⠀⣼⢰⡿⠀⣼⡟⠀⣿⢯⡿⠀⣰⣿⣿⠟⣩⣿⡇
⠀⠀⢬⣽⠓⠀⣿⠀⢸⣿⡷⠀⣿⠁⣾⣿⣿⣦⠀⢿⠃⢰⡏⢸⠃⢠⣟⣄⠀⢏⣾⡇⢠⣿⢟⣥⣾⡿⠋
⠀⠀⠀⠀⢀⣾⡏⠀⢸⣿⡷⢀⣿⠀⣿⢧⣿⢿⠆⣸⣀⣻⣾⣤⣷⣤⣾⣿⣷⡟⢻⣷⣶⣿⠿⠛⣡⡄
⠀⠀⠀⠀⣸⣿⢷⠀⣾⠻⢃⣼⣿⣦⣽⣿⢿⣷⡟⢻⠛⣿⠁⣿⣿⠿⢿⣿⣿⠀⣼⣿⣯⡀⠀⠸⠷⠶⠶
⠀⠀⠀⠀⣿⣿⣾⠀⣿⣿⣿⣿⣿⢿⣍⠃⠀⠛⠀⠞⣒⠁⢠⣶⣾⠿⣿⡿⠋⢰⣿⠋⡉⣿⣤⣤⡙⠷
⠀⠀⠀⠀⣿⣿⣿⢠⣿⣿⡿⠋⡀⢸⣿⠁⣾⠃⣼⠏⣹⠀⡏⢠⡟⢰⠏⢠⠂⣸⠇⣰⣾⡿⣡⣿⣿⠂
⠀⠀⠀⠀⣿⣿⠟⢸⣿⡿⠀⣼⢇⣿⡏⢰⡏⢰⠏⢠⡏⢸⠁⢸⠇⡟⠀⢊⡆⢫⣄⣻⣯⣾⣿⠿⠃
⠀⠀⠀⠀⣿⣿⡄⢸⣿⡇⠸⢏⢸⡿⣶⣘⣦⣈⡆⠸⣤⣨⣷⣶⣿⣾⡷⣿⣿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠸⣿⣷⣿⠋⡙⡲⢿⣿⠞⠉⠻⠛⠻⢿⡿⠛⠛⠋⠀⠉⠉⠁⠴⠟⣱⣷⡆
⠀⠀⠀⠀⠀⠀⠉⢡⡆⣿⡝⠇⠀⠀⠀⠀⠀⠀⠴⠟⣱⣷⡆⠀⠀⠀⠀⠀⠐⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢸⡆⠼⢌⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠛⣴⠀⡀⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢹⣾⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠃⠠⠐⠂⠀⠀⠀⠀⠀⠀⠰⣄⠸⣯⣽⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡷⣾⡆⢄⡀⠀⠀⠀⠀⠀⠸⢧⣟⢶⣿⣿⣬⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣒⠀⠀⠀⠀⠸⠟⠋⣧⠨⠔⠀⠀⠀⠀⠀⠀⡜⢿⣹⣏⣉⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢀⠀⢮⠃⠀⣴⠂⠀⠀⠀⠘⣟⠞⠁⠀⠀⠀⠰⡜⣒⢠⣿⠋⠛⠟⢂⠘⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠆⠀⢰⡷⢰⡌⠛⠀⠀⣠⢀⠈⢦⠀⠀⠀⢀⣀⣏⠁⣾⠋⠀⠲⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⠛⠃⠀⠀⠀⢾⠏⠂⠈⢧⢆⡶⠀⠹⠁⣦⡧⢬⣩⣁⣀⠂⢔⡐
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⢀⡀⠀⠀⠀⣤⣹⠀⠀⠀⠀⠀⠈⠀⠀⠼⢮⡌⠂⠀⢤⣫⠀⠀⠀⠀⠙⠃
⠀⠺⢱⢆⣾⠧⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⢆⠀⠀⢮⣈⡆⠀⠀⠀⢀⠀⠀⢰⣄⢸⡇⣤⣿⢂⠉⠐⠀⠀⠃⠈
⠀⡉⠘⡝⠉⠹⣦⠀⠀⠀⠀⠀⠀⠀⡀⠺⢄⣼⠀⠀⣴⡉⢿⡀⠀⠀⠈⠀⢀⠁⠲⢸⣧⡞⣳⠅⡆⠣
⠈⠓⠓⢾⣎⣩⣹⣼⡃⠈⣰⣀⠀⠀⠄⢰⠿⣿⡀⢐⡛⠴⠋⢷⠀⠀⠀⠀⠘⣛⣏⢸⡿⠳⠋⣤⠀⢰⡄⣀⠄⣀⡀
⠀⢄⢸⢿⠌⠳⣯⣿⠋⠀⣽⣷⠆⠀⠀⠁⠀⠙⣇⠈⢙⡀⡀⢸⣇⡀⠀⠀⠈⣉⣹⣿⠗⠡⣠⠜⠋⠘⠿⠿⠶⠞
⠀⠀⠀⠈⠲⢻⢟⡞⠛⠳⣤⡀⣤⡀⠀⣠⣄⠀⠘⣦⡜⡙⢻⣾⣯⠛⢠⣦⣆⡼⣣⣧⡌⢐⠙⡃
⠀⠀⠀⠀⠀⠀⢠⣄⣦⠀⠚⢿⣿⣧⣼⣽⣋⣔⡄⣹⣿⣵⠶⣹⣯⡖⠈⢻⣿⣥⠿⠿⠇⠸⡙⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠠⣽⠊⠙⠉⠿⢿⣿⣿⣸⣿⣿⣹⣮⢸⣿⢭⣾⣿⣿⠿⠶⠖⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣛⢻⠿⣿⣿⣿⣷⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠉⠁⠀⠈⠙⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄



⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⢢⣶⣤⣶⣶⣤⣤⢠⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣴⣤⣤⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣦⣤
⠀⠉⠻⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⠉⣿⣿⡏⠉⠉⠉⠉⠉⠙⣿⣿⠀⠀⠀⠀⣴⣿⡿⠉⠀⠀⠀⠉⠻⣿⣿
⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⣿⣿⣶⣄⡀⠀⠀⠀⣠⣾⣿⠟
⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣉⣛⣻⣿⣿⣿⣿⣿⣟⣛⣁⣀
