Buffet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠄⠠⠤⠤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠳⣤⣤⣤⣧⣼⣧⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠦⠄⠘⢳⣄⠀⠀⠀⠀⠀⠀⢰⡇⢰⣖⣒⣒⣒⣒⣒⣒⣒⣒⣒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣁⣀⠐⠒⢚⣋⣬⣇⣀⠀⠀⠀⠀⢸⡇⢸⡯⠭⠭⠭⠭⠭⠭⠭⠭⢭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⣶⡌⣩⡟⠉⠉⢿⣶⠀⣽⣦⠀⠀⠀⢸⡇⢸⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣧⣤⣭⣤⣽⢦⣤⣤⣼⣯⣤⣬⡿⣤⠀⢠⡼⠧⠼⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⢷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠙⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⣠⠟⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠉⠀⠆⠤⠤⠤⠤⠤⠶⠛⠁⠀⠀⢀⣠⠴⠋⠁⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⠖⣳⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡄⢻⣜⢿⣡⠞⠁⣸⠀⠀⠀⠀⠀⠀⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠈⣿⠁⠀⠀⡟⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⢀⠴⠷⣄⡴⠷⢤⡤⠿⢦⣠⠶⢧⡀⠀⠀⢀⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡆⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣬⣭⣭⣭⠉⡉⢩⣭⣭⣭⣭⣥⣼⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢰⡆⣶⢰⣖⢲⣖⡂⣶⡒⢲⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠈⠓⠋⠘⠁⠘⠃⠀⠛⠒⠘⠃



⡿⠿⠿⠿⠿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠀⠚⠀⠛⠛⠛⠛⠿⠶⠆⢠⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣴⠟⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣀⣴⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠉⢻⣦⣤⣤⣤⣤⣿⣦⣤⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣟⣉⠉⠉⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣿⠅⠉⠛⠛⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣯⣨⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣍⣩⣿
⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⠰⠶⠶⠶⠟⠋⠀⣨⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿
⠀⠀⠀⣴⠟⠛⠛⠛⠿⠶⣶⣶⣶⣶⣶⢶⡾⠛⠋⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣟⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣿
⠀⠀⣴⠟⠀⣾⠛⣷⠀⢀⣴⡟⠀⠀⠀⠈⣿⡟⣿⡄⠀⣾⠛⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣟⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣿
⠀⢀⣿⠆⠀⠙⠛⠋⠀⠸⣧⠀⠀⠀⠀⠀⢸⣿⠛⠀⠀⠙⢿⣏⠀⠀⠀⠀⠀⠀⣸⣇⠀⢸⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿
⣿⡟⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⢿⡗⠀⠀⠸⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠙⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠋
⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠘⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⠀⠙⠿⠀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠛⠀⠀⠀⠀⠉⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣀⣴⠞⢻⡦⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠸⣧⠀⢻⣆⣴⠟⠁⣀⣼⠇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠀⠻⣧⡀⠻⣿⣤⡾⠋⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠈⠻⢶⡾⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣦⣄⣠⣴⠿⢶⣄⣀⣤⡾⠷⣦⣀⣠⣶⠾⣷⣄⠀⠀⠀⠀⠀⠀⢠⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⢀⣤⣾⣯⣤⣤⣤⣿⣿⣤⣤⣤⣽⣿⣥⣤⣤⣬⣿⣯⣤⣤⣤⣽⣧⣤⠀⠀⣠⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠘⣿⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠐⠃⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣿⠄⣿⠀⠀⣿⠀⣿⣛⡛⢸⣟⣛⡃⢸⣟⣛⠃⠛⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣿⠆⢿⣄⣠⡿⠀⣿⠉⠉⢸⡟⠉⠁⢸⣏⣉⡁⠀⣿⡇
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣾⣿⣿⣷⣾⣿⣶⣶⣾⣿⣶⣶⣿⣿⣿⣷⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡲⢿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠄⠈⠀⠀⠈⠐⠂⠀⠚⠐⠲⠈⠉⠀⠀⠀⠈⠁⡀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⢒⠀⠆⠠⠀⢀⣄⣠⣴⠄⠀⠄⠺⢬⣼⣷⣾⣿⣷⣿⢿⠛⠚⠓⠀⢈⠙⢓⠂⠀⠀⠀⡀⠀⢩⠭⠿⠅
⠀⠀⠀⠀⢀⠀⠀⢈⠀⢠⠗⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⣤⣤⣤⣤⣤⣤⣴⣾⣄⣍⣍⣨⢽⣾⠾⢂⣁⣰⡤⠀⠀⣧⣤⣤⣧
⠀⠀⠀⠒⠋⠉⠀⠂⠀⠂⠀⠀⢀⠀⠀⠄⠦⣀⣤⠆⠰⠺⠁⠸⡷⠯⠿⠿⠿⠿⠿⠯⠉⠉⠉⠉⣈⣦⣸⠚⠾⢻⡣⣤⡤⢿⠿⣿⠋⠀⢰
⠀⠀⠀⠀⠀⠀⢰⡃⠀⢘⠗⠒⠚⠁⠀⠹⢄⠉⠉⣄⣓⣛⢞⢄⣀⣠⣤⣦⣤⣀⣤⡀⠘⣿⠟⠋⠉⠉⠀⠀⢋⡰⣾⣿⢿⡿⡇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢿⡀⠔⣀⣦⡠⠀⠀⠠⣠⣨⣉⠍⠹⠖⠿⢵⣲⣟⣿⣷⣍⠺⠾⠟⠁⠀⠀⠈⠋⠉⢀⡌⠉⠹⠿⠃⠀⠀⠀⠀⠀⢰
⠀⡄⠀⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⠃⠴⠷⠛⠁⠀⠀⠀⠀⠀⠀⢠⠀⢸⣸
⢡⠃⠀⢻⡄⠀⠀⢼⠆⠀⠀⠀⠀⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⡆⠀⠀⢠⠀⡀⠀⢀⠀⠀⠆⢠⣾⣿
⠀⠀⠑⡿⠁⠘⠀⠈⠘⠃⠸⠇⠸⠏⠀⡇⠀⠀⡇⠀⣿⠀⠀⢰⠀⠀⠀⠀⠀⡀⢰⡇⠀⣿⠀⠀⢰⢃⠀⠀⢹⠸⣷⢀⢾⠀⠦⠴⠈⣿⠘
⠈⠀⡀⠈⢠⣎⠀⣀⠄⠀⠸⢄⢠⠀⠀⡇⠀⠰⡇⠀⠙⠀⠀⠈⠃⠀⠄⠀⠀⡃⠄⠇⢸⢹⠃⡀⠀⠸⡄⡀⢸⣀⠇⢠⢛⡆⠀⠸⠀⢹⠈
⠀⠀⠤⠀⡎⢸⠁⡀⠐⡆⠀⣆⠀⠂⠀⢱⠆⢤⠅⠀⠀⠀⢀⡀⣀⠀⠀⢤⠀⠅⡀⠀⠄⠀⡀⣄⡰⠦⢤⠄⠀⠁⠀⠀⠀⡇⠀⢀⠀⢸
⢀⠀⠀⠸⠃⠈⠀⡄⢠⠹⠀⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⡏⠁⠘⠀⠃⢸⠃⠀⢸⠀⢶⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⢈⠀⠘
⠀⠑⢯⣀⢀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠸⠀⠀⡈⠀⠘⠆⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢈⣀⣼⠁
⠀⠀⢿⡿⠻⢤⣌⣄⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⡀⠀⠀⠆⠀⠰⠀⣥⣼⣟⣿⣿⣿
⠀⠀⠈⠳⠘⣷⣿⣹⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⣀⣀⡀⠒⠀⠐⠐⠦⠀⣀⠴⠄⠄⠦⠀⠤⠜⠉⠁⠉⠉⠀⠀⠀⣟⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣶⣷⣄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠉⠉⠻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣾⢻⣿⣿⠛⠿⠋⠉⠲⠶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢁⡄⠀⠀⣤⣠⣴⣾⣝⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠃⣸⣿⣿⢀⣻⣿⣂⣻⣿⣂⣻⣟⣀⠀⠀⠀⢸⣿⣿⣿⣥⣾⠇⠀⠀⡿⠍⠡⠿⠍⠩⠿⠍⠩⢿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⢺⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠠⣿⠀⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣯⢀⣿⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⡟⠛⢻⣿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⣰⣶⣦⡀⠀⠀⢰⣶⣦⣀⣶⣶⣄⡀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣿⣷⣶⣾⣿⣶⣶⣶⣶⣶⣶⡦
⠀⠀⠀⠀⢀⣾⣿⠟⠻⣿⣦⣴⣿⠟⢻⣿⡿⠛⢿⣿⣄⠀⠀⠀⠀⠈⠙⢿⣿⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣿⡿⠋⠁
⠀⠀⠀⠀⢸⣿⣧⣤⣤⣼⣿⣿⣧⣤⣿⣿⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⡿⠿⢿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⢸⣿⡟⠛⠛⢻⣿⣿⡟⠛⢻⣿⡛⠛⠛⣿⣿⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⣿⣧⠀⠀⣾⣿⣿⣿⠀⠸⣿⡇⠀⠀⣿⡟⠀⠀⠙⢿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⡿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⣿⣿⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣠⣄⠀⠀⠀⣿
⠻⣿⣦⣤⣾⡿⢿⣷⣤⣴⣿⠿⣿⣶⣤⣾⣿⠿⣿⣦⣤⣾⡿⢿⣷⣤⣴⣿⠿⣿⣶⣤⣶⣿⠿⣿⣦⣤⣾⡿⢿⣷⣤⣴⣿
⠀⠈⠙⢻⣿⡇⠀⣿⣿⠋⠁⠀⠈⠉⠛⠉⠀⠀⠈⠙⠋⠉⠀⠀⠉⠙⠋⠁⠀⠀⠉⠛⠉⠁⠀⠈⠙⣿⣿⠀⢸⣿⡟⠋⠁
⠀⠀⠀⢸⣿⡇⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⣿⣿⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠸⠿⠃⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⢀⣀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣤⢠⡄⣤⠄⣤⠄⣤⠤⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠗⠻⠼⠃⠏⠁⠏⠁⠿⠥⠘⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⡴⠀⢀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣉⣉⣆⣤⣽⣯⣤⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⢻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢲⠃⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢊⣩⣉⢑⡒⢤⡀⠀⠀⠀⠀⠀⠀⣴⣷⣄⣠⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣰⠍⠷⣗⣮⡹⠾⣄⠙⢆⠀⠀⠀⠀⠲⢟⣛⣛⣚⣛⡻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣴⣓⠮⠭⣐⡒⢤⡼⠉⢱⡈⡆⠀⠀⠀⣴⣙⣆⢸⡇⣰⣋⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡫⢊⠭⠭⠷⣾⡿⠋⣱⡞⠀⡇⠀⠀⠛⠿⠯⠯⢯⡭⠭⠽⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠳⣇⡎⣩⣍⣲⡟⢱⡼⠃⡰⠁⠀⠀⢠⠖⢦⢀⡶⢲⡄⡴⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣈⠓⠧⠴⠟⠒⠉⣀⠜⠑⢦⠀⢤⣾⣭⣽⣾⣯⣽⣷⣯⣭⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠋⠁⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠁⠒⠤⡀
⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠀⠀⡀
⠀⣀⢀⡀⡀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠸⠆⠀⠈⠁⠀⢀⡤⢄⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠈
⡄⠀⠀⠀⠀⠀⠀⠀⡌⣙⠡⠈⡤⠠⠤⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⠒⡦⠤⡤⠀⠀⠀⠀⠂⣜
⢇⠀⠀⠀⠀⠀⡁⠀⢣⣀⠇⠈⠀⠀⣀⠔⠉⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠤⠤⠤⢴⠩⠈⣟⠉⠳⠐⡄
⠈⢢⡀⠀⠀⠞⢀⠀⣠⠄⠀⠀⠀⠚⡤⠀⠀⠀⠀⠁⣆⣀⡤⣐⣅⢼⠂⣠⡅⢀⣐⡁⠀⠀⠀⠀⠑⠠⢀⠈⠑⠚⢇⣀⡰⠓⠦
⠀⠀⠀⢦⠀⠈⠉⢃⠸⣧⠄⠂⠉⠀⠀⠀⠀⠀⣬⡽⠁⠘⠀⢀⡄⣠⢲⠏⠠⠈⡙⢤⠂⢀⠀⠀⠀⠀⠀⢀⠑⠀⠀⠈⠀⢀⠂⠿⠋⠀⠀⠀⢀
⠀⠀⠀⠀⢃⠀⠀⠈⡄⢿⡄⠀⠀⠀⠀⠀⠘⠑⣹⠥⢴⣴⣲⣸⠹⠿⢳⠶⠷⣄⣀⢈⢀⠀⠀⠀⠀⠀⠰⣁⡀⠀⠀⠀⠀⢠⠀⢊⢉⣉⡉⠁⠁
⠀⠀⢠⡠⠆⠀⠀⠀⢀⠘⡽⢉⠀⠰⣉⢲⣍⣲⣾⠟⢋⣃⢰⣶⣶⣉⠼⣯⣁⣨⣱⣯⣜⡎⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⣀⠀⠡⣀⠠⠜
⠀⠀⠀⠂⠤⠒⠠⠤⢾⠀⢀⠎⠀⢘⠩⣁⣸⠆⠚⣮⣿⠟⢭⣯⠷⣷⡶⠛⠛⡉⠉⡩⢒⠄⠀⡠⡄⠀⠀⠘⠦⠤⠂⠁⢀⣸⡦⢄⠦⠄
⠀⠀⠀⠀⠀⠀⠀⣠⡎⣰⠁⠀⠀⠀⣱⢀⠤⠭⠚⠁⠁⠀⠺⠋⠀⠉⢁⣦⠌⠑⠒⠋⣇⠀⡠⠒⡏⠙⣧⠌⡂⠀⠀⠠⢁⠅
⠀⠀⠀⠀⠀⠀⠀⡝⠵⠿⠢⡀⠀⠠⠁⠿⠦⠀⣠⡔⢳⡒⣆⣲⡐⢲⡇⠀⠀⠀⠀⢀⣤⣇⣨⢛⣛⣤⣤⢴⣕⢄⣀⣸⡿⡀⠀⢨⣤⠤
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣱⠻⣒⣀⠓⠚⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠛⠒⠚⠛⠻⣉⠃⠈⠃⠙⠫⢤⡸⢦⢣⢄⢠⢩
⠀⠀⠀⠀⠀⢀⡨⡟⡏⡀⠿⢡⡘⠁⠀⠀⠈⠁⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠸⡽⣟⡘⠐⠊⠈⢂
⠀⠀⠀⠀⠀⠈⠀⠣⠝⠊⠉⠉⠀⠈⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⠓⠒⡶⠶⠖⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠒⢶⣶⡦⠄⠤⠔
⠀⠀⠀⠀⠀⢀⣀⡇⡆⢇⡐⠀⣤⡜⠧⠀⠀⠠⠆⠤⠀⢀⠀⠤⠄⠀⠰⠀⠀⠄⠠⠔⠐⠐⠆⠀⠰⠄⠤⠤⠄⠰⣶⡠⡄
