Tongue Out Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢠⠀⣀⠀⠀⢠⣀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢂⠠⠴⠶⠶⠬⢌⣀⣙⣛⣀⣡⡤⠤⠶⠤⠌⡑⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣔⠕⣠⢞⣡⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣦⣍⡑⡄⢀⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡇⣰⡿⣻⣵⣷⣴⣴⣾⣿⣷⢭⣥⣭⣤⣶⣾⣿⣤⣴⣬⣙⢳⣾⣆⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢰⣿⣤⡿⣛⢫⡥⠭⢛⠴⠒⠲⢩⠵⠚⠒⢝⠉⠭⠻⢟⣻⣷⡌⣿⡄⢸⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠆⣾⣿⡯⠉⡁⠀⡀⠀⣨⠀⠀⠀⢸⠀⠀⠀⢰⡀⠀⢀⠀⠈⠻⣿⣜⣷⠘⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⢰⣿⣿⣹⣀⣷⣤⣷⣶⣿⣶⣶⣶⣾⣷⣶⣶⣾⣷⣶⣿⣴⣇⣠⢘⣿⣿⡆⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠈⣖⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⢸⣿⣿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⡇⢨⣭
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠈⡿⣿⢠⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⠻⣿⣿⡇⠬⠤
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣷⡀⣇⣿⡖⢒⣻⣿⡿⠋⠉⠀⠉⠻⣿⣿⠟⠃⠁⠀⠉⢻⣿⣗⡒⢷⣿⣿⡇⣾⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠼⠿⠇⢿⣿⡄⢠⠾⣿⠃⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⣿⣿⡀⢸⣿⣿⢠⣛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠸⣿⣷⠏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢿⠏⣿⣿⣿⡇⠼⣿⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡀⢻⣿⣷⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣬⢟⣾⠟⢸⣷⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣴⢆⢹⣷⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢛⣿⣿⠟⢰⣷⣌⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠋⠀⢿⣿⣷⣿⣷⣤⣆⣤⢀⡄⢀⡠⣌⣤⣶⣾⣷⣿⣿⡷⢠⣿⡙⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠙⠻⢿⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠻⢋⠰⣦⠙⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡰⢀⣌⠁⡻⣿⢿⣿⣿⣿⣿⡿⢁⡀⠄⠂⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⠁⡌⠓⢤⡡⠄⠋⠔⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣶⠾⠷⢶⣄⡀⠀⠀⣀⡴⠞⡓⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⠋⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠉⠛⠓⠮⣝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣠⣤⣤⣿⣦⣄⣀⠀⠀⣠⣾⣥⡤⠶⢦⣤⣄⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠉⠉⠙⠛⠛⠉⠉⠀⠀⠀⢀⣾⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣇⣠⣤⣶⣿⣿⣄⠀⣰⣦⣤⣤⣄⣠⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⠟⠉⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠙⢿⣿⣿⠿⠟⠛⠉⠉⠉⠁⠈⠉⠻⣿⣟⠛⠛⠛⠻⢿⡿⠃⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠙⣦⡀⠘⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠈⢳⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⢻⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡳⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡐⠳⣶⣤⣤⣤⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢬⣭⠥⠖⠋

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠳⣄⠀⣠⠶⠛⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣶⠋⠁⠀⠀⠉⠳⠦⠤⠶⠚⠉⠁⠀⠉⠛⢦⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⢀⡴⠞⢁⣴⣿⣿⣿⣿⣿⣷⣀⠀⠀⣀⣤⡀⠀⠀⠀⣠⣤⣀⠈⣧⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸
⣿⠀⠀⠐⢿⡀⠰⣿⣿⣿⣿⡿⠟⠉⠀⠉⠙⣻⠿⠛⠙⠲⠶⠚⠁⠀⠉⠉⠙⠳⢦⣤⡄⠀⠀⣹⡆⠀⢸
⣿⠀⠀⠀⠀⠹⣆⠘⣿⡿⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⡼⠋⠀⠀⢸
⣿⠀⠀⠀⠀⠀⢸⣶⠋⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⡴⠋⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⣼⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠾⠟⠛⠛⠛⠻⠶⣦⣄
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⣀⣤⣴⡶⠶⠶⢶⣦⣤⣀
⠀⠀⠀⢸⣿⡛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠀⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⢻⡏⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠘⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣠⣿⠉⠉⠉⠉⠉⢹⣿⠛⠛⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⢻⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⣿⡇⠀⠀⠀⠀⢨⣿⠻⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⡆
⠀⠀⠀⠀⠀⠘⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⣿⣦⣤⣤⣭⣽⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣹⣿⠿⠛⠉⠉⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡿⠟⠋⠁⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠋⠁⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⠶⠶⠶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠈⠉⠙⠓⠋⠉⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⣠⠴⠒⢿⠉⠉⠁⠙⡏⠀⠉⠉⡿⠒⠢⣄⣀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⢀⡞⠁⠀⢀⡴⠊⠉⢃⠀⠀⢘⣄⢀⣀⣠⣇⣀⡀⣠⠃⠀⠀⡘⠉⠑⢦⡀⠀⠈⢳⡀
⠀⠀⠀⠀⡞⠀⢀⣴⠃⢡⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣧⡀⠀⡌⠙⣦⡀⠀⢳
⠀⠀⠀⢸⠁⢠⡫⠈⣤⣴⣿⡿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⠿⠛⠛⠛⠛⠿⢿⣿⣦⣴⠀⠿⡄⠘⡇
⠀⠀⠀⢸⠀⣿⣱⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣿⠀⡇
⠀⠀⠀⠸⡄⠈⠻⣍⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⠟⠁⢠⠇
⠀⠀⠀⠀⢳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡞
⠀⠀⠀⠀⠀⠱⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⠎
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣀⣀⣀⣀⣤⣤⠴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢄⣀⠀⠀⠀⠀⣀⡠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠈⠑⠦⠔⠊⠁⠀⠀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠉⠀⠈⠑⠒⠤⢄⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢻⠻⣿⣿⣿⣿⣭⣁⣈⣻⠉⠉⠉⠉⡏⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⢉⣋⣉⣭⣽⣿⣿⣿⠟⢩⠏