⣿⣿⣋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡆⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣀⠀⠀⠀⠆⠸⡄⢻⣿⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⢷⠍⣉⣉⣛⣻⣷⣤⣻⡇⠀⢀⠴⠖⠛⢩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠙⠻⣇⠀⠃⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣤⣤⣌⣳⣦⣆⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣷⣾⡿⠟⠻⡟⠁⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠱⠀⠀⣠⡶⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⣀⠀⠀⣇⣰⣯⣔⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢮⡳⣦⣼⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠛⣧⠀⠀⣀⣤⣤⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣟⠟⡉⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣣⡾⠚⣀⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠟⠉⣡⡴⢛⡽⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠁⡆⢰⢏⠜⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻⣮⡳⣄⠀⠀⣿⣤⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠏⠹⣆⠀⠀⠀⠀⣾⡇⠀⠀⠀⣷⣄⠀⠀⠀⠀⢸⡇⢭⣿⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢂⠀⠀⣠⢿⢿⠀⠀⢠⡿⠏⠳⢦⡀⠀⢸⣠⣾⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠀⠀⠀⠘⡆⠀⢩⠈⠘⡇⠀⠸⣣⠀⠂⠌⣷⠀⠈⣿⣿⣷⡿⠟⠛⠉⠛⠲⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢠⣴⠃⠀⠈⠣⠀⣜⠀⠀⠉⠛⢶⣷⣣⡴⠚⠉⠀⠉⠉⠒⠤⠤⠤⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣾⠏⠀⠀⠀⠀⠀⣿⠀⠀⢀⡠⠼⢯⣥⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠲⢾⣷⠤⠤⠤⠤⠤⠤⣾⠖⠊⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣦⡀⠀⠀⠀⢰⢏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⡹⣧⠀⠀⣀⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣧⡹⠀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣉⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠄⠐⢤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠑⢤⠊⠁⠀⠀⠀⠈⠑⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠀⠀⡅⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⡃⠀⠀⠀⠀⡄⠀⡄⢀⣇⣀⢰⡀⣰⠀⠀⠀⠰⠃⠉⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⣣⡀⠀⠀⢄⡨⠂⣉⡁⠀⠀⠀⢉⣉⡑⠢⣴⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⠉⢲⠎⠀⠙⠛⠁⠀⠀⠀⠈⢙⠉⠀⠈⢣⠒⠁⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⡌⠀⡔⠉⠉⠱⡀⠀⠀⡎⠁⠈⢱⡀⠀⠓⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⡇⠀⡍⢰⣶⣿⠇⡀⠘⣹⣿⡯⢁⠃⠀⠷⠤⠄⣀⠤⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠒⢃⠀⠈⠂⠙⠋⠀⠧⠀⠈⠛⠒⢁⠀⢠⠇⠀⠀⠈⢢⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡀⢀⠤⠂⠙⡄⠀⠑⠤⣀⡀⠀⣀⣀⡠⠔⠁⢠⡊⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⢸⠁⠀⠀⠐⠚⣢⣀⠀⠀⠀⠀⠁⠀⠀⣀⡔⠁⠈⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