⠀⠰⠂⠉⠉⠧⣄⣀⣿⠀⣤⢎⡉⠑⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠐⠰⢟⣓⣂⣠⢐⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠁⠉⠀⠘⠛⠂⠠⠭⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠞⠛⠉⠁⠀⠀⠀⠀⠉⠁⠉⠐⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠀⠀⢠⣟⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡛⠋⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠃⠈⣉⣀⣠⡿⢶⡄⠀⠀⠀⠀⠀⠀⣿⠀⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢛⠲⠦⢤⣬⡭⢤⣖⡛⠓⢦⡀⠀⠀⠀⠀⣿⠀⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠰⢯⠗⢠⡞⠁⠀⠈⣯⡿⠀⢿⣽⠀⠀⠀⠀⣿⠀⣿⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠳⠒⠒⠒⠖⠛⠒⠒⠲⠟⠒⠖⠲⠛⣶⠀⠀⢶⡛⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⢀⣴⠏⠀⠀⠀⠀⠀⣀⡴⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠈⠁⠂⠰⠶⠶⠶⠶⠶⠖⠋⠀⠀⠀⠀⣠⡴⠚⠉⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢁⡴⢚⡦⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣤⠹⣌⠳⣏⣴⠞⠁⣶⠀⠀⠀⠀⠀⠀⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠈⢳⡟⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡀⠀⠀⠀⢀⣼⣧⡀⣠⣿⣄⢀⣼⣧⡀⣠⣼⣇⠀⠀⠀⠀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠀⣴⠿⠤⠤⠿⠧⠤⠼⠿⠤⠤⠿⠧⠤⠼⢷⡄⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠙⠁⠉⠈⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⢀⠀⣀⡀⢀⣀⢀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣿⢸⡇⣸⢸⡯⠅⣿⠭⢸⡯⠍⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠈⠁⠀⠉⠀⠈⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢤⠀⠀⠠⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢈⠀⠀⠀⠘⠈⠀⢲⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢔⠊⠁⠉⠂⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣼⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣿⣀⠁⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠉⠘⣇⣴⣂⠂⠘⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠈⠀⢘⠀⠀⠀⠀⠀⠆⠂⢀⠀⠀⠀⠀⠸⠶⠏⢏⠈⠻⢀⠀⠀⠀⠀⠀⠀⠙⠀⠙⡀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣄⠈⠀⢸⠀⠀⠀⠀⠀⠀⠠⠄⠘⢀⠸⠀⠛⠀⠀⢠⠅⠀⡄⢀⠀⠀⠀⠎⠀⠀⠀⠀⠈⠀⠀⠀⠀⣢
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⢳⡀⠘⠀⠀⠐⠀⠀⡄⠀⠠⡀⠀⠀⠀⠐⢀⢀⡸⠀⠀⢹⡈⠀⠀⠃
⠀⠀⠀⠀⠀⢰⠀⠀⢈⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠷⠀⠀⠂⠘⢦⣄⠀⡔⠈⠃⠀⠀⠈⠃⠀⠀⠀⢸⠓⠢⠤⣤⠀⣴⠀⠀⠀⠁⠔
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⠁⠢⠤⠁⢈⢢⠀⠀⠈⠀⢀⠐⠀⠀⠀⠀⠠⠀⠌⠓⠒⠀⣌⠀⠀⠀⠀⠠⠀⠀⠀⢐⠠
⠀⠀⠀⠀⠀⠰⠤⠀⠄⡀⠀⡎⠈⠁⠄⠀⢹⡄⡌⠀⠂⡀⠀⠀⠀⠀⡀⠀⠈⠛⠱⠀⠐⣈⣇⣀⠀⠀⢀⡷⠞⠂⠚⣶⣄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠂⠠⠤⢌⣀⣀⣀⠠⠀⠂⠀⣀⢠⡌⢣⠇⠀⣀⡨⠭⠀⠂⠼⠗⠒⡌⠀⠀⠀⠀⠀⡉⠈⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠉⢑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠄⠀⠀⢀⠔
⠀⠀⠀⠀⠹⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠰⠠⢀⠑⠀⠨⠀⣂⠁⠀⠘⠀⠀⠀⢀⠀⠈⠀⠀⠄⠠⠀⠠⠀⠀⠄⣀⠀⠀⠀⠀⠸⠁⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⡃⣠
⠀⠀⠀⠀⠂⠘⠀⠆⠈⢈⠀⠰⠀⠀⠀⠀⠀⠀⢀⡇⡀⢀⠠⢆⠀⠀⡀⠈⣠⠀⢠
⠀⠀⠠⠄⠄⠀⠀⠠⠀⠖⠰⠀⠀⠠⠀⠀⠀⢀⠦⢄⣁⡄⡂⠴⠂⠀⡁⢀⠁⢘⠂⢀⢄⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠁⠈⠀⠉⠙⠠⠂⠺⢀⡀⠀⠀⡀⠀⠀⠄⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠰⠀⠘⠉⠁⠀⢀⠀⠰⠀⠠⠄⠈⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡐⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠠⠄⢀⡘⠔⠄⠸⢫⡶⢦⠄⠂⠔⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠠⠵⠆⠉⠢⣠⠦⢠⠐⠘⢠⠂⠁⠻⢃⡞⠷⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠝⠄⣂⡼⡁⠀⠄⢉⢩⣝⡵⣱⡾⠆⠒⣸⣡⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠈⠨⠞⠂⠍⡁⢉⣱⠂⠙⠸⠙⠋⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡲⢒⡀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠐⠀⠠⠄⠚⠂⡀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡀⠄⠨⡗⠋⢀⠀⠀⡀⠀⣾⠃
⠀⠀⠀⠠⡄⠀⠀⠐⠢⡃⡄⠀⡔⠁⠀⠀⠀⣀⡠⠔⣊⠁⠀⠀⠄⠠⠤⠤⠀⠚⠉⠀⡏⠉⠙⠃⠙⢲⣾⣷⣾⣵⢿⢻⡽⢀⣠⣤⠤⠔⠂
⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠈⣂⡧⠄⡠⠒⠉⠀⠀⡀⢨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⢣⣄⢀⠉⢉⣉⣉⣉⣅⠫⡀
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠑⢐⠛⠣⠀⢀⣀⠤⣠⣾⢔⡆⠀⠀⣰⡀⠀⠀⣴⣞⡗⣴⠒⠀⡀⠠⣄⡈⠓⠤⠾⠉⢈⡁⡀⠁
⠀⠀⠀⠀⠀⠀⡠⡀⠂⠑⡠⠏⠀⠀⠀⠁⠀⠀⠴⠴⠚⢉⠠⢔⡨⠌⠀⠀⠒⢁⡠⡌⢼⢡⣃⣦⡢⠈⠀⠉⠉⠉⠈
⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣐⣭⠔⠚⠉⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⢁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡉⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⡿⠀⣠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡿⢁⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣆⠀⠃⡿⢡⣿⡿⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⡀⠸⡄⠘⣧⡀⠁⡎⠀⠀⠀⠀⠀⠈⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⢳⡀⠹⣆⠸⣿⡄⣇⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡈⢿⡄⢹⣆⠹⣷⠘⢆⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⣷⠘⣿⡄⢻⡧⠼⠇⠀⠙⣶⠖⠚⠋⠁⠀⠀⠀⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡄⠀⠀⠻⣧⡽⠙⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⣀⣠⣇⣠⠤⠤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⠀⣀⣀⠤⠤⢒⣒⣫⣭⣭⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠤⢒⣛⣩⣭⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠇⡧⣿⣾⢄⡹⠁
⠀⠀⠀⠀⠀⠀⢸⣋⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢟⣛⣛⣛⣯⣭⡭⣤⣴⠶⢶⣶⠖⣒⣲⣾⢋⣿⡻⢏⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣭⠽⣶⣶⣾⣿⣏⠉⠉⠁⠀⠀⠀⣰⣿⠃⢠⣿⡟⠀⠿⣫⣶⣿⣿⡿⣷⣉⡤⠄
⠀⠀⠀⠀⢀⣠⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣏⠉⠁⠀⠀⢠⠃⢹⠃⢻⣿⣆⠀⠀⠀⣠⣾⡿⠃⣠⣿⡿⠀⠀⠀⠁
⠀⠴⣒⠴⣿⣿⡸⢟⣻⣭⣥⡄⠹⣿⣶⣄⠈⠻⣿⣶⣄⣀⡆⠠⡿⠀⠀⢧⠈⢦⣴⣿⡿⠋⢠⣾⣿⡟⠁
⠀⠀⠀⣱⢈⣿⣿⣿⣯⣽⡟⠳⠀⠈⠻⣿⣷⣤⡈⠛⠻⣿⠁⢐⣿⣿⣿⣿⣇⠘⣿⣉⣤⣾⣿⡿⠋
⠀⠀⢠⡧⠽⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣶⡏⠀⣼⣤⣤⣤⣤⣾⣆⠘⢿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠀⠐⣿⣿⣿⣿⡿⠿⠿⡄⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⣹⡇⠀⠀⠀⠀⠀⠀⢹⡄⠘⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⢠⡀⣷⡿⢊⠀⠀⠀⠀⠀⠀⣀⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠑⠂⠉⠁⠀⠂⠀⠀⢠⢤⣾⣬⡿⣴⣻⣿⣦⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⠀⢀⠀⡤⠀⠀⠀⢀⣤⠀⠀⣿⠤⡀⠀⠀⠈⠉⠉⢻⡄⠀⠀⠀⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⢃⣀⣦⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⢡⠀⠀⢻⠀⠀⠉⠀⠘⠉⠁⣼⡇⠀⠀⠀⠉⢀⢴⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠉⠉⠉⣵⣇⣀⠀⠀⠄⠀⠀⠀⠀⠀⠊⠀⠀⠘⠦⠀⠀⠀⣀⣀⡸⠟⠀⠀⠀⢀⠀⠀⠀⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠹⠬⣙⣒⣒⣛⣩⣴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡤⠈⠛⠶⠿⢟⣠⡀
⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⢩⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⠀⠀⣀⣤⡽⠿⠃⠀⠀⢀⠀⠀⠁⠀⠀⠐⠉⢙⣲⣤⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠉⡂⠄⠠⠀⠠⠐⡋⠡⠈⠀⠃⠉⠿⠁⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠶⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠩⠉⠀⠀⣄⠀⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠲⠤⠄⠠⠠⢖⣫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⣿⣿⣿⣲⣤⠀⠀⠄⠺⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠟⣿⣟⣹⠙⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⡆⠀⠀⣀⠀⠀⠀⠀⢲⣴⠄⣄⣀⣀⣀⣤⣤⣒⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠰⠄⣈⠛⢃⡄⠀⠀⠀⠀⠀⠀⢘⠓⠀⠈⠁⠀⢘⠛⢿⣃⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠒⣄⠀⠉⢀⡀⢨⣄⠐⠀⠺⠤⠀⠀⠀⠀⢼⣍⣀⢉⣉⣰⣶⣿⡿⣿⠀⠀⠀⠀⣴⣦⣈⠒⢶⣶⣷⣦⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠈⠀⠉⢳⠻⠏⠀⠀⠀⠀⠶⠘⠛⠫⠽⢖⠓⠋⢁⣭⠇⠀⠀⠀⠨⠶⣼⣶⣤⠈⠉⠝⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣄⠀⣄⠀⣄⣀⣾⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂⠈⠉⠀⠀⠀⠀⠀⠀⠈⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠈⠀⠀⠄⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⡃⠀⠀⠀⠀⡇⠀⠀⠀⢀⣥⡀⠀⠀⠀⠀⠀⠀⠀⢰⣂⠀⣠
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠇⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⣧⣶⣀⠀⠀⠀⠀⠀⠻⠿⣿⠏⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡏⠃⠁⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠠⠄⠀⠀⠘⠀⠀⠀⠲⠄⠰⠈⢃⠀⠀⠁⠀⠀⠸⠒⠀⠤⢤⠄⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠂⠐⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠉⠀⢢⠀⠀⠀⠀⣀⡀⣤⡀
⠀⠀⠀⠀⠀⠁⠁⠀⠑⡄⠀⠀⣘⡉⠀⢀⠀⠀⠀⢀⠲⡤⠀⡀⡄⠈⠁⠦⠤⡊⠀⠀⠀⠛⠀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠉⠀⠈⢁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠄⠀⠈⠐⠠⠀⠀⠀⠀⠀⢠⠀⠈⣀⠀⠈⠀⢀⠈⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠄⠀⠀⠠⠀⠂⠀⠀⠄⠀⠀⣠⡀⢀⣈⠴⠂⠀⠀⠁⠐⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⢀⠠⠀⠀⠁⠊⠈⠠⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠁⣼⢻⡀⠉⣿⠁⣿⣭⠅⣿⣩⡗⠈⣿⠀⡿⣦⡿⢰⠏⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠉⠃⠀⠋⠀⠛⠒⠂⠛⠈⠓⠐⠛⠀⠃⠘⠛⠈⠓⠚⠃

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢨⡀⣒⠀⠀⠀⠀⠀⠁⠁⣀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣀⠀⠀⠀⢀⢍⣛⡩⡁
⠀⠀⠀⠀⠐⢽⠛⠛⠛⠟⠆⠀⠀⠈⣀⡀⠀⣍⠀⠀⠀⠀⣀⣏⣰⣀⠀⠀⠀⠐⠀⠒⠊⠒⠛⠀⠀⠀⢨⢍⢭⢉⡍
⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠂⠦⠀⠀⠰⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠋⠉⠉⠉⠙⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠅⡀⠀⠈⠐⠀⠀⠀⠀⠘⢥⣲⡄⠀⠀⠀⠄⠀⣀⠀⠀⠠⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⡀⣐⣂⢐⢀
⠀⠀⠀⠀⠀⠃⡈⠠⠠⠤⠀⠀⠀⢠⠔⡄⢀⠀⠀⠀⠀⠀⣀⣏⣰⣀⠀⠀⠀⠀⡏⠀⠐⠒⠦⠀⠀⠀⢠⢣⠔⠜⡄
⠀⠀⠀⠀⠘⠄⠤⠀⠠⠄⠄⠀⠀⠘⠀⠈⠁⠁⠀⠀⠀⠄⠀⠀⠀⠀⠰⠀⠀⠀⠋⠁⠉⠈⠃⠀⠀⠀⠚⠚⠓⠓⠓⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢀
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠠⡄⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠶⠀⠀⠀⠐⠈⠂⠀⠀⢺⡑⣟⢺⣛⠀⠀⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⡀⢰⠆⡁⠈⠀⠀⠀⠀⡧⢰⡄⡶⠀⠀⠀⢺⡄⢄⡀⠀⠑⡆⠀⠀⠙⣉⠋⡙⣩⠀⠀⠀⠞⠙⠋⠋⢛
⠀⠀⠀⠀⠈⠐⠛⠛⠟⠃⠁⠀⠀⠒⠛⠓⠚⠚⠂⠀⠀⠘⠙⠄⠂⠀⠀⠂⠀⠀⠨⠔⠅⠦⠴⠀⠀⠀⠐⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠤⠀⢰⡀⠠⠄⠀⠀⡀⠆⠓⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⠀⢀⠂⠐⠋⠀⣤⠀⠀⠈⠈⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠈⠛⠖⠂⠈⠀⠀⠁⢀⠂⠀⠀⠈⠀⠀⢰⡷⣸⠏⠱⠢⠀⠀⠈⠉⠉⠉⠁⠑⠀⠀⠀⠃⠆⠒⠘⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣐⣐⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣦⣄⢀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⡷⠾⠿⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⡿⠿⣿⣿⡿⡿⠿⠿⠟⠛⠉⠀⠀⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣭⣝⠳⢶⣤⣤⣥⣌⡇⠈⢀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠴⠖⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣧⣄⣀⣄⣠⣄⣀⣀⣠⣤⣤⠶⠖⢛⠉⠃⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠉⠛⠹⠛⠉⠙⠋⣉⠉⠙⠋⢉⡉⠉⠹⡋⠉⠛⠉⠰⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣥⣄⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⡿⠭⣻⠟⠿⢿⣦⣄⡀⠀⠀⡀⠀⢀⣀⣠⣤⠴⠶⠖⠚⠛⠉⠉⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣦⠄⣀⡀⠉⠉⠉⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⡿⠟⠋⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠛⠛⠛⣛⣻⣿⡻⠯⠃⡀⠀⠀⠀⠀⢀⣠⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡛⢿⣿⣿⣿⣾⣧⣄⣀⡁⠀⡀⢀⠀⡀⣁⣀⣀⢀⣤⣤⣤⣶⡶⠞⠛⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣬⡉⠐⠬⣽⣛⡻⠿⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡿⠟⢉⠠⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣦⣄⣈⡉⠀⠁⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠲⠦⠤⠄⠠⠀⠠⠦⠴⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠤⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠣⡀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣈⡀⠀⠠⢦⡀⠀⠐⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠈⠡⠀⡴⠒⢦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⡄⡟⢀⣤⠀⡇⠀⠀⠀⢀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠄⠻⠷⡇⢸⣷⢆⠇⠀⠀⠀⠀⠁⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⠔⠚⠒⠛⠚⠦⠴⠊⠀⠀⠀⠀⠀⠀⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣇⠀⠀⠀⠀⠀⢀⠀⠎⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣠⡀⠈⠳⠶⠤⠶⠖⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣼⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠣⣄⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠙⠓⠒⠲⡎⠉⠁⢻⢦⡀⠀⠀⢆⣀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⠊⠀⡐⠇⡠⠖⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⣀⠜⢀⠈⠉⠀⠀⠀⣼⠃