⠀⠀⠀⠀⠀⠀⠀⢳⡈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠻⣿⣿⣿⠟⠋⠉⠉⠉⠙⢻⡿⠛⠋⠉⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⠟⠁⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢨⠏⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢬⡿⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⠃⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⡰⠋⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡠⠊⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠶⢤⣀⠀⠀⢀⣠⡴⠞⠛⠛⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠂⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣠⡴⠒⠒⠚⡏⠉⠉⠒⠒⠒⠲⠒⠒⠋⠉⠉⢹⠉⠑⠲⢇⣀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⣤⣾⣿⣿⣧⣤⣄⣠⡇⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢸⣀⣀⣠⣾⣾⣷⣶⣄⡀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⣠⣶⣿⣿⣿⡿⠟⠛⠛⠛⠿⠿⢷⣶⣤⣤⣤⣾⣧⣤⣤⣴⣶⡿⠿⠛⠛⠉⠉⠉⠛⠿⣿⣶⣦⣉⠄⠀⠙⠷⣄
⠀⠀⠀⠀⠘⣇⠀⠠⢴⣾⣿⣿⣿⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣿⣿⣿⣿⣶⠄⡀⣹⠆
⠀⠀⠀⠀⠀⠸⣆⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠁⢠⡟
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣾⣿⡿⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠁⠂⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢰⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢦⣤⣤⣤⣤⣤⣤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⢦⣄⡀⢀⣠⣴⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⣤⠶⠟⠛⠉⠉⠉⠉⠛⠳⠶⣤⣄⡀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣴⠟⣁⣠⣤⡶⠟⠋⠁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠉⠛⠳⢦⣤⣀⡈⢳⣄⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⣿⣿⣏⣩⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣹⣿⣿⠏⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠻⣿⣿⣿⣿⠿⠟⠛⠛⠻⠿⢿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠛⠿⣿⣿⠟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠹⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⢿⣟⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠙⢷⣌⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠙⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠶⠖⠛⠛⠋⠁




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⢀⣀⣤⣴⣶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢷⣶⣤⣄⣀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⢃⣠⣴⣾⣟⣛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣻⣿⣶⣤⣀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠷⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⡄⠉⠙⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠉⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣶⣶⣶⣶⡾⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠈⠉⠓⠲⠶⠖⠚⠋⠁⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣠⡄⠀⠱⠦⢄⡀⠀⠀⠀⣀⣠⣴⠂⠰⠶⢀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣠⡔⠈⠀⠁⠀⢠⡀⠀⠀⠀⠙⠁⠀⠀⠀⠳⠈⠀⢢⠑⢦⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⣿⣿⣶⣾⣀⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣨⣷⣶⣿⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣴⣿⣿⣿⠿⠟⠛⠻⠿⠿⢿⣷⣶⣶⣿⣿⣷⣶⣿⣿⡿⠿⠿⠿⢿⣿⣿⣷⠄⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠛⠛⠳⢦⣄⣀⣤⠶⠛⠛⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀
⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀
⢀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀
⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣦⣄⣠⣴⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⢿
⢸⡇⠈⠉⠛⠻⣿⡟⠛⠛⠛⠛⣿⠋⠉⠉⠀⠀⠈⣿⠀⠈⠉⠙⠛⠛⣶⠶⠶⠶⠶⠶⢶⣶⠚⠛⢛⣿⠋⣩⡿⠋⠀⠀⣾
⠀⢿⡀⠀⠀⠀⠙⢿⣷⣶⠶⠶⠻⣦⣤⣤⣤⣤⣼⣿⣦⣀⣀⣀⣀⣠⡿⠷⠶⢶⣶⡶⠟⠉⠛⠛⠋⢁⡾⠋⠀⠀⠀⢠⡟
⠀⠘⣷⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠻⢦⣄⠀⣀⡴⠋⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠘⣧⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠘⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣠⠴⠛⠁
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⣀⣀⣠⣤⣤⡴⠶⠛⠉
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⣄⡀⠀⠀⣀⡤⠴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠙⢦⠞⠉⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣤⠶⣿⠉⠉⠉⠉⠉⢻⡏⠉⠁⠉⠉⠙⡷⢦⣄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⣀⣠⡴⠚⠉⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣟⠀⠈⠙⠲⢤⣀⡀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣯⣴⣶⣶⣿⣿⣿⣷⣶⣦⣤⣤⣿⣤⣤⣄⣀⣀⣼⣧⣀⣀⣤⣤⣤⣿⣤⣤⣶⣶⣾⣿⣿⣿⣶⣶⣬⣽⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠙⣧⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠿⢿⡿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠛⠁⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣶⣶⣶⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣷⣶⣶⣶⣿⢟⡻⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣯⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠛⠛⠹⠋⠉⠉⠛⠛⣿⠛⠉⠉⠉⢹⠉⠙⢻⣿⣿⣿⣟⣽⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣅⡀⠀⠀⠀⣡⠀⠀⠀⢀⣸⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠈⠉⠹⢿⣿⣿⣿⠿⠛⠊⠉⠛⠉⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠈⠀⣰⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣷⣦⣄⣄⣴⣂⠈⣀⣠⡴⣞⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣻⣿⣿⣟⣫⡴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠻⣷⣄⠀⠀⣠⣴⣾⡿⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⢀⡀⠀⠀⠘⣿⣤⣾⣿⡟⠁⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣷⣶⣿⣷⣦⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠛⠛⠙⠛⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⣠⡀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣼⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠉⠛⠦⣤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢺⠗⠛⠲⣄⠀⠀