⠁⠌⠉⠲⠒⠒⡖⠒⡏⠁⠈⢆⡀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠙⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠠⡤⠤⠔⢳⠀⠀⠀⠀⠀⠀⠀⠀⡸⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⣄⡀⠀⠀⢀⡠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢉⣀⣉⠀⠈⡏⢹⠁⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠉⠠⣀⣀⡀⣠⡬⢱⡇⢸⡮⠥⠤⣤⡀⠀⡀⠈⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠀⠀⠀⠒⠈⠁⠀⠒⣁⠔⠊⡇⠀⠈⠢⢄⣀⠈⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠒⠒⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⠀⢀⣀⠠⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⣈⣉⣉⣉⣉⠥⢶⡇⣷⠊⠤⣤⡤⢤⣔⡂⠀⠈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠠⠐⠊⠉⠚⢁⠴⠊⡇⠆⠑⠤⡀⠉⠀⠀⠀⠉⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⣀⡀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⡇⠀⠀⠀⠈⠁⠒⠀⠐⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⢀⠀⠀⠀⢲⣤⡄⠀⠀⢀⠀⠀⡸⣆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⣿⣶⠘⣧⣿⡟⠀⠀⠈⠿⣿⣄⢐⣾⡷⢳⣽⡍⠀⠀⠀⠀⠀⢻⣖⠀⠀⣤⣶⠧⠀⠀⠀⢀⠀⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⡤⣤⣠⡿⣌⢡⡄⢶⣷⣤⢨⣉⡱⣎⣠⡔⠊⠀⠀⠀⠀⠻⣤⣀⠘⣿⡦⠴⠛⣧⣴⠀⠀⠙⣾⣇⠈⣯⣵⡄
⠀⠀⠀⠀⠀⠀⣀⣀⣴⡓⢿⡀⠘⡯⣞⠛⢿⠃⠠⣍⣡⣔⠛⣵⠋⠸⣿⡍⠀⠀⣰⡦⡿⠶⣏⢠⡟⢀⠀⠀⠸⠻⠄⢠⣄⡄⢉⣌⣰⡞⠟⠃⢰⣠⣆⡤
⠀⠀⠀⠀⠀⠀⡼⠟⠋⠀⢉⣭⡿⡿⢟⢧⣈⣯⣟⣯⠃⠀⠙⢻⡄⢀⠙⠠⣄⣤⠀⣀⣼⣄⡎⣻⠹⡿⠶⠂⠀⢀⡰⠀⠽⠻⡟⢣⠶⣀⢀⣤⣊⠃⠛⠛⠃
⠀⠀⠀⠀⠀⠀⢠⣄⣰⠀⠀⠀⠀⠀⡿⡿⠙⣷⢼⡟⠀⠀⠀⠀⢻⣜⣿⣤⡽⢿⠆⡁⢀⠈⠁⢿⡘⣶⡂⣀⡴⣮⡛⢃⣀⣺⣡⡴⠞⣉⠁⠀⠨⠗⠢⣴⣧⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣽⠿⡃⢦⣾⣧⠄⠀⢀⠙⣲⣆⢺⣴⣧⢀⡄⠹⣿⢿⣟⢪⡴⣷⠿⣄⠀⡀⢹⡝⠁⣼⣟⣋⡉⢚⡿⠋⠀⢙⡘⠿⢾⡀⠀⢸⣷⠃⠉⠟⠷
⠀⠀⠀⠀⠀⠀⡼⠟⠋⢉⣿⢶⣿⡁⠀⠒⠻⠟⡿⠛⢿⡁⠀⢠⣿⣶⣿⠉⣽⢦⡶⣤⣤⠀⠀⠽⣾⢀⣔⠉⣀⠿⢳⢎⣴⠃⠀⢿⡿⠁⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠻⠃⠈⠙⣦⡷⣏⠀⢠⠄⠈⣷⠀⠀⠀⠀⠹⣦⡆⠈⠞⢳⢾⡇⠀⢀⡟⠋⠈⠽⣋⣠⢸⠋⠉⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⣾⢷⣄⣀⣬⣷⡀⣹⣿⣶⠀⢿⡄⠀⠀⡽⡏⢻⡇⢀⠴⢶⡍⢉⡝⢺⡇⠀⢠⣴⣍⣇⢸⠀⠀⠀⠀⢀⢠⣤⠄
⠀⣀⣶⣼⣦⢤⣤⣄⡤⢿⣿⡿⠟⠋⠀⠈⠻⢶⡶⠿⠶⢾⣷⣦⣤⣅⣄⣼⡇⣸⠻⠎⢀⣻⡛⠀⣷⢢⣴⠚⠟⠙⣿⠀⠀⣳⢆⢸⠟⠁⢀⣦⡞⠀⢠⡀⣴⣀⡀
⠘⠉⠋⣸⠗⠋⢀⣹⠳⠈⠸⠆⠀⠀⠀⠀⢻⡻⠀⢀⢀⣤⣤⡋⠉⠉⠉⠛⢿⣷⡄⢤⡬⠉⣥⣠⣟⠁⠉⣉⣢⠀⡏⠰⣾⣈⣋⡇⠀⣀⣼⢷⠶⢖⣉⡛⠉⠈⠁
⢀⣀⡞⣋⣓⠀⠈⠏⠃⠰⣆⣀⡀⢲⡤⣶⣫⡝⢳⣿⠀⡴⣿⠏⠀⠀⣄⣲⠺⣉⣿⣎⣹⠏⣙⠈⣧⢼⡔⣊⢉⡾⢡⣸⡏⣙⣫⣷⡋⠀⠛⠻⠦⠈⢿⡦⠄
⣘⣽⠻⠁⣯⠀⠀⠀⢀⣏⣹⣻⣥⣿⠾⠧⣿⣛⣹⣏⣀⡀⠘⠂⠀⠀⠚⣫⡾⢹⠇⢻⣇⠰⣿⢷⡇⣰⣽⡛⢻⣇⣹⡿⠛⣉⣡⣸⣷⢀⣠⣦⣶⡀⠀⠛
⠉⡎⠃⠀⠀⠀⠀⠀⢶⣾⣣⡝⠁⣞⡆⠀⠀⣉⢹⡭⠛⠛⠻⠶⢦⣴⣿⣤⠈⣏⣻⣾⢻⣧⢀⣾⣥⡿⢟⡏⢹⡟⠻⢞⣰⡜⢻⣽⠖⢺⣿⢩⢧⣇⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠘⠁⠾⡿⠀⠙⠇⠀⠈⡽⠟⠃⠀⠀⢠⣠⡄⠈⢛⣿⣶⠋⠓⠀⠀⢻⣿⠋⣷⡤⠘⣿⣿⠘⢶⣸⣻⣶⠻⡄⢐⣤⠖⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣝⢫⣽⣍⠛⣦⡀⠀⠀⢰⣿⣆⠘⠿⠀⢠⡿⠤⠚⣹⡦⠈⢿⡉⠉⢩⢾⠃⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣯⠐⢻⡏⠀⠈⠻⣦⣀⡿⠀⣿⣄⣀⣀⣿⣁⣰⡧⠄⢹⢢⣼⣧⣗⢀⣼⣤⠤⠴⣚⣟⠻⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⣿⣉⣿⣿⣽⣫⡴⠶⠂⡉⢸⣯⢀⡟⠀⠀⡀⠀⠋⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡷⣰⠄⠻⣷⣄⣼⣿⣿⡇⢡⡈⢯⣥⡄⠙⠛⠛⢻⣾⠖⣰⡮⠷⠍⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣼⣿⣱⣦⣿⣿⣿⣿⣿⡇⠺⣟⡄⡿⠀⠲⣿⠋⣸⣿⣉⠀⣻⣆⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣤⣸⣿⡎⢸⣿⣿⣿⡇⠈⠉⢙⠇⠀⢸⣠⡾⣅⠀⠞⣗⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⣹⣾⣿⣿⣿⣿⣶⣶⣾⠶⣤⣾⠻⣟⠟⠃⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡝⠀⢹⣿⣿⣿⣿⡏⢠⢷⡂⠸⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⣿⣿⣿⡇⠀⢫⡟⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢄⣰⣿⣿⣿⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢹⣆⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡾⠀⠀⠀⠛⠛⠛⠋⠉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⢷⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⡞⠁⠀⠀⠙⢦⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠙⠋⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⡻⣆⢻⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⢷⣌⣷⡘⢿⣷⠘⣧⡾⢻
⠀⠀⠀⠀⠀⢰⣦⡀⣿⣇⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣦⠉⠛⠁⠈⠉⠀⠛⢃⡟
⠀⠀⠀⢠⣦⣌⣿⡻⣿⢿⡿⣿⣴⢻⡆⠀⠀⠀⠀⠀⠈⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠹⢮⡛⠃⠀⠀⠀⠙⢣⡞⠀⢀⣀⠀⣤⡀⢠⣄⠀⠈⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⡏⠀⠀⢸⡝⣿⡇⣿⣿⢹⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⣤⡀⣼⢧⢀⡶⣦⢸⡇⠀⣶⠾⣷⠈⠃⠘⠋⢾⡾⢻⠆⣿⠀⠀⢠⣦⡀⣿⡆⢀⣤⡄
⠀⠀⡶⣼⡏⣷⣿⢸⣿⠃⡿⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⣰⠏⠀⣿⢀⠀⢸⡌⣷⡟⣿⣸⢃⣇⣴⡦
⠀⠀⢷⡘⣿⠘⠟⠈⠛⢸⣧⡿⣦⠀⠀⠀⠹⡆⠀⠀⠀⣴⠃⠀⠀⣿⣏⠻⣾⡇⠻⠃⣿⡟⢸⡟⣹⠇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢁⣴⡃⠀⠀⠀⢠⡇⠀⠀⠀⣿⠀⠀⠀⣿⠙⢷⡀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢀⡇⠀⠀⠀⢠⡴⠋⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢿⡀⠈⠷⣄⣀⠀⠀⠀⢰⡏
⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠈⣷
⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠸⣇⠀⠀⠀⠘⣧⠀⠀⠀⢸⣇
⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢻⡆⠀⠀⠀⢻
⣿⣿⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠀⠀⢀⠜⣽⠋⠁⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠜⠁⠠⠒⠉⠉⠁⠒⠤⠀⢀⣀⣤⡶⠏⠀⠀⠀⠒⡲⠖⠐⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⢀⢀⡴⠅⠀⠀⠠⢤⣤⣶⣶⢿⢿⠭⠭⠓⠒⣚⠡⠄⠊⠁⠀⠀⠁⠀⠄⠀⠀⠀⢠⣤⣦⡾
⠀⠀⠀⢀⣠⣴⡏⠀⠀⠀⣀⣤⠶⠚⠉⠀⠀⠀⠀⢀⠔⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢝⣿⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⡀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⡴⠒⢒⣲⡖⠉⢉⣈⠉⠉⠋⠀⠀⡄⠐⠀⠆⠀⠀⡍