⠀⠀⠀⠀⢀⠔⠚⢣⣠⠏⠀⠀⠀⠘⡄⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⠤⢤⡀⠀⠀⠀⠀⠂⠁⠀⢀⡾⢧⣀⡀
⠀⠀⠀⣠⠆⣤⣀⡞⠀⠀⠀⡘⠀⠀⢱⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠈⠉⠳⢤⡀
⠀⡠⠈⠁⠀⡸⠁⠀⠀⠀⢰⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠓⢶⠊⠀⡻⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⢠⠇⠘⢲⠀⠐⢄⠀⠀⠀⡼⠀⠀⠀⠀⠄⡘⠀⢀⡀⣀⡀⡤⠖⠅⢄⠀⡆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⡆⠀⢠⠊⢦⡠⠎⠀⠀⡾⠁⠀⠀⠄⠀⠰⢁⡠⠂⠀⠀⠀⠀⠸⠤⠼⠀⠀⠀⠈⠢⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡇⡰⠅⠂⡀⠀⠀⠀⢰⡷⠐⠀⠈⡰⢀⠟⠁⠀⠀⠀⠀⠠⡖⠒⠤⠐⠒⠒⢦⠀⠀⢀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢰⠁⢄⣠⠆⠀⠀⠀⠀⠻⣄⣀⣹⠔⠁⠀⠀⠀⠀⠀⣀⣀⡹⠦⠤⣤⣀⡀⠀⠹⡀⡀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⠰⣇⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠓⣄⢣⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸
⡇⢌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⠧⠍⠛⠛⠛⠳⢄⠀⠈⠂⠀⠀⠈⡆⢧⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸
⢸⡈⠙⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠹⢤⣤⣤⣴⣤⡀⠀⠙⠀⠀⠀⠀⠀⠈⠈⡇⢀⠀⢿⠀⠀⠀⠀⠀⢸
⠈⠱⡀⠀⢰⠈⠙⡆⠀⢠⠐⠠⠀⠀⠀⠦⣀⠤⠁⣰⡛⠋⠀⠉⠈⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠑⢾⣇⠀⠀⠀⠀⠸
⠀⠇⠙⢄⠈⠒⠚⠁⠀⠳⣄⡠⠃⠀⠀⠀⡠⠒⠉⠀⠙⠛⠛⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⠀⠈⠓⢦⡀
⠀⢸⡀⠀⠉⠒⠢⢤⣀⣀⣠⣄⣀⣠⠴⠋⠀⠀⠀⠀⣀⠤⠖⠉⠀⠈⠙⠒⠶⠤⠤⣤⣤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⢷⡀⠀⠀⣀⠞⠁⠀⡟⠙⠒⠶⠤⠤⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄
⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⢀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠏⣻⠇⠀⢀⠃⠀⠀⠀⠀⣰⣿⣿⠟⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡠⠄⠒⠙⠠⠤⠐⠁⠀⠀⠀⠀⠀⢿⣿⣯⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⠘⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠐⠒⣸⣿⣯⣐⠒⠂⢰⠦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠘⢿⣿⣷⣦⣤⣀⠔⠊⠁⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⢀⠆⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡟⠀⠀⠀⠈⢛⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⣿⣿⠏⠀⠀⡠⠃⠀⠀⢠⣶⣄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⠾⠋⠀⠀⠀⠀⡠⠁⠀⠈⠙⢿⣿⣿⣷⡀⠀⠀⠙⠿⠄⠄⠊⠀⠀⠀⠀⢺⡟⠁⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⠐⠢⢄⣴⣿⣿⣷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢀⡤⠖⢐⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⣠⣿⠟⢡⣿⠁⠀⣾⣿⣿⡟⠀⠈⠁⠂⠤⣀⠀⠀⠀⠀⠀⠀⡙
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⢰⣿⣿⡿⠁⠑⠢⢤⣤⡾⠆⠀⠈⠉⠉⠉⠉⠀⠀⠘⠛⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣈⠁⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⢦⠀⠀⠀⣿⣿⣿⠁⠀⢠⣶⣶⠀⠀⠙⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⢀⣴⣾⡿⠷⣆⠀⠀⣾⣇⠀⠀⢠⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⡆⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⢠⣿⡟⠁⠀⠀⣰⣶⣤⡹⣿⣦⣠⠃⠀⠀⠀⣿⣿⠁⠀⠀⡆⠻⣿⣀⡠⠀⠀⠀⢘⣿⣷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢸⣿⠀⠀⢀⣴⣿⣿⠿⠃⠙⣿⣿⣦⣄⠀⠀⢻⣿⠀⠀⠀⠃⠀⠈⠉⠀⠀⡠⠒⠁⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⠃⠈⠉⠁⣼⣿⠟⠁⠀⢀⠌⠀⠛⢿⣿⣷⣄⠈⢿⣇⠀⠘⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢀⠂⠀⠀⠀⢰⣿⠃⠀⣀⠔⠁⠀⠀⠀⠈⠻⣿⣿⣷⡀⠙⠒⠁⠀⠀⡠⠃⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠐⠁⠀⠀⠀⠀⠈⠃⠄⠊⠀⢀⠤⢤⣄⡀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢹⣿⡄⠀⠀⢹⣿⣿⣧⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠈⠋⠉⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠁⠂⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⣀⣠⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠐⠂⣤⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠒⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣔⠖⡈⠀⠀⠀⠀⠀⢠⣸⠃⠀⠀⠀⠀⠀⠀⠰⣶⣤⣤⡠⣪⡾⠀⠀⠀⠉⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠈⠙⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠶⣄⣢⠄⠀⠈⢲⢢⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠗⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠢⡀
⠀⠀⠀⠀⡠⢀⠀⠀⢀⣼⠆⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣭⠇⠀⠀⠀⠀⠀⠀⠀⢠⠂⡀⡀⠀⠀⠀⠀⣤⡘⠄
⠀⠀⠀⡰⠁⠆⠀⠻⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠏⠀⠀⠀⢰⡾⠀⠈⠄
⠀⠀⣀⠡⣄⠀⠀⠀⢰⢸⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⢰
⠀⠠⡥⠞⠉⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣯⣾⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣴⠀⠆
⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠲⡄⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠆⠀⠀⠀⠀⠀⡀⠸
⠀⢰⡀⠀⠀⠀⢰⣵⢳⣦⠿⠿⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠄⠀⠀⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣾⡿⠀⠀⠀⠀⢠⣾⢁⠆
⠀⠀⢆⠰⢶⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢇⣾
⠀⠘⢌⣄⡈⠻⣷⣤⡀⠀⢀⠄⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠀⣀⢠⠀⠀⠀⠀⢰⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢛⣥⣾⡟
⠀⠀⠸⠛⢿⣷⡙⡿⣿⠷⢬⣒⠖⠃⠀⠀⣰⣹⠃⣀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⢐⣿⣾⣿⡟⠁⢠⣿⣿⣿⠃
⠀⠀⠀⠆⠀⠉⢻⣮⣭⡀⠀⠨⣤⣤⠄⢠⢌⣥⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣤⡜⣻⠟⠉⠁⠀⣠⣿⣿⣿⠃
⠀⠀⠀⠈⠢⡀⠀⠈⠻⢿⣦⣀⣀⣉⢉⠀⠈⠉⠛⢿⣿⣿⣯⣯⣽⡿⠿⠿⠿⠟⠛⣚⣉⡉⠉⠉⠉⠉⢀⣠⣶⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠈⠙⠛⠟⠿⢿⣿⣷⣄⡀⠉⠉⠋⠉⣁⣤⣶⣶⣶⣷⣿⣿⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠈⠋⠛⢿⣦⣀⣠⡾⠿⠿⠿⠻⠟⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠰⠤⣀⣀⠀⠈⠁⠉⠀⢤⣴⣶⣳⣿⡳⠿⣿⣿⣿⣿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡤⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠉⠃⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⡄⡨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣦⡌⠀⠸⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠚⠈⠀⠈⠂⠐⠂⠈⠑⠀⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣐⣻⠿⠟⠓⠁⢻⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⡀⠀⠀⣀⣀⠘⠉⢑⠠⠠⠄⣄⣀⣰⡂⠉⠁⠀⠀⠀⠁⠈⠀⠀⢀⡀⠀⣄⣤⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣷⣶⣷⡎⠸⢦⣶⣾⣷⣶⣷⣶⣷⣤⣿⣯⣭⣄⡨⣉⠀⢂⡰⢦⠒⣊⣥⣾⣾⣿⣿⣿⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣄⡼⠿⠛⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣧⣿⣤⣸⣶⣿⠿⠿⠛⠋⠉⠀⠀⢀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠉⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⠘⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄⠀⠀⣀⠄⠀⠖⠒⢀⡉⠙⠤⠤⠥⣱⠀⠀⣀⠈⠐⠒⣒⠂⠀⣀⣊⠈⢧⡈⢢⣽⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⣀⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠂⠀⠀⠀⠀⠈⠄⢀⡬⠩⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⢰⠁⢠⡄⣀⡤⠂⠒⠀⠤⢄⠀⠀⠀⠀⠈⠃⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠥⠔⠋⠁⠀⠀⠀⠀⠀⢀⠱⠢⢀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⢀⡠⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⡀⠱⠒⠤⠤⠤⠤⠄⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠾⠛⠛⣻⣿⣿⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣯⣽⣷⢻⡷⠇⡠⢦⠀⡠⢎⠉⠛⢻⣿⣿⣷⣶⣻⡶⠶⢿⠶⣶⣤⣤⣀
⠀⠀⠀⠀⣠⣾⡿⡟⠋⠋⠁⣢⠄⠈⠴⠒⠊⢀⠘⢂⣶⣾⢯⡻⣿⣮⣷⠁⠀⣀⠀⢠⠞⠴⣋⡽⠷⠦⣄⡀
⠀⠀⢀⣼⡟⠏⠀⢰⠆⠤⠒⢠⠀⠆⠀⠒⠁⣱⡾⠛⣫⢭⡁⣡⠏⠁⠳⠖⠋⠉⢳⣀⣠⣆⡴⠚⠛⣦⡴⢿⡒⢄
⠀⠠⠋⡼⠁⡄⠠⠆⠠⠒⠀⠀⠐⠀⠔⢀⣾⡩⡠⠖⠁⠀⠉⠁⠀⠀⢀⠴⠀⢀⠄⠉⠁⠁⠴⠂⠀⠀⠀⠉⣇⠀⠙⣦
⢠⠧⢀⡄⣈⠀⠀⠀⠐⡀⠀⠃⠀⠄⡴⢿⠟⠀⠠⠆⠠⠃⢠⠖⠀⢀⠀⠀⠀⠡⠀⠐⠁⡤⠀⠀⠀⠃⠀⠰⠙⠋⢳⡀⣷⡄
⡟⠀⠉⠘⠁⠠⠂⢀⡜⠁⠀⠀⣠⣾⠁⠀⠀⢠⠀⠀⣀⠀⠀⠀⠀⠊⠀⠠⠃⠐⠀⠀⠀⡀⠀⠂⠀⡀⠀⢠⠄⠀⢹⠃⡘⠛⣆
⡏⠀⢠⠆⠀⡀⠈⠠⠀⠀⣨⣿⣿⡇⠀⠈⠀⠂⠀⠐⠁⠀⠀⠁⠀⠀⠀⠀⠂⠀⡄⢁⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠷⠋⢹⣰⣿
⢀⠀⠀⠀⠘⠁⡀⠀⠈⣀⣺⣿⣿⠀⡰⠀⣠⠀⡀⠠⠁⠄⠀⠎⠁⢠⢠⡧⣤⡦⣥⣜⣀⡀⢀⠀⠀⠰⠀⠰⠀⠠⠁⢰⣿⣵⣻
⠸⠀⠚⢠⠀⠀⡤⠖⠀⡈⢦⣿⡟⠀⠀⠐⠡⠀⢡⠀⠀⠀⠀⠤⠀⠀⣨⠟⠀⠀⠀⠉⢻⡅⠈⠀⢰⠂⠀⠀⠀⠀⠈⠉⣁⣿⣽
⠀⠐⢦⠀⠀⠀⠠⠚⠀⠁⠈⠛⣧⠀⢀⠖⢈⠀⢸⠄⡦⠀⡀⠀⠈⡼⣿⣦⣀⠀⠀⢀⣸⣿⡆⠰⠒⠀⠰⢀⠀⠀⠀⢸⡿⣟⡁
⠀⠀⠈⢧⣀⠀⠠⠃⢈⠁⠴⠀⡇⠀⢀⡄⠞⠀⠘⡀⠀⠤⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠂⠀⠈⠀⡆⠀⠀⣴⣿⣷
⠀⠀⠀⠀⠙⢶⣀⠀⠘⠀⠴⠂⠈⡄⠈⠀⡾⠀⠘⣁⠀⢂⡴⠀⠀⠀⠀⢸⢹⣿⡿⠿⠿⣿⠃⠀⠀⠐⢠⠄⠀⠰⠀⠸⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠲⢶⣀⠀⠀⠀⠘⡄⠀⠁⡆⠘⢁⡰⢈⡤⠀⠄⠀⠀⠀⠀⡀⠀⢀⡜⠃⡀⠀⠃⠀⠀⡠⠃⠀⠀⣰⠯⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣦⣤⣬⣦⡀⠃⡏⠀⡀⠀⡄⣠⡄⠈⠀⠀⠐⠀⠀⡠⠀⠐⠁⠀⠐⢀⠀⢁⡀⠀⢠⡏⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⢿⠀⠀⠁⢀⠀⠚⠀⠀⠀⠀⠃⠀⠁⠀⠠⠀⠐⠀⠀⠀⣄⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⠰⠏⠔⠀⢠⠄⠄⠀⠂⠈⠀⠂⠀⠀⠀⠐⠀⣀⣴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⡀⠁⠀⠀⠀⠋⠈⠁⠐⠁⠀⢀⣠⠴⠛⠁

⠀⠀⡇⠘⣦⠈⡇⠀⠀⣿⠀⢀⡄⡇⠀⣶⠛⣿⠀⠀⢸⠀⠛⢣⣿⠣⡆⢸⠀⠀⡶⣾⡏⢻⡇⣼⠃⣸⡏⠀⠠⡗⠀⠀⠀⣿⡾⠈⢿
⠀⠠⣇⠀⢘⢧⢻⠛⠛⣟⢛⡛⠛⣟⠛⣛⣛⡿⢛⢛⢻⠟⠛⠛⡇⢸⠀⠸⠀⠀⡇⢸⠀⣼⢱⢏⠀⣿⡗⠒⠺⡿⠒⠒⢲⡗⠒⠒⣾
⠀⠀⣿⣀⣾⢾⢿⡇⠀⣿⠙⠃⠀⠁⠀⢀⠀⠀⠀⠀⠈⠓⢆⠀⡇⢸⡀⠀⢰⡄⠇⢸⠀⣿⡿⢸⠀⣏⣇⣰⠷⡇⠀⠀⠀⡇⠸⡿⢹
⠀⠀⣿⠻⠃⢸⣈⣃⣀⣿⣠⠃⢀⣈⡓⠀⠀⠀⠀⠀⡄⢀⢈⣆⡇⢸⣅⣤⠟⢿⡇⢘⠀⣿⠁⢸⡆⡇⡏⣛⣀⣇⣴⣶⣾⣷⣶⣦⣼
⠀⠀⣿⠀⢀⢸⢤⠀⠀⣿⢸⠽⠛⣓⠛⠀⠀⠀⠀⠀⠀⠉⢸⠁⡆⢸⠉⢟⣀⡾⠃⢸⠀⠁⣠⣼⡷⠆⣧⡀⠀⣿⡏⠛⠿⠛⠙⣿⣿
⠀⠀⣿⣿⣿⣿⡄⢁⡀⣿⠀⢄⠠⠇⠐⢚⣳⠦⠄⠀⢀⣀⣼⣦⡇⠈⠀⠈⠻⠃⠀⢘⠀⡀⠛⠛⠂⠀⡇⠘⠀⠻⣧⡀⠀⣀⠈⣿⢿
⠀⠀⣿⣿⣿⡿⢀⢂⢉⣿⡄⠆⠀⠀⠀⠈⠉⠁⠀⠀⠛⢲⣛⣻⣿⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣤⡀⠧⠀⠠⠀⠈⡆⠠⠀⠀⣉⢸
⠀⠀⣿⢗⡓⣦⠒⡼⢘⣿⡾⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⣿⡿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠄⠈⢫⠀⣀⠔⢹⣿
⠀⠀⣿⠀⠀⠉⠛⠷⣾⡟⠁⠀⢀⠀⠀⠀⠀⣀⣀⠀⣰⡋⠄⣼⣿⠿⡟⣵⣿⣿⣿⣿⢾⣯⣽⣭⡻⣿⣿⡄⢠⠄⠸⢾⣩⣄⠀⣾⣿