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⢀⣠⡴⠚⠉⢰⠏⠀⡀⠀⠘⢿⡏⠁⠀⠀⠀⠀⢀⡏⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢸⠳⢤⣄⣀⡟⠀⠀⢻⠀⠀⠘⢿⣶⣤⣤⣄⣀⣼⡁⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠸⡆⠀⠈⠻⣇⠀⠀⠈⢧⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣿⣿⣄⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⠳⢦⣄⡈⢧⡀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠿⠿⣿⣿⣿⣦⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠙⠳⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⣄⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣹⣿⡿⠿⠒⠒⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠁⠀⠈⠉⠛⠻⠶⠶⠟⠛⠋⠉⠀⠀⠀⠉⠙⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⣉⣁⣤⠤⠤⠤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣤⣤⡴⠶⠶⠶⠶⠶⣦⣤⣙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⡄⠀⣀⣠⠤⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠉⠉⢉⣯⠁⠀⠀⠀⠀⠸⣇⠀⠀⠈⠙⠳⣮⣙⠂⠀⠀⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⡀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⢷⣤⡶⠻⣧⣀⣀⡀⠀⠀⣀⣀⣁⠀⠀⠀⠀⣀⣀⣼⣧⣀⣀⣠⠳⣄⡴⠀⠉⠛⠛⢿⡖
⠀⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉⠙⠛⠋⠉⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠋⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⡰⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⢈⣭⣴⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⠤⣴⣞⠁⠀⠙⢿⡄⠀⠀⢀⣾⠏⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢸⠀⠀⠀⠹⡏⠉⠉⠙⣿⠷⠶⠶⢷⡟⠁⠀⠀⠈⠓⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠁⠀⠀⠀⡏⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣀⣠⡴⠟⠋⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠰⣆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡆
⠀⠀⠀⢻⣧⣜⠿⡇⣀⠀⠀⠀⠀⠀⠉⣨⢽⣿⣷⡂⢠⣤⣾⡿⡶⠓⠂⠀⠀⠀⣀⢐⡿⢉⣴⣿⠁
⠀⠀⠀⠀⢿⣿⣿⣏⠛⠓⠂⠀⠀⠀⠀⢤⠔⠒⠒⠶⠓⠒⠃⠤⠀⠀⠀⠠⠘⠛⠛⢋⣿⣿⣿⠇
⠀⠀⠀⠀⠸⣟⢻⣿⣿⣷⣴⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⡿⢹⡏
⠀⠀⠀⠀⠀⠻⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠙
⠀⠀⠀⠀⠀⠀⠸⠀⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡉⠛⠿⣿⣿⣛⠉⠉⠉⠉⠉⠈⠉⠻⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠙⢀⣀⠀⠈⠉⠙⠋⠙⠚⠉⠁⠛⠉⠉⠀⢀⣀⠀⠀⢀⣼⣷⡄
⠀⠀⠀⠀⣠⣼⣿⣿⣿⣆⠀⠠⠬⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠋⢀⠀⣠⣾⣿⣿⣷⣤⡀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠈⠛⠛⠖⠲⠒⠚⠛⠁⠊⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⠀⠀⠀⣿⢿⣷⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⠋⡿
⠀⠀⠀⠙⠀⢿⣿⣮⡛⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⣶⣶⡶⠶⠶⣶⣶⠶⢶⣻⠿⢛⣭⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣮⣍⠂⠉⠉⠓⠂⠁⠀⠉⠙⠲⢌⠛⠷⣦⣤⣤⣴⠞⠋⠀⠒⣉⡥⠴⠖⠛⠩⠥⠖⠊⣉⣤⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣇⢿⣿⣿⣧⠀⠙⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢹⡜⣿⣿⣿⣷⣤⣾⡇⠀⠈⠙⣿⣿⡿⠷⢶⣿⣶⣶⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣩⣿⣿⣿⣿⣿⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣧⢹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠛⣿⠀⠀⠀⠈⢿⣿⡟⠛⠛⠿⢿⣿⡏⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⡇⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣄⡀⠀⠀⠘⣼⡀⠀⠀⠀⣘⣽⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠁⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⡏⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⣿⣿⠃⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡈⢿⣿⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣴⣿⣿⣿⡟⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠈⢿⣿⣄⣼⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣠⣼⣿⣿⣿⣿⠃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠚⠻⣿⣿⣆⠀⠀⠈⠉⠉⠉⠛⠻⠛⠋⠉⠙⠃⠀⠀⣴⣿⣿⣿⣿⢟⣿⡏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠈⠻⢿⣿⣶⣶⣦⡀⠀⢰⣸⡄⠀⢀⣼⣷⣶⣾⣿⣿⡿⠛⢋⣾⡿⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠟⢻⡿⠿⠿⠿⢿⣿⣿⣾⣿⣿⣿⠿⠟⠿⠉⠓⢀⣾⡿⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠹⡆⠀⠀⠀⢀⣱⣿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⣄⣸⣇⠀⠀⠀⠀⠀⣄⠀⢀⣀⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡀⢀⠀⢀⣤⡀⡇⠀⣧⣀⠀⢀⣣⢇⣠⢡⠅⠀⣀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⢾⣦⡴⣷⡘⣷⡸⣿⣷⣷⣀⣿⣿⣆⣸⣿⣾⣿⣿⣏⣼⣾⣾⣳⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡢⡣⡠⣳⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣴⠏⢀⢀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣏⣴⡷⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠓⣿⣿⣿⣿⣿⣿⣿⣿⠉⠐⠒⠒⠛⠩⠭⠟⠛⢭⠭⠿⢛⣒⡀⢙⡻⠿⣿⣿⣿⣿⣷⠞⣠⣀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣌⣿⣿⣿⣿⢋⣝⣥⢾⠷⠿⢷⣿⡿⣿⣿⣾⠿⠿⢿⣿⠿⠿⣶⣬⡣⠹⣿⣿⣿⣿⣿⣯⣕⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠪⣶⣿⣿⣿⣿⢇⡾⢛⣽⣾⡿⢾⣿⡿⠿⠲⣶⡶⢶⠿⣿⡷⣶⣾⣶⣍⠿⣷⡸⣿⣿⣿⣿⣿⠗⣁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⣉⣻⣿⣿⣿⣿⡏⣾⣷⣿⣭⠉⠷⠓⢪⠈⠉⠉⢱⠊⠁⠉⠃⠈⠓⠙⠫⣽⣷⡸⣧⢸⣿⣿⣿⣿⣿⣽⡪⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣌⣹⣿⣿⣿⣿⢻⣿⣟⡃⢠⠀⣦⠀⣰⡄⠀⢀⣸⣀⠀⠀⣸⡀⢀⡄⢠⠀⠻⣿⣿⡏⣿⣿⣿⣿⡿⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣻⣿⣿⣿⣿⢸⣿⡷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣢⣿⣿⡿⢹⣿⣿⣷⣶⠿⠒⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⣛⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⢸⣿⣿⣿⣿⣿⣷⣒⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣯⣭⣥⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣒⣻⣿⣿⣿⣿⡷⢻⣿⡇⠢⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⡠⣽⣿⣇⣸⣿⣿⣿⣯⣭⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣛⣿⣿⣿⣿⣧⢸⣺⣇⡍⠸⣿⡛⠉⠀⠀⠀⠉⢿⡿⠉⠀⠀⠀⠈⣹⣿⠠⢥⣼⣿⡿⢹⣿⣿⣿⣿⣩⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣶⣿⣿⣿⣿⣿⡾⣿⣏⠀⣃⠸⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡿⢥⡒⠀⣿⣿⡇⣾⣿⣿⣿⣿⣿⣝⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠛⠋⢹⣿⣿⣿⣷⣿⣿⣴