⠀⠀⠀⠀⠀⡸⣋⠄⠀⠀⠁⠀⠀⠀⠀⠀⠁⢐⠀⠀⠠⢀⡂⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠄⠀⠀⠀⠘⠀⠀⢀⠄⡉⢆⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠁⠔⠁⠠⠁⠀⢀⡀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣼⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⢾⣦⡀⣀⡜⠊⠅⢰⠂⠰⠀⠀⠀⠀⠚⠋⠁⠀⡀⠠⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣦⣿⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⢀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐⢂⡀⢬⣿⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡞⠀⠀⢠⢃⠄⣀
⠀⠀⠀⠀⠀⠀⠀⡁⢠⠊⠁⠀⠀⢈⠡⠴⢒⠂⠒⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡾⠉⡿⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⢛⣶⣧⡀⠂⢀⠀⢀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠓⣄⢸⣶⢸⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢉⡿⠿⡇⠄⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠞⠀⠐⢠⠄⠀⠀⠀⠀⠀⠀⠀⠹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡆⠀⠀⠀⠀⢠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠿⠿⠇⠀⠀⠀⠀⠸⠿⠿⢿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠈⠛⢦⡀⠀⣠⠖⠉⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠃⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣤⣄⠀⠈⣿⠀⢀⣤⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣿⡀⠀⠉⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠻⣤⣀⠀⠀⢀⣠⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠶⣤⣀⣀⣀⣤⡾⠋⠀⠀⠀⠈⠙⠛⠛⠋⠁⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠐⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⠦⣄⣀⣀⣀⣀⣀⣠⣤⠶⣏⢹⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠸⠦⠋⠉⠉⠉⠉⠉⠀⠀⠀⠈⠋⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⠞⠉⠙⡆⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠘⢄⠀⣀⠞⠀⠀⠀⣴⣿⣿⣧⣤⣤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠁⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣾⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣼⣿⠇
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣾⣿⠋⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⢀⡀⢀⡀⠀⠓⠒⠊⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⡴⠉⠁⠈⠙⢦⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⡇⠀⠀⠀⠀⢨⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠙⢆⣀⣀⠴⠋⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣷⣶⣤⣄⣀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⠃