⡀⣀⣟⣀⣤⣤⣶⣿⣿⡀⠀⢢⠘⣷⣄⠀⠀⠀⠁⡼⡅⠀⢸⣿⣿⣾⣿⣿⡟⠛⠋⠁⠀⠙⢿⣿⣿⣿⣿⣇⡀⡴⣆⠟⣸⡇⢸⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⠾⣿⣿⡿⠟⣯⡐⢃⠀⢸⣿⡟⡿⠋⠁⠀⠠⠤⣄⡀⠀⠀⠈⠉⣿⣿⠇⠀⠉⡹⢲⠟⢷⣾⣿⣿
⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣥⣄⠀⣿⣿⣦⢨⣈⠿⣷⡅⠀⠀⠀⠦⢥⡀⢁⠀⣠⠴⢶⡟⢁⠀⠀⡼⢡⡇⠀⠈⢻⣿⣿
⣎⠂⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡴⠋⢹⣿⠙⠧⣿⣿⣿⠿⠟⢳⠏⡆⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⢳⡇⠈⠀⡼⠁⠸⡇⠀⠀⠀⠹⣿
⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣾⡿⠖⠒⣩⣽⣟⣦⡀⠀⠛⡄⠻⣄⠀⠀⠠⣤⣴⠃⡄⢸⠀⢿⡄⡼⠁⠀⠀⠙⠐⣄⠀⠀⠘
⣎⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡜⠉⠀⠀⠉⠀⢀⣀⣉⡛⠀⠀⠘⠱⢹⣶⣤⣀⣀⠏⠀⠀⠀⠀⠘⡟⡅⠀⠀⠀⢠⣴⣿⣷⣄⡀
⡙⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡎⠀⣠⠊⠀⠀⠀⠐⠀⢈⣿⠿⣶⣄⡀⠈⠘⠙⠹⡟⠀⠀⠀⠀⠁⠀⠙⡘⡄⠀⠀⢠⣿⣿⣿⣿⣿
⣿⡷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⡔⠁⠀⠀⠀⠀⢀⡀⢸⣯⣿⢬⣿⣿⣿⡗⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⢑⡞⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣦⣸⣿⠿⠿⣿⣟⣿⣿⡟⠀⣼⠀⠀⠀⢀⡴⠊⣷⡞⣻⣿⣿⣾⡿⣾⣿⣷⣾⣷⢶⢺⣵⡦⣄⣠⣴⣾⠁⣠⠄⢿⣿⣿⣿⣿⣿⣿
⣵⣿⣷⣶⣴⣿⣿⣿⣿⣿⡇⠀⢻⣤⡖⠉⠁⠀⢰⣿⣿⣏⣿⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠉⠉⢆⠀⠀⠈⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⠄⠁⣄⠠⠀⠀⠀⠀⢠⣿⠷⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣶⣶⠆⠒⠛⠛⠛⠉⠀⠀⠀⢒⢶⡆⠍⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡝⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⣀⠉⠀⠀⠠⠦⣷⠀⠀⠀⣾⣿⣷⡀⢳⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡉⢱⡆⢀⠀⣄⠠⣾⣿⠀⠀⠹⡇⢀⠀⠀⠀⠀⠀⠐⣿⣿⡄⢠⡀⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⣅⣉⣁⣻⠠⣼⣇⣹⣿⡤⠀⠀⢁⡌⢀⡀⠀⠀⠀⠀⣿⣿⣷⠀⢳⡄⢹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠰⣿⣼⣷⣾⣿⣟⠛⠻⣿⣿⣿⣿⡁⢺⠙⠣⠀⠹⡇⠀⠀⠀⢰⣿⡟⠻⣇⠀⢣⠀⣥⣿⢫
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡉⢹⣧⣿⣷⡀⢰⣿⣿⣉⣧⣬⠀⣀⣦⣇⠀⠀⠀⠀⠈⡟⠀⠀⠈⠃⠀⠀⣿⠙⢾⣇⡄
⠀⠀⠀⠀⠀⠀⣆⣹⣧⣿⣿⡝⠻⣯⣤⣾⣿⣏⡛⠁⠉⣿⣿⣿⡟⠇⠀⠀⠀⢠⠃⠀⣰⣄⠀⠀⠀⢿⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠿⢰⣿⣿⣿⣷⣄⠸⣿⣿⣿⣷⣿⡄⠀⣿⣿⣿⠁⣀⢰⣦⡀⡆⠀⢀⣿⣿⠀⠀⠀⠀⠀⢸⡿⠇
⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣷⠶⡾⠦⠬⣩⣿⣿⣿⣇⣤⣿⣿⣿⣷⣿⣼⣿⣇⣿⠀⢸⣿⣿⡆⠀⡀⢀⡀⠼⢷⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣴⣦⡤⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣧⣿⠀⣼⣿⣿⡇⠀⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠶⣿⣿⣦⠄⣴⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣍⣿⠀⣿⣿⣿⡇⢰⣿⡃⣧⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠛⠻⠛⠻⠿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠏⠉⠋⠉⠉⠉⠁⠉⠉⠉⠉⠉⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣀⢀⣤⣶⣦⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠿⣸⣿⣿⣿⣿⡆
⠀⢀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⠟⠀⠚⢿⣿⣿⣿⣿⣧⣶⣶⣦⡄
⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⢠⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⠿⠟⣋⠽⠒⠂⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣄⠉⠉⠑⠿⠟⠃
⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⣛⣋⠁⠀⠻⣿⣿⡿⠿⠋⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠉⠛⠃⠀⠐⠂⠐⠒⠂⠀⠈⠁⠀⠂⠈⠐⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⡱⡆⡱⣊⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠄⠀⠀⠀⠀⣀⠀⢀⠀⡀⠀⢀⢠⠀⡀⠀⡄⠀⣤⢀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⠀⠋⠀⠘⠚⠘⠃⠀⠘⠂⠒⠀⠉⠂
⠀⠀⢀⣶⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠦⠤⠶⠶⠛⠛⢥⣤⣤⣔⣀
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣉⣻⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢺⣿⣿⣶⠆
⠀⠀⣾⣿⣿⣿⣷⣬⡙⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣴
⠀⠀⠈⠩⣿⣿⣿⣿⣿⣷⣦⡝⠋⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⠉⠉⠻⠿⠿⠿⠃⠀⠀⢈⠿⣶⡄⣀⢀⣀⠀⣰⡿⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣾⣿⣿⣙⣿⣷⣿⣷⡆⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣠⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢀⡬⠙⠛⠿⣿⣿⣿⡿⠿⠛⠁⠀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠒⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠛⠛⠉⠛⠒⠒⠲⠦⠄
⣶⣶⣶⣶⠶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⡶⠶⣶⣶⠶⡶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⢹⠟⠋⠉
⠀⠀⠀⢾⡇⠀⣴⡄⠐⠆⠰⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⢀⣀⡀⠀⠀⢰⡆
⠀⠀⠀⠀⠁⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠈⠉⠃⠀⢠⡿
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠒⠠⠀⣀⣤⡴⠀⠀⠀⢰⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠒⠂⠀⠀⠀⠀⠙⡅⠀⠀⠀⠀⠀⣷⣄
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⣀⣤⡀⠘⢿⣿⡇⠀⠀⠀⠀⠙⠀⠀⢰⣄⣀⣀⣤⡴⠶⠶⠾⣿⣿⣿⣿⣿⣷⣿⣶⣦⣤⣾⡁⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣙⣿⣿⣄⠈⢻⡇⠀⠀⠀⣀⣠⣴⣶⣿⣿⠿⠛⠃⠀⣀⠀⠀⠀⠙⠿⠿⠿⠛⠛⠛⠛⠻⠿⠿⣷⣶⣤⣀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⣿⣦⢀⣡⣤⣾⠇⠱⠋⢻⣿⡟⠁⠀⠀⠀⠰⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣈⣿⣿⣿⣿⣿⢁⡤⡄⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠑⢄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣿⣿⡟⠛⣿⠟⠛⠋⠈⠃⠀⠛⠉⣩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡀⢀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠞⠁⠀⠀⠀⠀⠰⠆⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤
⠀⠀⠀⠀⠀⠀⣼⣶⡦⡈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⢀⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠛⠆⠀⠀⠀⢤⠒⡛⠀⢰⠘
⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⠀⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠊⠀⠈⠃⢸⡐
⠀⠀⠀⠀⣸⡏⠁⣀⠈⠙⠻⠇⠀⠀⠐⣀⠀⣈⠉⠀⠀⠘⣿⣿⣿⡟⠁⠀⠀⠻⢿⣿⣿⣿⠃⠀⠀⢠⡄⠀⠀⡴⠀⠚⠀⠀⣹⣤⣶
⠀⠀⠀⠀⣻⣿⣿⣿⠘⣷⣦⣀⠛⠖⢈⠨⠅⣙⡿⠏⠸⠤⢩⠹⣏⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠋⠀⢰⡉⠀⠤⡔⠈⠁⢈⣱⡤
⠀⠀⠀⠐⠚⢻⣿⣿⡇⢹⣿⣿⣷⡀⠀⠀⠀⠀⠉⠀⠠⠀⠀⣷⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⡷⠟⠀⠀⠀⠐⠛⠛⠁
⢀⠀⠀⠀⠀⢸⣿⣿⠷⠞⣻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⡰⢶⠆⠀⠒⠰
⠘⠁⠀⠀⢰⡿⠟⢿⣷⡴⣿⡿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⣀
⠀⠀⠀⢠⡀⣀⣠⣼⣿⣇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣦⣴⡄⠀⠁⠠
⠀⠀⠀⠘⠃⢹⣿⣿⣿⠋⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠻⢿⣿⠿⠇⠀⡀
⠀⠀⠀⠀⠈⠿⢿⡿⠁⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠈⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠔⠚⠀⠀⠀⠀⠠⢄⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠓⠒⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡬⠷⠀⠀⠀⠀⡀⠀⠀⠈⠙⢿⣷⡟⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠁⢈⣀⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣘⠛⣙⣿⡿⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠰⣶⣄⠀⠀⠀⠀⠀⠉⢛⣿⡟⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴
⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠋⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿
⠀⠀⠀⠈⣤⠗⣄⠀⠀⠀⠀⢠⠒⣴⠂⠀⠀⠀⣤⣀⡄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣤⣤⣀⡀⠀⠀⣂⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⢠⣿⣷⣄⠀⠐⠏⠁⠀⠀⠀⠄⠀⠉⢻⡇⠀⠀⢠⣾⠿⠛⠁⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢩⡑⠒
⠀⠀⠀⠀⠀⣸⣿⠋⠻⣷⣄⠲⠀⢀⠐⠀⠀⠀⠀⣸⡇⠀⠠⠟⠁⠀⠀⠀⢸⠿⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠩⠏⠉⠀⠂⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢀⣤⡀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠠
⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠔⣠⣶⣦⠀⠀⠀⠀⠀⠆⢸⣿⡇⠀⠀⠀⣿⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⡀
⣠⣶⠀⠀⢸⣿⣷⣦⣤⡀⠀⠀⠀⣿⣿⣿⠄⠀⢀⡀⠀⠀⠘⠛⠃⠀⠀⠀⠹⠏⠈⠉⠉⠛⠛⠛⠻⠿⠿⠛⠋⠉⢽⠀⠈
⠈⠙⠂⠀⠸⠿⠿⠿⠛⠁⠀⠀⠀⠙⠉⠀⠀⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣇⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠏⠐⠂⠒⢄⡀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢢⡀⢀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣀⡀⠂⢀⠀⠈⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⢀⠀⠀⡫⠵⠀⢤⡔⠌⠀⠀⢱⣦⡈⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢼⠡⢠⡶⠋⠀⢀⣀⠀⡀⠀⠁⠀⠀⠀⣸⠃⣝⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢄⠑⠃⠈⠃⠠⠄⣠⡖⢀⡴⣻⠟⠂⠀⣀⣀⣼⣿⠎⣩⠇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠈⠁⡤⠛⠀⢘⣇⣴⣀⣤⣾⣿⣿⣿⠃⠀⡟⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠘⠹⠿⢿⠿⠟⠛⠉⠀⠀⠀⣇⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠀⠀⢀⠰⡀⠀⠀⠀⠀⠀⠀⡏⠀⢢⠈⠉⡇⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡠⠴⠄⡁⠀⠀⢀⠀⠀⠀⡠⠀⢸⠀⢆⠸⠀⠈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣂⣤⠖⠁⠀⠀⠀⠁⠀⠀⠶⠀⠊⠀⠈⠢⡁⠈⠂⠀⠀⠸⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣘⠁⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣀⣀⠀⢀⠀⢀⢱⣀⣀⣀⠀⠁⡀⠁
⠀⠀⠀⠀⠀⠀⣠⠃⢃⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢀⡀⠀⠀⠀⢔⠛⣻⣿⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⡴⠁⠀⢸⠀⠀⠀⡐⠸⠀⠀⢀⡝⢶⣄⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢒⣒⠒⠒⠒⠀⠀⠀⠀⠒⡒⠞⠋⠉
⠀⠀⠀⠀⡜⠀⠀⠀⠸⠀⠀⡐⠀⡀⡧⠀⠀⠑⣄⠙⠿⣦⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⠃⡉⠛⡋⠉⢩⡍⠀⠡
⠀⠀⠀⠰⠁⠀⠀⠀⠀⡆⠰⠁⠀⡇⠱⣄⠐⢄⣀⠁⠀⠈⠛⢿⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢒⠃⠠⢾⡇⠀⠀⢣
⠀⠀⠀⡧⠀⠀⠀⠀⠀⠱⠃⠀⠸⠁⠀⣨⠗⠸⠁⢀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢦⣀⠠⡄⠀⠀⠀⠄
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⡠⠖⣿⠐⢉⡤⠛⣧⠀⠀⠙⠳⣦⡀⠀⠉⠒⢄⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠘
⠀⠀⣜⣀⡀⠤⠤⢴⠖⠉⠀⠘⠁⡠⠋⠀⠰⠁⠀⠸⡀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⢤⢚⠀⠀⠀⢀⠆
⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠁⠈⠁⠀⠈
⠀⠀⠀⠀⠈⠒⠦⠠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠈
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠐⠀⣠⣴⣶⣶⣶⣶⣶⣦⣤⡀⠐⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣰⣿⣿⣿⢿⣿⣿⢋⠽⢿⣿⣿⣷⡙⣾⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣶⡏⠙⢶⣿⣽⣿⣿⣿⣷⠹⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡄⢸⣿⣿⣿⣿⣿⡟⢰⣾⣻⣿⣿⣿⣿⡿⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣧⣄⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⢇⣄⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢄⢿⠻⠯⠛⢩⡑⠒⠀⣠⣉⠀⣨⡝⠿⣫⢾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢻⣾⣦⣄⣀⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠉⠻⣦⣉⣛⡒⠠⠤⠀⠀⠴⠖⢒⣛⣭⣿⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣼⣿⣿⣿⡿⢛⠻⢿⡿⠟⢻⣿⣿⣿⣿⡄⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢹⡿⢻⠛⠉⠈⠉⠀⠀⠁⠈⠟⢿⠿⢿⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠋
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⣷⡆⠀⠀⠀⠀⠀⠰⢶⠶⠶⠴⠄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠁⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠆⠀⠀⠀⠀⣠⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡏⠀⠀⠀⠀⠐⠁⠀⢀⠀⠀⠰⠄⠀⠀⠃⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⠀⠀⠐⠂⠂⢒⡴⠖⣂⣀⡀⣤⣬⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠔⠉⠁⠀⠀⠈⠀⠀⣰⢞⣁⡀⠀⠀⢻⠇⣾⣿⡁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠠⡀⠀⠀⢾⣄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣠⠄⢀⡔⠈⠀⢀⠀⠀⠀⠀⣀⣀⣾⢱⣿⣿⣿⣿⣟⣡⣾⣿⣿⣇⠀⣠⠧⠿⠀⠀⠀⠀⠀⠀⠈⣲⣄⠘⣿⣧⣀⠀⡀⠀⠀⠀⠋
⠀⠀⠀⠀⣼⡟⣱⠟⠀⢀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠃⠀⠀⠀⢈⠀⠀⡀⠀⠀⠀⠈⠦⡈⢻⣿⣿⣿⣧⠀⠀⢀⡀
⠀⠀⠀⢸⣿⠛⢫⠀⠀⡏⠀⠀⠀⠀⠀⣠⠝⠛⠛⠿⢿⠿⢿⠿⠿⠛⢋⣽⡻⠿⠿⠷⣶⣿⣶⡄⠀⠀⡀⠀⠀⠀⡈⢓⣹⠀⠙⠿⣿⣿
⠀⠀⠀⢸⣿⣷⣄⢀⠀⠙⠤⢤⠤⠔⠊⠁⠀⠀⠀⡐⠁⠀⠀⠀⢀⠔⠋⠉⠀⠀⢀⡴⠣⠛⢻⣿⣷⡌⠛⢄⠀⠀⣽⣮⢿⡇⠀⠀⠀⠤⠀⠀⡆⠀⠠⡄
⠀⠀⠀⠈⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠂⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⢨⣿⣿⣿⣆⠀⢀⣤⡐⢾⣿⡇
⠀⠀⠀⢠⠈⣙⠿⣿⣿⣦⣤⣄⠀⡄⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡶⣬⣽⣿⣯⡉⠀⠀⠈⠉⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⣅⡈⠛⠮⢙⣿⣿⣿⣿⣧⣤⣄⣤⣀⢀⠀⠀⠀⢀⣀⣤⣠⣄⣠⣤⣤⡶⠶⠟⠛⠙⠉⠴⣿⡿⣷⣄⣿⣿⠉⢿⣄⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠘⠿⣄⠀⠀⠙⠂⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣰⣿⣿⣿⠏⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠉⠁⠁⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠋⠀⠀⠙⠿⡋⠀⠀⠀⠀⠀⠘⠒⠲⠴⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠦⠤⠤⣤⣤⣤⣠⣤⣀⣤⣤⡤⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠉⠐⠒⠀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣤⣀⣀⣀⣤⣴⡖⠚⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣏⠀⠀⠉⠉⢢⡉⠉⠓⣶⢭⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣹⡛⠋⠉⠩⠽⢿⣄⠀⠙⠀⠈⢻⣏⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠉⠀⢲⣿⣷⡶⠉⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⠱⡦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁⠂⠔⠋⠉⠉⠙⠀⠀⠈⠀⠀⠈⠻⣶⣄⠀⠀⠀⠙⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠲⣤⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢸⠸⡇⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡞⠫⣝⠛⡿⠧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⡆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⣂⡤⠞⠛⢏⡀⠘⢒⣲⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠈⠑⣛⣽⢟⠀⢶⢹⢡⡑⠠⣹⣭⡓⢦⣄⡀⠀⠀⠀⠔⢁⠔⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⡶⣻⢇⡣⠛⡱⢸⡜⢎⢧⠳⢄⢢⣩⢟⡾⣿⠀⠀⠀⠔⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣴⡛⡱⢺⠷⠇⠃⢘⣨⠒⠼⢛⣵⠟⢁⣿⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠛⠓⠛⠃⠛⠚⠚⣁⡤⠖⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠈⠉⠉⠁⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠀⠀⠀⠀⠀⠸⢿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⢺⣿⡇⠀⠀⠀⠀⢀⠀⣒⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⢶⢦⠄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡇⠀⢀⡀⠀⢰⡄⣿⡷⠖⣘
⠀⠀⢀⣤⠀⠀⠀⠀⠈⡢⣀⡀⢊⠄⠒⠰⠾⠿⢿⡿⠿⠶⠀⠐⠀⡀⠀⠀⢾⣿⡇⠀⢄⠠⡄⠄⣿⡥⠶⠄
⠀⣰⠏⠉⡇⠀⢴⡞⠟⠟⡇⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠿⢧⠀⣀⠁⢸⡞⠁⡔⠁⢀
⠸⠯⠀⠤⡀⠀⠀⣑⣦⢜⠀⢰⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣈⠐⠌⢳⣏⡡⣍⢉⡃⣴⠂⣠⠄
⠀⣠⠾⣆⠑⣀⡾⣋⡩⠈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠸⢏⠑⢶⠄⣶⣠⡾⢿⣿⣀
⢸⠏⠁⢸⣤⡿⠳⣄⠐⢄⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠣⡄⠈⠛⠀⠊
⠀⠀⠀⠈⠛⠖⡚⠂⠉⢲⡷⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠐
⠀⠀⠀⠀⠀⡴⠿⢷⣤⣤⡶⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⢠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣵⠤⠠⠀⠚⠐⠃⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠏⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠯⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⠋⠻⢿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣁⣔⢀⠓⠈⣤⣀⡀
⠀⠀⠀⠀⠀⣤⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣬⣰⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢐⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣹⣿⣿⣿⣅⠀⠁⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠤⠼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣀⠦⡈⡀⣿⡗⢰⣼⡀⢰⣦⣶⣶⡀⢉⣡⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⢳⣿⣿⣿⠿⡇⠐⢻⢟⡛⠁⠹⣿⣁⡀
⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⡇⠐⠃⠘⣻⣿⣿⣿⣿⡟⢡⣽⠁⢀⡘⠀⠀⢀⢧⠀⠚⠂⠀⠰⡎⠃⢀⣤⣀⣀⣠⡄
⠀⡀⢀⢀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣳⠁⡐⠛⠀⠀⠀⢾⣿⣿⣿⣿⡏⢀⣸⣿⣄⡉⠄⢸⡆⡈⢰⡀⢿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠀⠈⢳⡀⠀⠀⠹⣿⣿⣿⠁⢸⣿⣿⣿⣿⣶⣿⣿⣵⣿⠀⠈⡄⢀⣀⣵⣞⣸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢈⣀⠀⠀⠘⢷⣤⠀⠐⠿⢿⠋⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠇⠸⢻⣿⡖⡘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣇⠀⠀⠰⣏⢀⣤⣀⡘⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣄⡆⢹⣿⡟⠀⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠂⠀⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢭⠃⠀⠀⠀⠀⢱⣐⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠽⠿⠿⠿⠛⠋⠉⠠⠞⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡞
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣲⠆⠀⠀⢀⡀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠉
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡄⠴⠞⠀⠀⠀⡰⠏⠀⠀⠀⠀⣦⠐⢯⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣥⣄⠀⠀⠀⠀⠛⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⡍⠙⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣿⠟⠟⢋⠉⠉⠀⠀⠀⠻⣄⠀⠉⠉⠉⠉⣏⣙⣇⠀⠂⠀⠀⠀⠀⠀⠀⢺⣯⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⠠⠄⠀⠉⠻⣀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠀⠀⠈⠛⠛⠓⠢⠄⢀⡴⠟⠋⠉


⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠬⡗⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣾⡿⠾⠼⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣦⡀⠀⠀⠐⢆⡀⠁⣀⡐⣹⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⢯⡓⣿⡄⠀⠀⠀⠀⠈⠊⢥⣿⡏⡉⠀⠙⣿⣧⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⢾⣿⣷⣠⣏⢠⣀⡀⡀⠀⢀⣿⠿⣿⣷⠋⠙⢷⣿⣿⣿⡟⢿⡄⠀⠀⠀⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡖⠘⠛⠋⢸⡟⢤⣹⠀⠻⠈⠀⠘⠛⢿⠀⠀⣿⡏⠋⠱⢿⡄⣿⡄⠀⠀⠀⠀⠀⢆⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠓⠀⠀⡀⢰⠖⠻⠿⠚⠏⢈⡈⣿⡤⠀⠀⡀⠀⠸⠁⠀⠀⢀⣭⣤⣬⣽⣿
⠀⢀⣀⣴⡶⢚⣁⠀⠄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠂⠒⠤⠠⡠⠐⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉
⢀⡩⠤⣞⠟⡉⠀⠄⠀⢢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠠⢦⡀⠻⠁⢀⡀⢠⠔⠀⠀⠀⠀⠴⠀⠀⠀⠈⠀⠀⣠⣼⣿⢤⣤⣤⣴
⠨⡁⠀⡷⠰⡅⠀⡨⠄⣠⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠄⡘⠢⡿⠃⠀⠀⠀⠀⠀⣀⡐⡀⢀⠀⠆⠀⠀⢸⡇
⠀⢳⣰⢵⡀⠨⠁⠺⣿⠄⠀⠀⠀⠀⠈⠃⠀⠤⡆⢠⠀⡾⠠⠴⠄⠑⢤⠎⠀⠀⠀⠀⡀⡴⢚⡾⢿⠗⠶⡌⠀⠀⠀⡾
⢀⣹⡋⠛⠓⠂⣀⣴⢻⣇⡀⠀⠀⣤⠈⠛⠠⠏⠻⠈⠋⠀⠣⠀⡴⠂⢸⡀⠀⠀⠀⠹⠇⣠⠟⠁⠁⠀⠀⣨⣵⠙⣺⡓⠦⢴⡷⣴⡦
⠠⣟⡷⢈⠓⠖⠛⠛⠷⠼⠃⠀⠉⠁⢠⣎⠐⠀⠸⣼⡄⠀⠀⠀⠀⠀⠀⠧⠤⠶⠤⠤⠬⠴⠾⠆⠀⠠⠞⢿⣿⠂⠙⠓⠒⠈⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠈⠉⣹⣋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⣀⠔⠊⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢐⣀⣩⣤⠤⠄⣤⣀⣀⠀⠠⡄⠤⢤⣀⡙⢅⠢⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣀⡤⠖⠋⢩⠏⠁⠀⠀⠀⠀⠀⠈⠉⠒⢼⡳⡄⠈⠉⠓⠧⠀⢠⡄⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢨⠁⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢸⡄⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠙⡆⠀⠀⠀⠀⠀⢸⠋⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⠖⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣄⡀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠑⠲⠦⠴⠖⠋⡁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠄⣤⣠⡤⡤⠼⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠒⡈⠃⠛⢐⠒⠂⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡀⠀⠀⠻⣄⡔⠁⠀⠀⠀⡄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⣇⣀⡴⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡔⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⢧⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡉⠂⢀⠠⠒⠈⠁⡴⠃⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠊⢁⡠⠤⠗
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⡀⡄⠤⠴⠒⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢊⣡⢄
⢁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⡵⠊
⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠤⠤⠤⠤⠶⠶⠒⢻⡉
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣢⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠉⠙⠒⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣠⣤⠤⠼⢰⣤⣤⡤⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⣸⠀⢸⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠁⠀⠀⠘⠢⠚⠡⠀⠀⡘⠀⠙⠋⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⣀⠀⠀⣀⣀⣀⣤⠴⠖⠒⠃⠀⠑⠦⣤⣀⡀⠀⠀⠀⠈⢢

⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣾⣿⣷⣦⡀⠀⠀⣠⣶⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡇⠀⠀⠈⠛⠃⣀⣼⣿⠃⣠⣾⡟⣿⣿⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇⠀⠀⠀⣠⣾⡿⠋⠀⢰⣿⣿⣶⣿⣿⣶⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⡿⠿⠿⠿⢿⠇⠀⠀⠀⠿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⢸⡿⠛⠛⠛⠛⠛⠛⢿⡇⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠻⣿⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⣿⣇⣀⣀⣼⣷⣤⣤⣤⣤⣤⣤⣾⣧⣀⣀⣀⣿⣧⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣿⣇⣀⣀⣠⣿⣦⣤⣤⣤⣤⣤⣴⣿⣄⣀⣀⣿⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢀⣀⠀⠀⡀⢀⠠⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⡀⢀⠀⠀⢠⠀⢠⠀⠀⡄⡀⠄⠀⠄⠀⠀⣀⡆⡀⠀⡀