⠃⠀⡠⠷⣄⡀⠀⠀⢀⡀⠀⠀⣀⣴⠿⣀⠀⢻⣴⣿⣿⢡⣿⣿⣿⣿⣶⣌⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠟⣿⣿⣿⣿⡸⣿⣷⣴⡞⠀⠀⡉⠙⡳⠲⠾⠷⠖⠟⠋⠃⠀⢈⣧⣸⢿⣿⢃⣿⣿⣿⣿⠿⣿⡿⠛⠅⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠾⣻⡿⣿⣿⣷⡝⣿⣽⣧⣥⣶⠄⢀⡁⠀⢰⠀⠀⢃⣀⢼⣶⣬⢿⣷⡿⢇⣾⣿⣿⣿⣿⣷⣤⡉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⣡⣾⣿⣿⣿⣷⡹⣿⣿⣿⡛⠿⠟⠃⠙⠛⠓⠈⠛⠿⠿⣻⣷⣿⣿⡇⣾⣿⣿⣿⣿⣎⠙⠿⠫⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣪⠟⣡⠟⣹⣿⣿⣿⣍⠻⢿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣾⣿⣿⠿⠿⣫⣾⣿⣿⣿⣿⣿⣿⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠞⠁⢀⢾⣿⣿⣿⣿⣿⣶⣬⣭⣙⠻⠭⠭⠭⠍⢛⣋⣉⣠⣶⣿⣿⣿⣿⣿⣟⠻⡯⡃⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣆⠈⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠟⢩⠏⢻⣿⠃⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡉⣏⢿⢿⠈⠻⠁⠀⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠃⠀⠋⠏⢘⠏⣿⡟⣟⡏⡇⢿⣿⡿⡟⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠃⠁⠀⠇⠇⠃⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⢀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⠿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢫⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣽⣿⠿⠻⣿⡟⠁⠀⠈⠻⠃⠀⠀⠈⠻⠏⠉⠉⢿⣿⣿⣮⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠻⣏⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⠀⠀⢀⡀⠀⣴⣷⣦⣤⣴⣿⣷⣤⣤⣴⣷⣦⣤⣤⣄⠀⠀⠀⠟⠛⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠵⠀⠐⠂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⠀⠀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣷
⠀⠀⠀⠀⠀⢰⣿⣿⢧⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⠁⠑⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣏⣀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢿⣿⣿⡆
⠀⠀⠀⠀⣾⣿⣿⣉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣼⣿⣿⣇
⠀⠀⠀⠀⣿⣿⢿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣽⣿⣿
⠀⠀⠀⢸⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡄
⠀⠀⠀⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠃
⠀⠀⠀⠀⢹⣿⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣿⡿⣼⡿
⠀⠀⠀⠀⢸⣿⣧⡿⠿⠟⠛⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠃⠀⢸⣿⢧⣿⠇
⠀⠀⠀⠀⠈⣿⣿⣧⠀⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⢸⣿⣾⡿
⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⠇
⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⡀⣻⣿⡟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⡀⠀⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣤⣱⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣹⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣰⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⢿⣆⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⢳⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⢻⣿⣄⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡿⣳⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡻⣿⣿⣦⣤⣦⡀⠀⣠⡄⠀⢀⡀⠀⢠⣄⣀⣴⣶⣶⣾⣿⣿⣿⢳⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣼⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣮⣟⣻⠿⢿⣿⣿⡿⠿⠿⢿⣟⣻⣽⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠿⠶⢶⣤⣤⣀⣠⣤⣴⣶⠶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠍⠉⠉⠉⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⢶⡿⠛⠻⠶⢶⣦⣤⣤⣤⡶⠶⠶⠶⣶⢶⣤⡀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣁⣐⣀⣀⣤⣤⣴⣶⣿⣯⣄⣀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣯⣀⣈⣉⣳⣦⣤⣀⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣠⣿⣤⣀⣀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⡿⠋⣺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠘⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠋



⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠛⠛⠛⠻⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⣀⣠⣤⣤⣤⣀⣈⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣤⣤⣤⣀⣀⠀⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⣄⠀⢹⣿⣿⣿⣆
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⣀⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⣾⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⠋
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⣿⣿⡿⠁
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣼⣿⣿⣿⠟⠁
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⣾⣿⣿⣿⠋
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣠⣾⣿⣿⣿⡿⠁
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣠⣴⣿⣿⣿⣿⡿⠋
⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠸⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠈⠛⠿⣿⣶⣶⣶⣤⣶⣶⣿⠿⠟⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠻⡇⠀⠈⠑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣦⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠅⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⡟⠀⠀⠀⠀⠀⠀⣠⠤⠖⢾⠁⢀⠌⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠓⣴⠊⠉⠉⠙⠞⠀⠀⢀⠤⠊⠁⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠙⠒⠦⣄⠀⠀⠀⢀⡤⠖⠒⠛⠙⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢻⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀
⢴⣮⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⣤⠴⠖⠚⠉⠁⠀⠀⢸⠀⠀⠀⠉⠙⠒⠲⢦⡤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡭⣶
⠈⢯⠻⣿⣿⣿⣿⣿⣶⣭⣍⣉⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣨⣧⣤⣶⣶⣿⣿⣿⣿⠟⠋⡴⠁
⠀⠀⢧⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣴⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⠞
⠀⠀⠀⢣⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⠋
⠀⠀⠀⠀⢳⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡴⠁
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠙⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⡹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⠟⠁⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢖⡾⠋⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡰⠋⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣠⠞⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠚⠁⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⠀⣀⣀⣀⡤⠖⠊⠁
⣶⣶⡾⠷⠶⠶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠲⢦⣄⣀⡀⠀⠀⣀⣠⡴⠶⠛⠻⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢀⠀⠁⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣠⡤⣀⠈⠶⢤⣀⡀⠀⠀⠀⢀⣀⣤⡶⠂⠶⠶⢁⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣠⠖⠋⠘⠃⠀⠀⡀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠈⢦⠊⠀⢢⡝⠢⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣠⣾⣿⣦⣤⣦⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⣄⣨⣦⡀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⣤⣤⣤⣴⣦⣤⣤⣤⣴⣾⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⣿⣿⡿⠋⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠻⣿⣿⡟⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⡏⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢨⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⠤⠤⠤⠶⠖⠚⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢻⣿⣿⣿⣤⡉⠉⠉⠉⠉⢻⡏⢻⡏⠉⠉⣨⣼⣿⣿⣿⠛⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⢠⣬⣽⣿⣿⣿⡄⠀⠀⠀⠘⠃⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠈⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠃⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⢠⣿⣿⣶⣄⡈⠛⠀⠀⠀⠀⣾⣿⡆⢰⣿⡷⠀⠀⠀⠘⠁⣀⣤⣶⣾⣷⡀⠀⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⡇⠀⠈⣿⣿⠻⠿⣿⣷⣶⣤⣤⣀⣈⣉⣀⣈⣉⣁⣀⣤⣴⣶⣿⣿⠿⢛⣿⣿⠀⠀⢸⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣠⣿⡿⠃⢸⣿⣇⠀⠀⣿⣿⡆⢠⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⠿⠿⠟⣿⣿⣿⣷⡀⢸⣿⡏⠀⠀⣾⣿⠇⠙⣿⣷⣄⡀
⠀⠀⠀⣠⣾⣿⡟⠁⠀⠈⣿⣿⡀⠀⢸⣿⣿⣿⣿⠉⣿⣿⡄⠀⣠⣿⣿⣿⣷⣄⠀⢰⣿⡿⠙⢿⣿⣿⣿⠃⠀⢠⣿⡿⠀⠀⠈⢿⣿⣷⡆
⠀⠀⠀⠙⢿⣿⣷⣶⣶⣶⣿⣿⣧⠀⠀⠙⠿⠻⡿⠀⠘⣿⣿⣾⣿⡿⠁⠘⢿⣿⣶⣿⣿⠃⠀⠀⠙⠿⠋⠀⠀⣼⣿⣷⣶⣶⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⢻⣿⢻⣿⠛⢿⣿⣆⢀⣠⣶⣶⡄⠀⠀⠙⠿⠟⢿⠇⠀⠀⠀⠙⢻⣿⠃⠀⠀⢰⣶⣶⣄⠀⣴⣿⡟⠛⠛⢿⡿⠉⢹⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠘⠛⠀⠈⢻⣿⣿⣿⠿⣿⣿⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⣿⣿⠿⣿⣿⣿⠟⠀⠀⠀⠈⠁⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⢿⣿⣿⣦⣿⣿⡄⣠⣾⣿⣿⣷⡀⠀⠀⢀⣿⣿⣿⣷⣄⢸⣿⣿⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣿⣿⣿⣿⣿⠟⠁⠹⣿⣷⣄⣠⣿⣿⠃⠈⠻⣿⣿⣿⣿⡿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⣿⣿⣷⣤⣄⣀⠙⣿⣿⣿⣿⢁⣀⣠⣤⣾⣿⣿⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠉⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢹⣿⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠇⠀⢿⣿⣿⡉⢉⣿⣿⠟⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣤⠶⠚⠛⠛⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠁⠀⠀⠉⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡠⠴⠒⠒⠛⠛⠓⠲⠦⠤⠀⣀⣀⣀⡀⠤⠖⠒⠉⠉⠉⠙⠲⢤⣀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⠖⠋⠀⢀⠤⠖⠲⠢⠤⠤⠤⠒⠂⠠⠤⠶⠒⠒⠒⠚⠋⠉⠉⠉⠓⠢⢌⠳⣄⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠠⠃⣀⠤⠒⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠙⢮⣣⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣰⠇⡞⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠃⠀⠀⢀⡇⢣⡀⠀⣷
⠀⠀⠀⠀⠀⠀⢠⡟⠀⡰⢻⠀⢳⡀⠀⣠⠖⢢⣤⡤⠖⢦⣀⣀⣀⣀⣀⣁⣀⣀⣀⡤⠖⠉⠉⠐⡎⠉⠙⠒⠶⠞⠀⡿⠱⡄⢻⡀
⠀⠀⠀⠀⠀⢀⡾⠁⡴⠁⠘⡇⠀⠉⠉⠁⢀⠏⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢰⠃⠀⠙⢾⣧
⠀⠀⠀⠀⠀⠹⣵⡋⠀⡀⠀⢻⠀⠀⠀⠀⢸⠀⢀⣀⣀⡀⠀⠈⠣⠤⠤⠞⠀⢀⠠⠤⠠⠤⠤⠄⣾⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⢻⡵⠀⠀⠀⣸⠀⠀⢀⠄⠚⠉⠉⠀⠀⠀⠉⠙⠒⢄⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⢸⠀⠀⠘⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠈⣷⢣⠀⢰⠃⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢸⡀⠀⠀⢀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⢃⢸⡀⢸⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⡇⠀⣠⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢾⡇⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠹⡴⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⢧⡸⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⢧⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⣇⡜⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠑⢄⠀⠙⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠚⠁⠀⡨⠋⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠳⣆⠀⠀⠘⠲⠤⠤⡀⠀⠀⠀⢀⣀⠀⣀⣀⡠⠔⠁⠀⠀⢀⠔⠋⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠙⠢⠄⡀⠐⠀⠈⠒⠒⠒⠉⠀⢀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠤⠤⠤⠬⠤⠄⠐⠊⠁⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢤⣤⣤⣤⡤⠴⠞⠛⠶⢤⣤⣤⣤⡤⠶⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⠋⢹
⠀⠀⠀⠀⠀⠀⠚⡟⠳⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡶⠛⣿⢀⡾⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠸⣄⠈⢹⠙⠓⡶⠦⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠖⢲⡏⠉⠀⠀⡇⢀⡿⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠓⢾⣀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢹⠉⠉⠉⠉⡏⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⢀⣠⠟⠉⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠳⠤⣄⣀⡇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⣀⣀⣨⠷⠚⠉⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠒⠒⠶⠾⣤⣤⣤⣤⠷⣶⠒⠒⠚⠉⠙⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠻⣄⠀⣠⠏⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⡀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣠⠴⠒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⣀⡤⠤⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