⣿⣿⣿⣿⠿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢺⡐⠭⣧⠇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣸⣥⣤⠖⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⡂
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⢶⣄⠀⠀⡀⠀⢖⡲⠀⡊⠁⡆⠈⠉⠁⠀⣼⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡝⠛⣏⣹⠄⠀⣠⡄⠉⠈⠁⠀⠀⠀⠀⠀⡟⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⢡⡀⠀⢽⠆⠀⢀⢠⠀⠀⠀⡀⡔⠃⠀⠁
⠀⠀⠀⠀⠀⡀⠖⣀⣀⠀⢠⠖⠒⢄⠀⢿⡀⠀⠀⠀⠀⠄⠂⠀⠠⢇⣹⠃⠀⠄⠒⢌⠂⠀⢀⣼⠃
⠀⠀⠀⠀⣼⣿⠉⠉⠁⠀⠹⣀⣀⠜⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠸⡀⠀⡠⢀⢠⣾⡿
⠀⠀⢀⣴⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⢨⡿⣿⡀
⠀⠰⠟⠁⠠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠠⡀⠘⠀⠀⡇⠀⡇⠀⡄⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡀⠀⠐⢆⠀⠈⢦⠀⢳⠀⡆⠀⡇⢸⠁⡸⠁⡠⠃⠀⣠⣦⡤⠤⠤⠴⠯⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣶⢶⡞⠒⠒⠒⠓⠒⠒⠓⠒⠓⠓⠒⠓⠚⠒⠓⠚⠓⠒⠚⠓⠒⠚⠛⢲⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣭⠀⠀⠀⠀⠀⢰⡀⡦⢰⡆⣴⠀⣤⢰⢢⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢣⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⣿⣶⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠛⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣉⣛⣿⣭⣛⠛⠛⠛⠻⠏⠛⠻⠋⠟⠻⠛⠻⠭⢍⣉⣉⣉⣉⣉⣉⢉⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣓⣲⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣑⣲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡶⠦⠤⢿⢬⡄⠀⠀⣀⢀⣀⠀⡀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣽⠉⠁⠐⠒⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢸⣾⡍⠀⠀⠋⠘⠔⠀⠃⠀⠘⠀⠀⠋⠘⠘⠀⠉⠀⠀⠀⠀⠀⣿⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠘⠶⢶⡒⠲⠖⠒⢲⠖⢲⠒⡶⠲⡖⢲⠒⢶⠒⢖⠒⠲⡖⠒⠒⠺⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡽⠋⠀⡰⠃⢠⠃⢀⠃⡤⠁⠈⡇⠈⢆⠈⢣⠀⠈⠢⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⠇⠠⠂⠞⠈⠓⡆⢱⠀⠘⡆⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠎⠀⠐⠤⠂⠀⠐⠁⠈⡆⠀⠘⡄⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣸⠀⠀⠀⡇⠀⠀⢱⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡏⠀⠀⠀⠇⠀⠀⠘⡄⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠐⠘⡇⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⡀⣸⣿⡜⠰⣆⠀⠀⠀⠀⠄⠀⠀⠀⢠⣯⠙⣩⡃⢶⣴⡄⣿
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣤⢤⢰⡶⠔⢤⡝⠛⠉⠀⣆⠈⠀⠀⠀⢀⢠⡄⠀⠂⣿⠷⠿⢈⢥⢸⡿⠵⣏
⠀⠀⠀⠀⠀⠐⠛⢦⡀⡀⠿⠛⠀⢨⣧⠈⣦⣐⡇⠀⡘⠋⠀⠀⠀⠠⡾⢘⠁⠀⢠⣾⠓⠲⠆⣿⠿⠆⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠎⣣⡁⠐⢀⡀⠆⠉⠐⠀⡌⡗⠀⠃⠀⠀⡀⡄⠀⠀⠀⢀⣀⠀⠉⢨⡄⣸⣗⣶⠦⠀⣿
⡀⠀⠀⣀⠀⣠⠀⣹⠋⠁⢻⣿⣏⠁⠀⠀⠀⠁⠃⠀⠀⠀⠄⢁⣗⣰⣄⣠⣤⣼⡄⠘⠋⣠⢁⣙⣿⣿⠆⣿
⠁⠀⠝⢻⡇⠁⢠⣟⣶⡆⣸⣿⠉⠁⢸⠀⢳⡀⠀⠀⠀⢰⠀⢸⣿⣽⣿⣿⣏⠈⡗⣶⣰⠃⣘⠛⣿⣿⡿⣿