⠀⠀⠀⠀⢀⣀⡀⢀⠀⠀⢀⢀⠀⠀⠀⡀⠀⢀⣀⡀⣀⠀⠀⣀⠀⣠⡀⡀⠀⠀⣀⣀⢀⠀⠀⡀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⣀⡀⢀⠀⣀⡀⢀⢀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⣀⠀⢀⣀⠀⡀⠀⣀⢀⠀⢀⣀⠀⡀⠀⡀⢀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⢀⢀⠀⡀⠀⡀⡀⢀⡀⣀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⣀⢀⢀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠉⢛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠠⢜⡫⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⡀⠀⢢⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡐⠙⡢⠀⠀⠐⢒⣫⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⠓⠒⠲⠶⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠅⠤⡭⣭⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⢀⣀⣀⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠀⠀⠀⣸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢶⡀⠀⠀⣴⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢦⡀⠀⢸⡇⠈⣧⠀⢸⠃⠀⡇⠀⠀⣠⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠙⢦⠈⣇⠀⢸⡆⡟⠀⢰⠇⣠⠞⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠦⣤⣀⠈⢧⡀⠈⢳⣽⡀⠈⣿⡃⠀⣼⡼⠃⠀⡴⠋⢀⣠⡤⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠉⠛⠦⣽⣆⠀⠹⣧⠀⣿⠁⢰⡟⠀⣠⣾⡵⠚⠉⠀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠈⠙⠷⣄⠹⣆⢿⢠⡟⣠⡾⠛⠁⢀⣠⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠉⠉⠉⠉⠉⠛⠛⠻⠶⠦⣌⣳⣽⠿⣿⣞⣩⡤⠶⠟⠛⠛⠋⠉⠉⠉⠉⢙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠶⣶⣶⡶⠶⠶⠖⣺⣧⣀⣼⣿⡒⠶⠶⢶⣶⣴⡶⠖⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⢀⣀⣤⠶⠋⣵⢻⡟⡏⢧⡙⠳⣦⣄⣀⠈⠉⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣍⣠⣤⠤⠶⢚⡽⠛⠁⣠⡾⠁⣼⠁⣿⠀⠻⣆⠀⠙⢯⣛⠲⠦⣤⣄⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⢞⡟⠀⢰⣿⠀⢸⣇⠀⠹⣷⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣠⠞⢁⡞⠀⢠⡟⣿⠀⢸⡙⡆⠀⠹⡿⡗⢦⡀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⣼⠁⢀⡞⠀⣷⠀⢸⡇⠹⡄⠀⢳⠹⡈⣏⠑⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠞⠀⠀⣿⠀⢸⠀⠀⠙⣆⣘⡆⢳⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠦⠟⠀⠀⠀⠀⠉⠀⠸⡆⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠶⠶⠦⠤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⡇⠀⠀⣀⠴⠛⠉⠀⠀⢀⣀⡤⠶⠒⠛⢉⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠃⢀⡼⠁⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣼⡰⠋⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣏⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣅⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡇⠈⠛⠲⠤⠤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢛⠻⣿⣿⡿⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠟⣃⣿⡟⠵⠆⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣬⣭⣿⣿⣿⣦⣾⡿
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠉⢹⣿⠋⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠉⢹⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⡶⣾⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣼⣧⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠤⢄⣀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠁⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠠⠤⡀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⢸⠁⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠓⠄⡀⠀⢧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⢀⡈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⠟⠃⠀⠰⠟⠛⠛⠦⡈⠐⣄⠃⠀⠀⠂⠠⠆⠀⠀⠀⠀⠀⠞⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠽⠀⠀⠻⠥⠀⠀⠀⠀⢹⡆⠀⠀⠀⡨⢄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⢀⠁⠄⠀⢀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⢠⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⠄⢁⠀⠀⠸⠀⠀⠐⠿⢿⣛⣛⢻⡷⠖⠀⠀⠀⢸⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡀⠀⠀⣠⠜⠁⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡠⠚⠀⢨⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⢦⣤⡤⠔⠊⠀⠀⡠⠋⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠐⣾⡇⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⠙⠲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⢊⠁⡘⠃⠀⠉⠿⠦⣤⣀⣀⢐⣐⠧⠀⢀⡴⠊⣴⠁⠀⠀⢉⢑⠖⠦⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⢋⡜⠁⠀⠀⣠⠀⠀⠀⠀⠀⠉⣉⠉⠉⠆⠁⣸⠏⠀⡆⢰⠃⠏⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠐⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⣦⡿⠀⠈⢀⡟⣀⣔⢀⡀⠀⢰⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣸⣿⢣⡇⢠⢾⠇⣿⠟⠀⠀⢠⣤⠑⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠰⠙⣧⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢡⠏⠞⢸⣠⠇⡜⠸⢻⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠀⢸⠁⠀⠀⢸⡟⠀⠃⠀⢿⠀⣠⠄⢠⣤⠀⠈⠢⠀⠠⠂⠈⣁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠐⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣸⠃⠀⠀⠀⠈⠣⡄⢰⡿⠋⡁⠀⣤⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⢸⠇⡀⠳⡄⠘⠧⡀⠀⠀⡈
⠀⢀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠘⡷⠸⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⢀⡄⠀⡇⠀⠀⠘⠀⣰⠀⠀⠀⠀⢠⠂⠀⠁⠷⠄⢁⡀⡀
⠀⡇⠠⠀⠀⠀⠀⢀⠔⠠⠁⡤⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⢐⡅
⠀⢱⠐⠀⠀⠀⡰⠃⠀⡴⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢼⡇⠀⠀⠀⠘
⠀⠀⢣⣄⠀⠈⠀⣠⡌⠔⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁
⠀⠀⠀⠐⠢⠔⠊⠁⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠆⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢖⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⢀⣠⣤⣉⡛⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠉⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠷⠦⠤⠾⠋⢹⡆⠀⠀⢀⣠⠶⢻⡟⠀⠈⠉⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠲⠦⣄⣹⡎⠙⠶⣤⣀⣤⣤⣴⠶⣾⠁⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠉⠁⠀⣾⠁⠀⠀⣠⡟⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⣀⣀⣠⣿⠾⠛⠀⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⢸⡇⠀⠀⣰⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠉⠛⠛⠋⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⣷⠀⠀⠀⣾⣀⣤⠾⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⣸⠷⠶⢿⡶⠚⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⢻⣄⠀⠀⠀⣠⡏⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⠀⠙⣶⡀⠀⠟⠀⠀⠀⢨⣧⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢹⣇⣠⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣀⣀⣤⣤⣿⠀⠀⠀⠀⠈⢷⣤⣀⣀⣀⣀⣠⣤⣤⠤⠶⠋⠀⠀⢸⡇⠀⠀⠉⠉⠉⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⡟⠛⠋⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠄⣸⠏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠉⠐⢿⣤⡀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⣿⡀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠙⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠙⠿⠆⠀⠰⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠡⣄⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠚⠠⠶⣿⠿⠿⣷⠦⡀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡋⢠⡀⠨⣀⠀⠀⠠⠈⠑⡄⠀⠱⡌⢂⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⢠⣼⠏⠀⠀⠀⠀⠀⢀⣵⠆⠀⠪⡖⠘⡀⠀⢘⡀⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⢈⠔⠁⠐⣿⡿⢀⡐⣆⣀⠀⠀⠙⠿⠃⢠⣾⡿⠞⠀⠀⠸⢀⠇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠈⠀⠀⠀⠄⠏⠀⠀⠀⢻⣿⡐⠌⠿⠟⠁⠀⣀⡤⠶⡛⠄⠀⣀⣠⣴⡷⠃⠘⠀⠀⠀⠀⠀⠀⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣀⡡⠐⠀⠀⠒⠒⠤⡁⠀⡄⠀⣾⠿⡟⣧⣡⣤⣤⠶⠾⠋⠉⠀⠀⠈⠛⠛⠟⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠽⣿⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠈⢆⠈⠂⠤⠐⣡⡼⣿⠛⠛⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠠⠀⠈⠹⣧⣤⣶⣿⣿⣿⣿⣷⠄⣿⠿⠆⠀⠀⠀⢀⠸⠀⠀⣠⠎⠀⠛⠛⠀⠀⠀⠙⠁⠀⢙⣆⣀⠠⠤⠴⠋⠳⠤⣀⢂⣍⣟⡆⠀⠀⠀⠀⡇
⠀⠠⠃⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠋⠴⠊⠀⡠⢶⣶⠄⠀⠀⠄⠀⢠⡏⠀⠀⠀⠀⣎⠶⠀⠀⠀⣰⠟⠉⠀⠀⠀⢀⣴⣶⣦⣌⣿⣿⣿⡿⠀⠀⠀⢀⠃
⠀⠈⢦⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠴⠋⠀⠀⠄⡤⠴⠂⠀⠀⠀⢷⡀⢤⡤⠀⠀⣀⠠⣴⣿⢃⡤⠋⠁⠙⠒⠺⢿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠸
⠀⠀⡄⢀⣠⡴⠶⠶⣦⡀⠀⢀⣠⣤⣤⣠⣤⣤⣄⠒⠒⠂⠀⠤⠄⠀⠈⠙⢷⣤⣄⣀⣀⣀⣾⣿⣼⣆⠀⠀⠠⠀⠐⠂⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⡖
⠀⠀⠙⢏⠁⠀⠀⣀⣀⡙⣖⣉⣁⣀⣀⠀⠀⠀⢻⣄⣰⠟⠛⠛⠛⠻⣷⣀⣤⣤⣤⠉⠉⢉⣁⣘⠿⠟⠁⠄⠀⠀⠀⢀⣤⡶⠶⠒⠶⣦⡄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠉⠡⠤⠤⠄⢀⡀⠀⠀⠀⠐⢿⡀⢠⡿⠉⠉⠉⠙⠉⠙⠶⣤⡴⠋⠀⠁⠀⠀⠀⠈⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂⠉⠁⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠤⠤⣄⡀⠀⢰⡃⠡⠀⠀⠀⠀⠐⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⠋⠐⠑⠁⠈⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠒⢀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠚⡄⠀⠈⢀⠆⠀⠀⠀⠅⠂⠀⠦⡀⠀⠀⠠⠐⠀⠀⡀⠴⠳⣱⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠞⣁⠀⠈⠁⠀⣠⠆⠀⠀⠀⡀⠐⣒⠖⢲⢫⠀⠀⠀⢀⡱⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠈⠃⠉⡀⠙⠐⠒⠒⠉⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠤⠤⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⢃⡀
⠀⠀⠀⠀⠀⠰⠂⠐⠎⠁⠀⠀⢸⣀⣠⢀⠅⠀⠀⠀⠀⠀⠉⠛⡛⠐⠒⠔⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠡⡀⠀⢀⠜⠀⠀⠀⡄⠀⠀⣄⡀⠀⠀⠀⠀⢀⣀⡇⢸⡀⠀⠀⠀⢂⠖⠉⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠘⠁⢠⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⡀⢠⡦⠂⠀⠊
⠀⠀⠀⠀⠨⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠘⣷⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣆⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣸⣷⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⣾⠇⠀⠀⠀⠀⠀⠸⡇⠀⢹⡆⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⣷⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸
⢴⣶⣤⣄⣤⣤⣄⣤⣄⣤⣤⣴⣶⣾⣿⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠁⣻⢿⣿⣿⣗⣷⣦⣴⣤⣤⣶⣶⣿⢻
⠀⠈⠉⠉⠋⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠰⡄⠀⢀⢸⡇⠀⣿⠄⠀⠀⠀⠀⠈⠀⠨⣝⣟⢻⢿⠟⢟⣻⡛⠟⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣶⡾⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⢸

⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⡇
⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⡇⢠⣾⠛⣿⡆⠀⣠⣿⡇⠀⢸⡇