⣠⠞⠁⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣟⣁⣤⣾⣥⣴⣖⣲⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⡖⠛⠋⠹⡏⠉⠉⠉⢹⠀⠀⠀⡇⠀⠀⢹⠉⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⣇⠀⠀⠀⢸⡀⠀⠀⣇⠀⣀⣸⡤⠖⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠚⠓⠒⠒⠛⠉⠉⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⢀⣀⣀⡤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢴⠀⠴⢶⢀⠰⡶⣦⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡀⡶⢻⣿⠋⠀⡄⠀⢘⡁⠀⠀⠈⠀⠹⢿⣿⣶⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠧⠇⢸⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠉⣿⣧⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⡄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⣻⢻⣿⠀⡇⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⠃⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⡟⢸⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⣇⣸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣠⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣿⣷⡀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣱⣤⣿⣶⣾⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣆⠀⠀⠀⠀⠀⠀⠀⣠⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣔⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠀⣻⣿⣿⣿⣿⣿⡇⢰⣿⣿⣦⡀⢠⣿⣿⣿⣿⣿⢿⡉⠈⢿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣰⣏⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢛⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⢉⣿⣿⣿⣿⣿⣿⣧⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠙⠻⠇⠉⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠹⡿⠉⠙⠿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⡀⣤⡰⢀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⡀⢠⡇⠀⢀⢸⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣷⣮⠀⡄⠈⡏⠹⣿⡿⣿⡿⢿⡿⠁⠀⡇⠘⣧⣠⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣧⠀⡇⠀⢾⠓⡇⠀⢸⡇⠀⠀⡇⣠⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣦⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠋⠹⠿⡿⠿⣿⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠀⣀⣠⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢿⣿⠻⢿⡟⠟⢻⠟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣹⡇⠛⠀⠇⠀⢸⠀⠀⣼⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⢻⡷⣀⡀⠄⠀⢀⡀⠀⣿⠄⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠃⠂⠘⠈⠋⠀⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⣤⣀⣀⠀⠀⠀⢀⣠⣤⠴⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠉⠀⢀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⢀⣆⣶⣿⣾⣤⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⣴⢻⡟⠙⠛⠷⢶⣿⡿⠛⠋⠉⠛⣿⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⡞⠁⠀⠃⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⢹⡆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⣴⣾⣿⣀⣀⣀⣄⣀⣀⣀⣀⣿⣀⣤⣤⣾⣶⣿⠇⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⣿⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠔⣫⣾⣿⣿⣿⣿⣿⣮⣝⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠉⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠠⢪⡾⠟⠛⠛⢿⣿⣿⣿⠿⠛⠛⠛⠿⣿⣿⡏⢿⠘⢀⠆⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠘⢿⣇⠘⠀⠘⠀⠀⡄⡴⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣴⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⡀⠀⠀⠀⠀⠈⢿⣷⣄⠀⢰⣼⣿⣳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⢿⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡀⠀⠀⠀⠈⣯⠉⠿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠹⣿⣟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠇⠀⠀⠀⠀⣿⠶⠶⣼⣿⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡘⠟⢧⡉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠠⠬⣼⡏⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡕⠄⠀⠻⣷⣦⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⡿⠷⠒⣞⠓⣼⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢦⠀⠀⠈⠻⢦⡀⠀⠀⠹⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡕⠀⠀⠀⠀⠙⠳⢤⣤⣀⣀⣀⣤⣤⠤⠤⠒⠊⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣑⠢⣤⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣙⠯⢟⠲⠬⠝⡛⠒⠒⠲⠒⠂⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠤⠤⠶⠶⠶⠶⠖⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠛⠛⠛⠛⠛⠿⣷⣦⡀⢀⣴⣾⠿⠛⠛⠛⠛⠛⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⡀
⠀⠀⢀⣤⣀⣤⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣤⣀⣤⡀
⠀⠀⢸⣿⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣿⡇
⠀⠀⠀⢿⣿⢿⣿⣿⣶⠶⠿⠿⢿⣿⠿⠟⠛⠛⣿⡏⠉⠉⠉⠉⣿⠋⠉⠉⠉⢹⣿⠛⠛⠛⠻⢿⡿⠿⠿⠿⣶⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠈⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣿⣧⣀⣀⣀⣀⣿⣆⣀⣀⣀⣸⣿⣄⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⠁
⠀⠀⠀⠀⠘⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣿⠃
⠀⠀⠀⠀⠀⠘⣿⡄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⠻⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠉⠉⠛⠿⣿⣿⡿⠋⠁⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠉⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣶⣶⣶⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢰⡆⠀⠀⡀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢳
⠀⢠⣾⣦⡅⢠⣄⣤⣶⣾⣷⣦⡈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⣿⣿⢰⡄⢹⣿⣿⣿⣿⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣠⠛⢣⣿⣇⠈⠉⠙⠙⢉⣤⣴⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡞
⢸⠁⠀⠈⠙⠋⠄⠀⢀⣹⡄⠀⠙⠂⠈⡉⣩⡥⣄⠀⠀⠀⠀⠀⠀⣼⠁
⠀⢳⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣤⣶⣿⣟⣿⣦⣿⡀⠀⠀⠀⢀⣾⠃