⢀⡀⠀⠀⢁⣴⠏⡜⠀⡿⢿⠛⠀⠢⣽⠀⠀⢷⢀⣄⠀⠐⡀⢉⣽⣿⣿⣹⣿⣷⡀⢠⣷⡔⠟⠀⢻⡉⠃⣿
⠃⢐⣃⠀⡸⢿⣀⡁⠀⣈⣭⣄⣠⣶⣿⠀⢰⢶⠚⢳⣿⢀⣁⣾⣿⣿⣿⢉⡿⡏⣧⣿⣟⠁⠘⠀⣸⣾⡆⣿
⠀⠈⠏⠲⠤⣾⠅⣼⠎⢩⡏⠙⢿⡿⡇⠀⠀⢸⠷⢣⣿⣄⠉⡿⠎⠟⠁⣿⠃⢠⣿⣽⣯⣿⣿⣿⣯⣭⣧⣿
⠀⠀⠀⠀⢰⣿⡈⣿⠀⣿⠁⠀⠀⣆⡇⠀⠀⢠⠞⡱⠘⠋⠀⠀⠀⠀⠀⠁⠀⢡⠟⢻⡿⣿⣿⣿⣷⣿⡇⣿
⠀⠀⠈⠉⠉⠁⠉⠈⠉⠉⠁⠀⠀⠉⠉⠂⠒⠊⠒⠙⠒⠒⠒⠓⠐⠒⠂⠐⠐⠋⠐⠃⠖⠚⠟⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡗⣭⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣰⡏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⢰⣟⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣷⣾⣷⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠛⠀⠀⠀⢀⣀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣶⣶⠞⠀⠀⠀⢤⣤⡴⠀⠀⣤⡄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⣆⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡟⠀⢀⣤⡀⠘⣿⠁⢠⡄⢸⡇⣠⣼⠇⣄⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣷⣾⣿⠀⣿⣿⣿⡇⠙⢻⡇⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⠀⣿⡿⢿⡇⣶⣾⠻⡆⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⠸⣿⡏⠈⣿⠀⠙⠃⣸⡇⠉⠸⠆⠐⠃
⠀⠀⣠⣴⣶⣶⣿⡇⠀⠀⠀⣤⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠸⣿⡿⠃⠀⠠⣿⣿⡀⠀⠀⠀⠈⠛⠃⠀⠀⠉⠁
⠀⠾⠿⠛⠛⠉⠉⣿⣷⣶⣾⣿⡇⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛



⠀⡁⣉

⠀⢀⣠⣤⡄
⠀⠹⠿⠿⠛⠀⠀⠀⡀⠀⠀⣤⡄⣀⢠⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠋⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣴⢿⣿⣿⠻⣇⠀⠀⠀⠀⢂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⢀⣴⣤⣿⠯⣼⣿⡂⠀⠀⠀⠘⠀⠀⠀⠀⠈⢣⡴⢤⡀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠟⠉⠸⠃⠤⣊⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠴⠆⠈⠀⠀⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⢒⣾⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠐⠂⡸⡇⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠖⠂⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠈⠛⠿⠗⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⠀⡲⢄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢋
⠀⠀⠀⠐⠀⠀⠀⠀⠁⠛⢠⣳⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠉⠛⠰⠆
⠀⠀⠀⠈⢑⡀⠀⠀⠀⠷⡄⢄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠞⠋⠀⠀⣀⠀⠀⠀⠒⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡈⠛⠠⣄⠀⠀⠀⠢⡍⠀⠙⠀⠀⠀⠒⠁⠀⠀⠀⢀⡀⠀⠀⠀⠘⣤
⠀⠀⠀⠘⠛⠆⠐⠂⠀⠀⠀⠀⠀⠀⡀⠉⠠⠀⠀⠀⠀⠛⠃⠠⠄⠀⠀⠀⠐⠈⠁⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⠟⢠⡄
⠀⠀⠉⠐⠂

⠀⢰⠃⠲⠴⣤⡤⠲⣦⣄⣀⣀
⠀⢸⠀⠀⠀⡇⠀⠀⣿⣯⡏⡏⡟⡆
⠀⢸⠀⠀⠀⠇⠇⠀⡿⣿⣯⡇⠏⡇
⠀⢸⠀⠀⠀⠀⠀⠀⣷⠻⠿⡅⢒⡇
⠀⢸⠀⠀⠀⠀⠀⠠⣷⢸⠀⠀⢬⡇
⠀⢸⠀⠀⢀⠀⠀⢸⣿⣾⠀⠀⢈⡇
⠀⣾⠨⠀⡾⠀⠀⢸⣿⡿⡆⠀⢸⠆
⠀⡟⢈⢈⠁⣸⠀⢸⣯⣷⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡴⠦⣤⣀⣀⣀