⢸⡇⠀⣠⡾⠟⠁⣾⣯⣼⣧⡄⢸⡇
⢸⡇⠸⠿⠿⠿⠇⠉⠉⠹⠏⠀⢸⡇
⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⠸⠿⠿⠿⠿⣿⠿⠿⣿⠿⠿⠷⠿⠇
⠀⠀⠀⠀⠀⣿⠀⠀⣿
⣶⠶⠶⠶⠾⠿⠷⠾⠿⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⠿⢿⣶⡀⠀⢀⣴⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⠀⠀⠈⢉⣠⣾⡿⠁⣴⡿⠋⣿⡇⠀⠀⢸⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣟⣁⣀⡸⠿⠿⠿⣿⡿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠉
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⢻⣿⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⢸⡇
⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⢰⡇⣿⡇⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠘⠇⣿⡇⠟⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⣿⡀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣿⣇⢀⣀⣀⣀⣀⣀⣸⣿⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⡇

⠀⠀⠀⠀⡀⠀⢀⣀⣤⣤⣤⣴⣤⣤⣴⣤⣤⣄⣀⣀⡀
⠀⠀⣀⣤⣶⠿⠛⠉⠉⣧⣤⠀⠀⠀⠀⠀⢩⠉⠉⠙⠛⠳⢦
⠀⠈⠛⠁⠀⠄⠂⠐⠀⠿⠈⠀⠀⠀⠀⠀⢸⡇⡇⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠘⡀
⠀⠀⠀⣀⣀⣐⣊⣁⣠⣤⣤⣤⣤⣀⣀⣀⣀⣠⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢚⣩⡷⠮⠭⠭⠭⠡⡞⠛⢒⡢⠭⠤⠤⠤⡴⡋⠙⡛⡏⠛⠶⠦⡄
⠀⢩⠱⡄⠇⠀⣀⡀⠀⣿⡄⡯⢀⣀⡀⠀⠀⡇⡇⠘⠀⠉⠉⠙⣶⠉
⠀⠀⠀⣿⠐⣉⣩⠠⠄⠿⠁⡄⢈⣀⡀⠀⠀⡇⠁⠈⣯⡀⠰⠀⣿
⠀⠀⠀⣿⠀⣁⡀⠀⠀⡃⠀⡇⠨⠄⠀⠀⠀⠷⠀⠀⠃⠂⠀⠀⢸
⠀⠀⠀⠸⢀⣀⡠⠀⠀⠇⠀⠁⠲⠶⠒⠀⠀⠀⠀⠀⠤⠤⠀⠀⠘
⠀⠀⡀⠀⠉⠀⣀⠀⠀⠂⠀⠀⠀⠤⠠⠀⠀⠀⠀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢨⠀⠀⢹⠠⠄
⠈⠀⢡⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠁⠁⠀⠀⠀⠀⠀⣂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡏⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⣤⣁⠀⡐
⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡶⠶⣶⣶⠤⢶⡖⣶⣿⣿⡆⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠘⢺⢿⠛⡿⠸⣟⠸⠛⢻⠀⠿⠘⠻⠈⠁⠁⣿⠀⠀⠀⠀⠸⠛⢹⠸⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠘
⠀⠀⠀⢠⣈⣀⣀⣀⡤⠬⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⡄⣀⣴⣄⠀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠐⢚⠟⠛⠛⠓⡄⠉⠉⠉⠉⠉⠁⠉⠀⠀⠁⠀⠀⠀⠀⠈⠉⢉⠉⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⡗
⠀⠀⠀⢀⣤⣤⣧⡄⠠⠀⠀⠀⣉⣿⡿⣿⣿⣿⡂⠀⠀⠀⠠⡄⡀⠀⠀⠱⡄⢸⣄⠀⠀⠀⢀⠀⠀⢰⡇
⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⢸⢿⡗⢿⡗⣻⡅⠀⠀⠀⠀⠃⠁⠀⠀⡀⠀⢱⡿⠀⡀⠀⠈⠐⢦⣾⡇⢀⡀
⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⢸⣛⣿⠛⣫⡻⡇⠀⠀⠀⠀⢠⠀⠀⠀⡿⢠⠀⣷⠀⣀⡄⠀⠀⢸⣿⣤⠺⡇
⠀⠀⠀⠀⡙⠋⠹⠆⠀⠀⠀⠀⢸⣿⣿⢸⣥⠘⣇⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⣿⡠⠉⠁⠁⡀⠐⣿⠀⢰⡇
⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠘⢿⡟⠈⣷⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣿⣧⠦⣤⠀⡇⠀⣿⡇⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⢺⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣿⠉⢠⣿⡍⣙⣿⣯⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⣾⣧⠀⠘⣿⠸⡍⠙⠛⠁⠀⠀⠀⠀⠀⠀⠐⢢⡄⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠝⠉⢿⣷⠀⠀⢿⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠆⠀⠈⢿⣷⠀⠙⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠂⠀⠀⢸⣿⣦⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡁⠀⠀⠀⠀⠈⠙⠷⡌⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢀⢁⣀⡀⠀⠀⠀⢰⡇⣹⣟⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⣷⣿⡟⢾⣿⢟⠠⠄⠀⠀⡸⣧⡟⡁⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠨⣿⣯⣹⠻⠿⡌⠓⠀⢠⡾⠉⠉⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣷⣶⡠⠀⠏⡀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⢀⣀⣤⢤⠶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣿⣿⢶⣿⢷⣦⡤⢶⣤⣄⣠⣤⣦⣥⣥⣴⣢⣤⡤⠞⠿⠋⠉⠉⠐⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠻⠻⡦⣾⡆⠉⠻⠋⠉⠛⠟⡍⠋⢛⡏⠁⠙⡿⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢹⡄⠙⡄⠀⠀⡀⠀⠀⡇⠀⠸⡇⠀⠀⠃⠀⠀⠀⢀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⣷⠀⢱⠀⠀⣇⠀⠀⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠆⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢹⡄⠈⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠸⠀⡀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣧⠀⠀⠀⠀⡅⠀⠀⠀⠀⠁⠀⠂⠀⠁⣠⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣤⣤⣅⡀⣠⣀⣀⡄⢀⣧⣾⡴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡏⣼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⡿⠿⠋⢩⣩⠆⢀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⡏⣋⠄⢠⣿⣿⣷⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⣿⠺⠟⢃⣀⣿⣌⣡⣿⣻⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⡀⠃⠀⢰⣾⣿⠟⡻⣿⣿⠿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⠀⠟⡋⣻⣿⡁⣼⣷⣝⣿⣶⣿⠆⠀⠒⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⣄⡀⠀⠀⠀⠈⢙⠿⠉⢠⣄⣻⣾⠛⠾⠿⣟⣿⣿⣿⡧⠒⠀⠀⠀⠀⠉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢹⣿⣪⣟⣵⡾⠗⠀⠒⣼⣿⣿⣿⠶⣶⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣾⣿⣿⣶⣶⡀⣀⡀
⠀⠀⠀⠀⡠⠀⠀⠿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠀⠠⠠⠤⠤⠄⠤⠤⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠂⠈⠌⡁⠀⠰⠀⠀⠐⠋⠉⠈⠀⠀⡤⣀⣄⡀⢔⡂⠚⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠠⠀⠋⠀⠀⠀⢄⠀⠘⠛⠀⢀⠀⣐⡷⠘⠋⠀⠀⠄⣈⣄⡈⠉⠁⠀⡀⠀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠲⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⠀⡀⠌⣈⢡⢶⠅⠘⠟⠛⠁⠘⢶⠂⠑⠉⠀⠖
⠀⠀⠀⠀⣴⡄⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢰⠈⢋⣁⣀⣰⣚⡉⠛⠁⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠠⠀⠁⠀⠁⠀⠐⠾⢃⡁⠒⠃⠀⢄⠀⠀⠀⠀⠀⠊⠁⠀⠈⠁⠀⠀⠀⢉⠀⢀⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠁⠠⠁⠐⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠈⠁⠀⠀⠈⠀⠠⢄⠄⠀⠐⠁⢈
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢅⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡏⠉⠉⠛⠛⠲⠶⠶⠶⣶⣤⣤⣤⣤⣤⠄⠀⠰⠀⠦⠀⠐⠶⢶⣶⣶⠒⠒⠲⣶⣶⣶⢶⣶⣶⣶⣶⣴⣤⣦⡴⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠤⡁⣀⠀⣈⣩⣨⡶⠿⠛⠛⠉⠏⠀⠀⠠⠀⠀⠀⢚⠁⢘⣄⣄⣀⢠⣌⡇⢀⣀⢠⣿⣍⡉⠉⠉⠉⠈⠉⠉⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠉⢛⠙⠀⠀⠁⠐⣤⣤⣄⠀⠆⠐⠙⢄⣩⡤⢯⡟⢢⠉⣉⣉⣉⣿⣿⣓⠒⠒⠤⠤⠤⠤⠄⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⣴⡧⡖⠀⠂⠃⠀⡀⠀⠰⠚⢿⣿⣿⡷⠊⠀⡀⠀⣤⣬⣏⣆⣩⣈⣁⡀⠈⠉⠉⠉⠁⠉⠀⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠈⠀⢁⠉⠀⠀⠠⣴⣿⣈⠁⠐⠊⠥⢷⢳⡞⢛⣻⣿⣿⣿⣧⣾⣇⣀⣼⣆⣭⣏⣛⣛⣻⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⡀⠀⠈⠁⠀⠠⢟⣳⣌⣹⡿⠏⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠀⠉⠉⠉⠀⠀⣀⠵⢿⠫⠹⣟⣿⢿⠶⠒⠂⠀⠐⢉⠃
⠀⠐⠿⠏⠰⡀⠀⠢⣈⡇⢫⣫⠀⠀⠁⢀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢺⡄⠀⠃⠀⣞⠿⡉⠀⠀⠀⠀⢀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠻⢣⠍⠏⠐⠀⢀⣰⣶⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠏⠡⡶⠅⠐⠀⠄⠱⢂⡀⡀⠀⠐⠀⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⢁⣀⡅⠀⣯⢹⠻⡟⢦⡀⠀⠀⠀⠀⡠⠎⠁⠀⠉⣒⣀⣀⡀⠲⡆⠀⢨⠶⠤⠟⢀⣘⣚⡳⠆
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠛⠿⠷⠜⠁⠀⠀⠆⠑⢄⠀⠀⠀⢴⠄⠑⠋⠀⠀⠀⠨⣉⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⠂⠀⠀⠠⠁
⠀⠀⠀⠀⠄⠀⠀⣰⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⢔⣤⣶⣶⣶⣶⠲⠴⠖⠒⢲⢶⣦⣤⣠⡄⠤⠐⠠⡆⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠐⠈
⠀⠀⠀⠀⠀⠈⠒⠼⢤⣀⡀⣀⣀⡠⣄⠀⠀⣀⠉⢚⣛⣓⠛⠒⠒⠒⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠀⣰⢀⣀⡀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠒⠒⠛⠁⠁⠒⠒⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣀⡄⢄⣀⢐⠀⡀
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⣲⣶⠛⠓⣻⠀⠀⠀⠀⠀⠠⠂⡔⠂⡜⡲⡠⣼⣴⣸⣧⣾⡷⣧⢢⡎⢠⡀
⠀⠀⠀⠀⠀⢿⠛⢦⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡔⣻⣭⡿⣃⣾⠏⠀⠀⠀⠀⠈⠀⢱⣧⣼⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡉⠻⠿⢿⣯⣽⣿⣏⠁⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠛⠶⠶⠿⠳⡟⠃⢹⢻⣧⡀⠀⠀⠀⠀⢠⠴⡻⠛⠀⠸⣿⣿⢿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⣴⣎⠀⠀⠀⠀⠀⠀⠙⢶⡿⠀⠹⣿⣦⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⡟⠀⣿⠐⠙⢻⡟⣻⡟⠉⠉⢹⡿⢿⣦⡭⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢳⡀⠀⠀⠀⠀⠀⠠⠀⢸⠗⠾⡟⢀⣰⡟⠀⣿⠁⠀⢀⡟⠀⠀⠗
⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠻⠉⠋⣝⠳⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠹⣹⡅⠈⠱⣼⢺⠀⣤⣿⠀⣠⠏
⠀⠀⠀⠀⠀⢴⣛⣿⣿⡃⠀⠀⠀⠀⢻⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠉⢳⡀⠀⠺⠀⠀⣿⢏⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣶⣄⠀⠘⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⣄⠃⣂⠀⢉⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⠁⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⣾⣷⠎⠙⠓⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⢿⣿⢿⣧⣶⣶⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡸⣿⣷⣴⣷⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⣀⣤⣶⣶⣶⠿⠿⠿⠛⠋⠉⠉⠙⢾⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣾⠋⠛⣷⡄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⢿⣦⣴⠿⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⣀⣠⣾⠟⢿⣄⣀⣀⣴⡟⢿⣦⣀⣀⣠⡿⠻⣧⣄⣀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠉⠛⠉⠁⠀⠀⠉⣙⣋⣁⣀⣀⣈⣙⣋⠉⠀⠀⠈⠉⠛⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣀⣀⣀⣀⡀⠀⣿⠉⠉⠉⠉⠉⠉⣿⠀⢀⣀⣀⣀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠛⠛⠛⢻⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⣿⡟⠛⠛⢻⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠻⠿⠿⠿⠿⠟⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠻⠿⠿⠿⠿⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿

⣿⣋⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⡉⣝⢯⣭⡑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿
⠀⠀⢀⣀⡠⢤⣤⣀⣤⡶⠟⠉⠁⠀⣄⠦⣱⠝⠎⢻⣕⠳⠨⣖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿
⠀⠈⠉⠉⠙⠛⠛⠯⠥⣄⣀⠺⣄⣀⠌⢩⡤⠚⠳⣄⡈⠓⢦⣈⠓⠤⠤⢆⣀⡀
⠀⠀⠀⠀⣴⠋⠀⠈⠀⠀⠈⡿⠀⢴⣦⡈⠙⠲⠦⣄⠉⠢⠄⣨⣵⣶⣿⡛⠿⣧⡀
⠀⠀⠀⠀⠉⠓⠒⠒⠢⡤⠶⣾⠁⠀⠙⢿⡶⣄⣒⠚⢣⣴⣿⣯⣟⠿⣤⣙⡷⠞⣛⠫⣠⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⢎⣥⡾⢿⣍⠻⣯⣉⢻⡾⢋⠰⣖⡨⣓⢮⡋⢍⠒⠦⢄⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣥⣴⣾⡟⠙⢿⣦⡙⢿⣌⠿⠋⣰⡮⠑⢮⣙⢮⣕⢯⡳⢥⡤⠲⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣷⣄⣀⠙⠛⠛⠁⠀⠺⢮⣙⢶⣄⠉⠳⢬⣛⠚⠁⢀⠠⣂⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡾⠟⠉⠀⠀⢀⡀⡀⠀⢰⣟⣷⣍⡳⢦⣶⠋⠀⢀⠠⠼⠘⠡⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣶⡄⠠⣖⠀⡀⣝⣿⠦⠈⠛⠋⠈⢻⡶⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠤⠜⠿⣽⡊⠂⣈⢱⠀⠀⠀⠈⠀⠀⠀⢑⠀⢠⠆