⠀⠘⢛⠙⠛⢻⣓⣒⣻⣩⠥⣿⣿⡿⠉⠙⠉⣾⡿⠿⠷⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⢠⠿⠭⠭⠯⠇⠧⠐⠐⠂⠡⠚⢀⣴⡄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠮⠭⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠙⠛⠒⠢⠤⠤⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠀⠀⠀⠀⠄⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⣠⣾⣷⣶⣦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠡⠀⢿⣿⣿⣿⣿⡧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⣶⣄⠈⠉⠛⠛⠛⠃⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠛⡿⠀⢲⡦⠄⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⢀⣠⡢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠁⢈⣿⣶⡶⠙⠋⡰⠉⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠒⠲⢲⢚⣲⠨⠿⠟⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠍⠙⡹⠉⠇⠃⠀⠁⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⡶⠶⣦⣀⠀⠀⠀⢀⣠⠶⠶⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠕⠋⠁⠀⠀⠀⠉⠛⠓⠒⠋⠁⠀⠙⠛⠲⠮⣙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣀⣀⣈⣷⣤⡀⠀⠀⠀⠀⣠⣊⣀⣤⣤⣄⣀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣶⡿⠛⠋⠉⠉⠛⠛⠿⠶⠶⠟⠛⠉⠁⠀⠀⢩⣿⣿⣶⣤⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣀⣴⣾⣏⠁⠀⢠⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣴⣿⣿⠿⠛⢩⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠋⠈⠻⢿⣿⣿⣿⣿⣷⠶⠿⠛⠛⠛⠛⠻⢿⣿⣿⠿⠿⠿⢿⣿⣿⡿⠃⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠈⠻⣅⠀⠀⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠘⢷⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⢻⣆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡑⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠳⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠛⠷⣶⣦⣤⣴⢶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⠶⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠛⠛⠛⠷⡾⠛⠉⠀⠀⠀⠀⠈⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⣀⣀⣠⠴⠖⠛⠛⠛⡛⠓⢦⣀⠀⠀⠀⠉⠙⠓⠒⠒⣲⠆
⠀⠀⠀⠀⢲⣶⣦⡴⠶⠟⠋⠁⠀⠀⣀⣤⣾⣋⠉⣸⡀⠀⢀⠈⠉⠉⡄⠀⠀⣰⣤⠴⠟⠛⠋⠉⠙⠒⠒⠒⣲⠖⣠⡞⠁
⠀⠀⠀⠀⠀⠙⣷⡄⠀⣤⣤⣤⠶⠟⠋⠁⠀⠉⠉⠉⠙⠛⠛⠳⠶⠛⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢰⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⡞⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠹⢦⣀⠀⠀⢀⣤⡶⠟⠛⠋⠙⠉⠛⢻⡟⠉⠁⠀⠀⠈⠉⠙⠳⢦⡀⣸⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⠙⢷⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠙⠻⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠞⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠉⠛⠿⣯⣿⣉⣉⡋⠙⠋⢹⠉⣹⣤⠿⠛⠁⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣀⣤⣴⣾⣶⣦⣤⣶⣀⣤⣤⡀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠢⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢤⣀⡀
⠀⠀⡼⠛⠛⠻⢿⣿⣿⣿⠿⠟⠛⠛⢯⠉⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⢄
⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣿⠈⣵⣶⣶⣶⣤⠀⣤⣶⣶⣶⣦⠁⣿⠇⠀⠀⠀⠀⢻⡇⢈⣤⣶⣤⣄⡀⠀⣠⣤⣴⣤⡌⠀⣿⠁⠀⠀⠀⢻⡇⢘⣤⣴⣤⣄⡀⢀⣠⣤⣤⣤⡛⢸⡟
⠀⢻⢸⣿⣿⣿⣿⣇⢀⠸⣿⣿⣿⣿⢧⡟⠀⠀⠀⠀⠀⠈⣧⢼⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿⢰⡏⠀⠀⠀⠀⠈⣧⢼⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣷⣼⠃
⠀⡜⠀⠉⠋⠉⠁⣽⣿⣇⠈⠉⠙⠉⠀⢣⠀⠀⠀⠀⠀⠀⡟⠈⠛⠛⠛⠉⣿⣿⡈⠙⠛⠛⠋⠘⡄⠀⠀⠀⠀⠀⡟⠈⠛⠛⠋⠉⣿⣿⡈⠙⠛⠛⠁⢹⡀
⠀⠙⣶⣀⣤⣼⣶⣿⣿⣿⣶⣥⣄⣀⣶⠋⠀⠀⠀⠀⠀⠈⠳⡆⢀⣀⠲⠄⠉⠙⠁⠴⣠⡀⠀⡶⠃⠀⠀⠀⠀⠀⠳⡆⢀⣠⠲⠄⠉⠉⠁⠖⣤⡀⢰⠞⠁
⢀⣀⣼⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢹⠿⣿⣇⣀⣊⣉⣉⣺⣿⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⢹⠟⣿⣇⠂⠈⠃⠐⣺⣿⠟⡏
⠀⠈⢹⣿⡏⠿⡿⣻⣻⢟⡻⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠸⣿⡿⢿⢿⠿⢿⡿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠙⠛⠒⠓⠛⠉⠁⠰⡇
⠀⠀⠸⣿⣿⣷⣶⣿⣿⣷⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⠉⠈⠉⠀⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠉⠹⠿⢿⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠈⠻⣦⠀⣠⡶⠛⠉⠁⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣠⡴⠞⠛⠛⠳⢦⣀⠀⠀⢀⣠⣤⠶⠞⠛⠶⢦⣀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⣀⣴⣿⣏⣀⣠⡄⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⣀⡴⠟⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣠⣶⣄⠀⠀⠀⢀⣴⠶⣤⣀⣹⣆⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠈⠻⣄⠀⢺⣿⣿⣿⣿⣿⠿⠋⠁⠀⠈⠉⢉⣿⠟⠋⠉⠛⠛⠛⠋⠁⠀⠀⠉⠉⠙⠳⢦⣤⡄⠀⠀⠀⣹⡗
⠀⠀⠀⠀⠀⠙⢧⡀⠹⣿⣿⠟⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⢷⣤⠟⠁⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⣰⠏
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣰⠏
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣰⠏
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⠏
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠋
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣠⡞⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⣴⠞⠁
⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠚⠉
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⡀⠀⠀⠀⢀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠷⢶⣤⣤⡶⠟⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⡾⠛⠉⠁⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣴⣿⣿⣷⣤⣤⣤⣴⣤⣤⣤⣾⣷⣿⣿⣦⡀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠛⠉⠁⠀⠀⠉⠙⠻⠿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠉⠙⠻⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣄⡀
⢀⣀⣀⣀⣤⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣀⣀⣀⣀
⢻⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣷⣶⣤⣀⣤⣴⣶⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿
⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠉⠁⠀⠈⠉⠙⢻⣿⣿⠛⠉⠉⠀⠀⠉⠙⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⢀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⣀⡀⠀⠀⣀⣀⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠙⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⡴⠛⠁⢀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⣧⢐⣤⡀⠙⠶⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⣠⠞⠁⠘⣿⣿⡆⢸⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿
⠀⠀⢻⣷⡀⠀⠿⠿⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⣄⠀⠀⠀⠀⠀⢸⣷⡟
⠀⢠⡿⡿⠁⠁⠀⠀⠸⣿⠻⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇
⠀⢸⡇⠀⠀⠈⠀⢀⣀⣠⣁⣀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡟
⠀⡟⢣⢴⡰⡤⢆⠤⡄⣹⣿⠉⠥⣾⣷⣾⣷⣶⣤⣀⠀⢀⣠⣤⣾⣿⣿⡟⠁
⠀⣗⢳⣾⣤⣧⡞⡄⢲⣾⠋⢀⣾⣟⡽⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⠿⠋
⢀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⡾⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠒⠲⠶⢤⣄⡀
⢾⡀⠀⠀⠤⠖⢀⣠⣤⣀⡠⣚⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠙⠛⠓⠒⠛⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⢳⣶⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣿⡿⣧⣦⠠⣿⣿⣿⣿⣿⣿⡂⡼⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡟⣿⣧⠈⠛⠛⠛⠉⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠀⠀⠈⠁⠀⠀⡲⣄⣀⠀⢀⡀⠀⠀⠈⠓⠂⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠱⣤⣭⣴⡏⠉⣧⣠⣶⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠱⠐⠎⠒⠒⠒⢚⣿⣿⡿⠁⠀⣈⣿⣿⣄⡀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡉⠛⢚⠒⠒⠚⠚⢛⣛⠟⠀⢠⣿⣿⠞⠻⢿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠉⠉⠉⠉⠛⠁⠀⢠⣿⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⠤⠤⠤⠤⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣦⣄⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⢟⣛⣭⣭⣭⣭⣭⣛⡻⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡻⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⣫⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣂⣙⠿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢟⣵⣾⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣷⣮⡻⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣶⣿⣿⣿⡿⣫⣴⣾⣿⣿⣶⣶⣭⡟⣫⣵⣶⣾⣿⣿⣶⣮⡻⣿⣿⣿⣶⣭⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣭⡻⢿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⠟⣫⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡴⠞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⡜⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⠂⠀⠀⢠⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⢀⣈⢂⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⠀⠠⠀⠀⢀⠤⢤⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣑⠢⠀⠀⠀⠠⠊⢠⡀⠈⠁⠒⠂⠤⠄⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡈⠠⠀⠀⠀⠀⠀⠇⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⣣⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡴⠉⡮⠘⢶⣾⠀⠐⠄⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⠁⠀⠀⠐⠀⠀⠀⠁⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠂⠠⠀⡀⡆⠀⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠀⠀⢀⠁⠀⢀⠆⠆⢰⢰⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠜⠀⡴⢁⣀⡀⣸⠀⠀⢬⣠⠀⡇⠈⠀⡄⡀
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣿⠇⠀⠀⠀⠁⠀⢰⠁⠆⠀⠃⠃
⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⠐⡇⠂⠒⠂⠀⠛⢄⠀⠀⡦⠠⣀
⠀⠀⠀⠀⠀⠀⠈⢰⠉⡄⠐⠃⠀⢀⡀⢀⠀⢀⠀⢀⠀⠁⠀⢀⣠⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠸⡈⢁⠀⢀⢌⣁⡀⠈⢦⡇⠀⢸⡠⠔⠊⠇⢐⠤⠜⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡗⠀⠀⠀⠀⢸⡇⠀⠀⠓⠚⠒⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⣎⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠛⠒⠒⠚⠃⠤⠤⠤⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠆⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡇⣰⣿⣛⣷⣆⢸⡇⠀⢹⠆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣷⢿⣍⣉⣭⡍⢸⣧⣤⣿⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠛⠋⠀⠉⠉⢉⣠⣬⠉⢹⡏⠀⠰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣥⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⣶⠀⢈⠛⡀⠀⠂⠀⠁⣶⢦⠀⡄⡄⠀⠞⠀⠀⡼⢫⠀⣸⠂⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⢷⡄⣀⠹⠃⠘⡄⢁⠀⠈⠁⠐⡹⠋⠀⡁⠁⠀⠐⠀⠄⣀⠉⠐⠀⡄⡀⠀⠠⡇⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠊⢆⠄⡀⢀⠁⠀⠀⢠⡀⠀⠁⠒⠄⠀⠀⠀⠀⠁⠀⠠⠀⡀⠀⠈⠀⠂⠄⢀⠐⠀⠴⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠁⠂⠄⡀⠀⠀⠀⠐⠠⢀⣨⠷⠦⠤⠀⢀⢀⠀⠁⠂⠀⠀⢀⣀⣁⣀⣀⣀⣀⠀⠀⠁⠀⠀⡀⠀⠀⠞⠡
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠙⠐⠁⠂⠄⠀⠁⠁⢀⠐⠋⠉⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⠀⠈⠀⠠⠀⡀⠀⠀⠐⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠄⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⠀⠀⠐⠂⠀⢀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠁⠄⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠁⢡⣿⠀⠐⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠐⠠⢀⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠚⠻⠟⠛⡉⠃⢀⢤⣴⣿⣿⣿⡶⡶⣶⠤⣰⢶⣾⣿⣿⠷⣶⣶⣶⠶⣶⣶⣾⣿⣿⣦⣤⣤⣄⣠⣧⡿⣿⢶⣤⣤⣀⣀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠉⠉⠉⠉⠉⢿⡍⠀⠀⠀⠀⠀⢹⠃⠀⠠⠀⠀⠀⡀⢳⡋⡉⠉⠉⠉⠉⢻⡟⠋⠐⠀⠀⣬⠋⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠆⠀⠀⠀⠠⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⡀⠀⣧⡊⡔⠀⠀⠀⠀⠂⠘⣿⠃⠐⠄⢠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡔⠈⠀⠠⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠀⠏⠀⠀⠀⠀⠤⢈⠁⠐⠊⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⠐⠠⠀⠙⠲⠤⣄⣀⣠⣀⣀⣘⡀⢀⣀⢤⠤⠤⢦⡄⢠⡄⠂⠀⠳⠠⢀⢈⠁⢳⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠗⠀⠤⢀⠀⠁⠀⢀⡈⠐⠀⠌⡁⠉⠀⠀⡀⠀⠀⠂⡄⢀⠀⠁⠢⠀⡀⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠀⢐⠇⣤⣘⠂⢠⠎⠀⢄⠑⠨⣦⢸⠀⠀⠠⣈⠐⠀⠼⡄⠀⢀⠀⢧⡀⠉⠀⠧⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠆⠀⡼⠀⠀⡇⠀⠀⣿⠈⠀⠀⡆⠃⢐⠀⠀⣗⠀⠙⠁⢘⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣄⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠲⠠⣤⣀⣠⣀⡀⡄⣤⠠⠀⠀⠀⠄⠠⠄⠄⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⠉⠁