⠀⡇⢈⠈⠀⠇⠀⢸⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⠀⡞⠁⢀⠞⠀⡠⠃⠠⠋⡉⠻⢓⡶
⠀⡇⠘⠀⠀⠂⣰⢾⡸⠂⠂⠀⡇⠀⠀⠀⠀⢀⠔⠻⠂⢉⠀⠙⠁⡰⠁⢀⠎⠀⡰⢁⡠⠓⠉⢀⡾⠁
⢸⡇⢰⠀⠀⡇⡾⢸⡅⣤⠁⠀⠇⠀⠀⢀⡴⠃⠀⠀⠀⠊⠀⠀⠶⠁⠀⣈⠤⠒⠛⠤⣀⡀⣀⡿
⢸⠀⢸⠁⢸⠅⠇⣾⡷⡼⠀⠠⠀⠀⡴⠉⠐⠀⠀⡂⠹⠀⠀⣀⡦⠶⡉⠀⠐⠤⣀⣀⣀⣉⡟
⢸⠀⠸⠂⠨⠐⠀⣿⡗⣿⡇⢀⡀⡘⠈⠀⢸⡇⠠⣀⣠⢶⠋⡇⠐⢄⡈⠂⢤⣀⣀⣠⡼⠃
⢈⠀⠀⠀⡇⠀⢠⣿⣧⡏⡏⣈⠁⡃⠈⠀⢀⣷⡾⠫⣁⠀⠳⣇⠀⠀⠉⠒⠀⢠⣴⠛
⢸⠀⠀⢇⢡⡄⠄⣿⣇⣷⣯⢩⡁⠱⣀⢶⠟⣅⠀⠢⡀⠁⠂⠠⡈⠒⢢⣤⠼⠋⠁
⢸⠀⠀⢘⡏⢀⢆⣿⣿⢿⣿⣸⣁⢔⡵⣍⠢⣈⠑⠢⠄⠈⣀⢠⡥⣼⠏⠁
⢸⠀⠀⢨⢰⠈⢊⣿⣻⣾⣿⢛⢏⡞⠀⠈⠲⠤⠥⠤⠖⠺⠋⠉⠁
⢸⠀⠀⢸⠸⠃⠨⣿⣿⢿⣿⡌⣿
⢸⠀⠀⢸⠀⠀⠀⣿⢹⣿⣿⡇⣿
⠈⡆⠀⢸⡀⢀⠀⣿⢼⣿⣿⡁⣼
⠀⡇⠀⢸⡇⠸⣀⣿⣿⣿⣿⡇⢻
⠀⣧⠀⠸⡇⠀⢿⣿⣿⣿⣿⣶⢸⡀
⠀⢸⠀⠘⣗⠀⢹⣿⣿⣿⣿⣿⡀⡇
⠀⠸⡤⠴⢾⡴⠾⠻⠟⠛⠛⠻⠿⠃

⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣶
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⣿⡴⠶⠶⢦⣄⠀⠀⠀⠀⣤⠶⠛⠛⠛⠛⢶⣄
⠀⠀⠀⢀⡞⠁⠠⠀⠀⠀⠈⢷⡀⢀⡾⠁⠀⢀⠄⠀⠠⡀⠙⣧
⠀⠀⠀⢸⠁⠀⠀⠐⠀⠀⠀⢘⡇⢸⡇⠀⠀⠁⡈⠉⠇⠈⠀⢸⡇
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣼⠃⠘⣧⠀⠀⠡⢈⠉⡀⠄⠀⣾⠁
⠀⠀⠀⠀⢸⡗⠦⣤⣤⠶⠛⠁⠀⠀⠘⢷⣄⣀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠉⠁
⢻⡟⠛⢻⡟⠛⠛⠛⣿⠛⠛⢛⣿⠟⠁⠀⣾⠁
⠈⢷⡄⠈⠁⣶⠀⠀⠉⢀⣴⠟⠁⠀⠀⣸⠇
⠀⠀⠛⢦⣄⣿⣀⣤⠾⠋⠁⠀⠀⠀⢀⡿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⢶⡆
⠀⠀⠀⢰⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣀⣀⣤⣤⡤⠶⠶⠞⠛⠛⠻⡇
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⠿⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠿⠶⠶⠛⠛⠛⠉⠉⠁⠀⠀⢀⣠⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣀⣀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⣸⠆⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠁⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢶⡆⠀⠀⠀⠰⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠙⠄⠑⠉⡄⠀⡠⠒⢄⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⡄⠃⠀⡂⠟⡀⠀⠀⢠⢀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣄⡀⠀⢀⡀⢠⠔⢄⣙⠃⠁⠀⠀⡀⠁⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠴⠀⠂⠀⠀⠐⢻⠀⠀⠹⠖⠃⠀⢠⣘⢤⠁
⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠈⠙⠄⠘⡀⢀⡈⢑⣤⢠⠄⡄⠀⠀⠠⣀⡉⠁⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠼⠆⢡⠀⠉⠴⠂⠈⠀⢄⠀⡙⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣥⠤⢾⢀⠳⠾⣀⠰⠦⢶⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠐⠘⠃⠂⠒⠐⠒⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠠⢀⡀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠀⠢⡠⠊⠉⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣍⠣⠡⣻⣦⠔⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠢⡑⠁⠀⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⠀⠰⢂⠀⠀⠀⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠑⢄⠀⠀⠀⠀⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