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠼⠈⣷⠀⠈⠁
⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠁
⢿⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢥⣳⣾⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⡄⡀
⠀⠀⠀⠀⠀⠀⢀⢸⡿⡋⠀⠀⢐⣤⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⢦⣄⡀
⠀⠀⠀⢠⠀⠀⠀⣰⣿⣧⣾⣿⣿⣿⣣⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⣿⡿⠟
⠀⠀⣀⣷⡄⢶⣧⠇⠉⠙⢛⣿⠿⢿⣥⡾⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡔⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⠏
⠀⠀⠘⠻⣿⡞⠁⠀⣰⣀⠀⠐⠚⠾⣿⣾⠅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠺⣕⡦⢦⣄⣤⣤⣶⣾⣿⠿⠟⠛⠉⠛⠏⣭
⠀⠀⠀⠀⢻⣽⡎⣾⣿⣣⡾⢂⡤⠚⠛⠿⠾⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠁⠀⠀⠀⠀⠀⠀⠈⢈⣿⡇
⠀⠀⠀⠀⠀⣹⡿⡟⣱⣿⣷⢋⢄⣤⠙⠃⠀⠀⠀⣀⣬⣷⣄⣢⣮⢁⡀⠀⠀⠩⠦⡁⠠⣠⣀⣠⣴⣦⣤⡀⠀⢀⣼⣿⣿⣶⣦⣀⣀⣀⣤⣾⠿⠃
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣛⣵⣿⡿⢣⡶⠙⠀⢠⣿⣿⣿⣿⡗⠈⠳⣮⡄⠀⠀⠀⠀⠀⠰⢦⡈⠙⠯⣽⣿⣿⣿⠿⠟⢛⣻⣿⣿⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⣷⣿⠷⠟⢠⣮⣽⡿⢯⡝⢿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣤⣶⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣛⢿⡦⠙⢀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣝⠾⡑⠄⣠⣌⢂⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠤⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣧⠀⠀⡨⠮⠙⣣⠅
⠀⠀⠀⠀⠀⠀⣠⣤⡶⠋⢁⡤⠄⠀⢤⣄⣠⠀⢀⡀⠙⠿⠀⢡⣀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠠⠆⠢⢠⡤⠋⠀⠀⠛⣹⢿⣷⣄⢠⡠
⠀⠀⠀⢀⣾⣾⠟⠛⠲⢎⣀⣀⡀⠀⢲⡶⠁⢀⠐⠛⠂⠀⢀⣉⣉⠁⠀⠰⡀⠀⠀⠀⠑⠄⠀⠀⠄⢸⢢⢠⡀⠠⣤⢭⡭⡿⣞⣍⡁
⠀⠀⠠⣿⣿⡟⠀⣠⣤⠈⠀⢠⠝⠀⠀⠀⠀⠘⠓⠂⠀⣤⠈⠋⢀⡽⢾⣦⢡⡀⠀⠀⠀⠀⠠⡌⠀⡽⠖⠚⠁⠀⠀⠟⣛⣓⣫⢩⠕⠃
⠀⠀⠠⡘⢏⠀⠌⡁⠀⠀⠐⠿⠿⠋⠉⢹⡶⠴⠀⠀⢔⣀⣀⡀⢀⣹⡿⢋⡞⠀⠀⠦⠤⠀⢱⠀⢀⠀⠀⠀⠀⠀⠉⠉⠁⣘⣛⣠⠀⣀⠐⠴⣤
⠀⠀⠀⠙⢦⠁⠻⠥⢈⣷⣤⡀⠀⠀⣴⣤⣤⣤⣤⡀⢀⣉⡬⠛⠉⠩⡾⠟⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡁⠂⠐⠀⡇
⠀⠀⠀⠀⠀⠳⣦⣀⡐⠀⠉⠡⠄⠈⠉⠈⠁⠉⠉⠁⠀⢀⣀⣬⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣶⡖⣦⠀⠀⠀⢀⢠⢦⠄⣇⣭⢵⡞⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠹⡞⠉⠋⠛⠒⠖⠶⢶⢶⣶⣶⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⠎⠱⡶⠀⠀⠀⠙⢻⠀⠈⠁⠈⠀⣨⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠐⠧⡏⢿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⢲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢲⡟⠁⠀⠀⠀⠀⢀⣾⠤⣀⣤⣗⠾⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠾⠿⣿⡿⠏

⠀⠀⠀⠀⠀⢀⣠⣤⡤⣤⣄⣀⣤⢤⡤⢶⣤⣀⣀⣀⣤⠤⠤⡶⢤⣤⣄⣀⣠⣤⣴⠶⠦⣤⣀
⠀⠀⠀⢀⡴⠋⠀⠀⠳⠤⣤⣤⠤⠞⠀⠘⢆⡀⠀⣀⣀⡤⠞⠁⠘⢦⣀⡀⣀⣠⠜⠀⡤⡀⠈⠳⣄
⠀⠀⠀⣼⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠀⠀⠀⠈⠉⠉⢀⣀⣀⣀⣀⣀⣀⣹
⠀⠀⣴⠛⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⢲⠲⠒⠒⠒⢒⡒⠒⠛⣉⣭⣍⡉⢉⣭⣍⣉⣉⣉⣀⣠⣤⣉⡗
⠀⠀⠈⣛⣿⣙⣲⣒⣉⣶⣖⣟⣶⣖⣉⣉⣓⣶⣫⣭⢯⣉⣭⡤⠤⠤⠽⠧⠤⠤⠤⠤⠤⠧⠤⠖⡟⣶
⠀⠀⠀⣏⠓⠒⠊⠓⠤⠴⠒⠲⠒⠊⠓⠒⠒⠛⠒⠒⠛⠉⠉⠈⠙⠋⠙⠋⠉⠙⠋⠉⠑⠒⠊⠉⢀⡏
⠀⠀⠀⠙⢦⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠞
⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⠀⠀⠀⠀⠀⢀⢰⣶⢀⢠⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢴⡀
⠀⠀⠀⢠⠶⠦⢨⣟⣛⣻⡥⠀⠀⠀⠀⢸⠒⠒⢺⣿⡏⢾⣿⠀⠀⠀⠐⢒⣒⢂⡒⣒⢐⣒⡒⠀⠀⠀⠀⠐⣚⣭⣷⡿⠟⠋
⠀⠀⠀⠀⣀⣀⢻⣿⣿⣿⡯⠀⠀⠀⠀⢸⣴⣤⣴⣿⡇⢸⣿⠀⠀⠀⠀⢸⠿⢸⡿⢱⠻⠿⠇⠀⠀⠀⠀⠀⠀⠉⠀⠐⠄⡀⡀
⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠸⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⣺⣿⣸⣇⣳⣖⣿⡇


⠀⠀⠀⠘⢫⣭⣭⣭⠛⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢸⣴⣦⣼⢀⢿⡇⠀⠀⠀⠀⡖⠒⠒⠒⠒⡆⠒⡒⠀⠀⠀⠀⠲⣠⡠⠂⢰⣿⣷⣿⠀⠀⠀⠀⠀⠀⣰⡀⣄⠀⡞
⠀⠀⠀⢸⡿⡿⡿⡿⣿⢰⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⢸⣿⣺⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠋⠛⠋⠋⠋⠘⠃⠀⠀⠀⠀⠉⠛⠛⠉⠛⠉⠉⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠠⠶⠶⢶⠶⠶⠶⡆⠀⠀⠀⠀⢀⣋⣀⣃⣘⣁⣙⡀⠀⠀⠀⠀⠨⠉⣏⣹⠍⢭⣉⡇⠀⠀⠀⠴⠾⠿⠿⠿⠿⠿⡿
⠀⠀⠀⠸⣿⡇⢫⣿⡡⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠋⠙⠉⠁⠀⠀⠀⠀⢠⣄⣿⣿⣄⣼⣻⡇⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣭⡀
⠀⠀⠀⠰⣮⡆⣱⣿⣷⡾⣃⠀⠀⠀⠀⠰⠷⠶⠲⠖⢶⠶⠆⠀⠀⠀⠀⠀⠉⢰⡇⠈⠀⠉⡇⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣷⠙⠂
⠀⠀⠀⠠⠥⠤⠭⠭⠭⠬⠅⠀⠀⠀⠀⠠⠦⠶⠶⠶⠴⠶⠄⠀⠀⠀⠀⠨⠭⠭⠹⠭⠭⠭⠇⠀⠀⠀⠀⠀⠣⠿⠿⠿⠿⠿

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠰⢀⢀⡀⡄⣀⡂⡂⠀⠀⠀⠀⢸⣧⣵⣶⣶⣾⣽⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⢐⠉⠚⠛⢛⠛⠈⢘⠀⠀⠀⠀⠀⣒⣒⣒⣓⣒⣒⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣧⣦⣶⣶⡀
⠀⠀⠀⢸⣃⣃⣸⣸⣸⣃⣻⠀⠀⠀⠀⠀⢰⢒⣒⣆⣒⡺⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢨⣭⣤⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠓⠒⠒⠚⠒⠒⠃⠀⠀⠀⠀⠀⠘⠀⠂⠂⠂⠃⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠛⠛⠃⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠊⠁⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡖⠒⠛⠦⠤⣀⠀⠀⠀⢸⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣷⠀⠀⢄⡀⠈⠳⢄⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢳⡀⠀⠀⠙⢆⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠢⠤⢭⠦⣌⣧⠀⠀⠀⠈⡆⠀⢸⠄⠀⣠⣴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⣿⣀⠼⠶⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⡬⣶⠖⠉⠙⠢⣄⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⢀⠂⠀⡞⣧⡀⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⡂⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣄⠀⠀⠘⠆⠀⠉⠑⠒⠒⠀⠀⠉
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⣈⠒⠤⡀⠀⡸
⠀⠀⠀⠁⠁⠒⠢⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠊⠑⡼⠇⠇⠀⠀⠈⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠘⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⢱⢸⢸⠁⠳⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⣀⣔⡀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢆⠀⠀⠀⠀⠀⡂⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠆⠠⠤⠅⠀⠀⠀⣶⣺⣇⠀⠀⠚⢚⠄⠀⠀⠀⠀⢉⢀⣰⢉⠏⠀⠀⠀⠀⠀⠀⡤⢡⡤⠆
⠀⠀⠀⠀⡄⠲⣚⠃⠀⠀⠀⠀⠸⠍⠇⢀⠰⡶⢰⡋⠀⠀⠀⠀⣟⣬⠁⢸⠁⢠⡖⠀⠀⠀⠔⢂⠀⠰⢭⠡
⠀⠀⠀⠐⠋⠁⠹⣆⠀⠀⠀⠀⠘⠓⣀⠩⠔⣢⠦⠀⠀⠀⠀⠀⠙⣡⣀⣿⡰⠋⠀⠀⠀⠀⠀⡀⢳⠜⠉⣁⡲
⠀⠀⠀⠴⠆⠢⠀⠇⠀⠀⠀⠀⠀⠀⠐⠓⠠⢈⡶⠂⠀⠀⠀⠀⠙⡛⢸⣟⠁⠀⠀⠀⠀⠀⠀⠁⠹⢛⣋⡼⠁
⠀⠀⠀⠀⠀⣀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣀⢂⠈⠀⠀⠀⠀⠀⠀⢠⣼⢟⣡⠀⠀⠀⠀⠀⠀⠀⠀⢘⣭⡈⠁
⠀⠀⣀⡄⠚⠛⠃⠉⠂⠀⠀⠀⠀⠀⠀⠙⢉⡛⠀⠀⠀⠀⠀⠀⠀⠛⠼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⠏⢉⠀⡈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠂⠀⠀⡍
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢇⠳⣀⢦⡤⡎⠑⠒⠲⢤⡀
⠀⠀⠀⠀⠀⣠⢋⡀⠀⠀⠈⠦⢎⣹⠒⠁⠀⠀⠀⣀⣨⣦⣤⣀
⠀⠀⠀⠀⠀⡇⠀⠈⠂⠀⠀⠀⣸⠙⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⢸⠀⣷⠀⠀⣿⣿⣿⠿⣋⣌⠻⡏⢹⣧⣀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⢸⠀⢸⠀⢠⢋⠋⡾⣪⠞⡩⡇⠀⠈⢁⠛⣍⠉⠓⠒⢦
⠀⠀⠀⠀⢰⡧⠖⠒⢤⡇⠀⠀⢸⠀⢸⠀⢸⢸⠀⠀⠀⢜⡾⠃⣠⠃⡸⠀⠟⠤⣷⣯⣿⠗⢄
⠀⠀⠀⠀⠸⠤⠒⠒⠢⣵⢀⣀⣸⠀⢸⣤⡼⡍⠀⡴⠒⠉⠈⡏⣉⣦⠁⣤⡄⠀⠀⠈⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⣴⠀⠀⢸⠈⠀⠐⠺⣄⢸⠃⣷⡇⠀⡇⠀⠀⠀⠘⠏⢻⢶⠏⠀⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡟⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⡇⠀⡀⠀⠀⠀⡜⠉⡆⠀⠠⠄⠀⠈⡄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡇⡇⠀⡇⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⢳⠀⣱⡀⠀⢰⠇⠀⣧⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢱
⠀⠀⢀⣀⣰⡇⡃⢀⡁⠀⠀⠀⡄⠀⠀⠀⡏⠀⠀⢸⢠⠇⠙⡄⡼⠀⢀⣿⡄⠀⠀⠀⠀⠀⣴⠒⣛⡓⠺⡆
⠀⠀⠀⣈⣭⠋⢀⠈⡟⠛⠓⠒⠓⠒⠲⠶⣇⠀⠀⢸⢻⣀⣀⣸⢃⡤⠾⢌⣁⣀⣠⠤⠴⠒⠋⠉⠉⠉⢣⢹
⠀⠀⠰⠿⠓⠊⢩⡔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⣯⠏⢠⠞⠁⢼⣿⡆⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⡤⠾⠯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠓⠒⠒⠋⠙⠂⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠐⠂⢀⠀⠀⠀⠀⠈⠀⠠⣄
⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠈⢿⠂
⠀⠀⠀⠀⠀⢠⠛⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠰⢷⣀⡀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢳⢲⡀⠀⠀⠀⠀⢨⣿⣴⣤⠶⠂⠀⠀⠉⠈⠉⢟⢷⠆⠀⠀⠀⠀⠀⠈⠳⡌⠂⣠⣾⠛
⠀⠀⠀⠀⢸⣷⣝⠷⣄⡀⣠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡽⠟⠅
⠀⠀⠀⠀⠀⣿⣿⣷⣮⣙⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⠂⣀⣀⡀⠀⠀⠉⠐⠀⣀⡤
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣔⣀⣉⠐⠛⠿⠾⠶⠦⠶⠶⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⢯⣿⣿⣿⣿⣿⣟⡻⠿⠶⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣎⠻⣿⣿⣿⡽⠭⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠥⠠⠄⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢿⣿⣛⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣆⣠⣴⣤⣠⣤⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⡄⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⣀⣀⢨⡤⣀⣀⣖⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⡀⠀⠀⠀⠳⠇⠀⠈⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠘⠋⠋⠈⢀⠲⠘⠚⠁⠈⠙⠃⠀⢠⠈⠀⣤⣤⠀⠓⠦⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠤⣤⠄⠤⡤⠤⠰⠦⠄⠀⢀⢀⣤⠀⠙⢀⢷⠀⠰⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠙⢱⠀⠀⠈⠀⠄⠀⢀⠀⠀⠸⠀⠀⠀⠀⢉⢠⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠯⠉⠉⠉⠉⠋⠉⡋⠁⠀⢀⠀⠲⠟⠀⠸⠆⠰⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣼⣤⣀⣀⡀⣀⣀⣩⡀⠀⠘⠓⠒⠂⠚⠁⠀⠀⠀⠄⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⡀⢀⠀⠀⠀⠀⠀⢀⣠⡀⠠⡜⠋⠀⠠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠴⠶⠤⠤⠤⠮⠧⠤⢒⠄⠀⢈⠉⠀⣀⡉⠈⡧⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠞⠀⡀⡀⠀⠠⠖⠀⠀⠀⡐⠬⠀⠈⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠐⠂⠉⠁⠀⠀⠐⠒⠊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁





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

⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣠⠖⠋⠉⠁⠉⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠀⠀⠉⠙⠶⣄
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠋⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⠀⠀⠀⠀⠀⠀⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠈⠙⠒⠦⠤⢤⣤⡤⠴⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⡠⠤⠔⠁⠀⠀⠀⠀⣀⣀⣀⠀⣠⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠉⠙⣦⠀⠀⠀⠀⠀⠀⢀⣀⠛⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⢷⡈⠉⠙⢄⣀⡀⠀⣀⣀⣠⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠀⡴⠋⠉⠙⣆⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣼⠃⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣒⡚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⢀⣿⡀⠀⠀⠀⠀⢀⣠⣬⣙⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠙⣷⣤⡀⠀⠀⠀⠀⠀⣸⠃⠙⠲⠶⠛⠉⣷⣀⣀⣤⠖⢫⡏⠀⠀⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠙⠲⢾⣄⠙⠓⠒⠒⠛⠛⣿⣠⡄⠀⠀⠀⠀⣿⡏⠁⠀⠀⣾⠀⠀⣠⠏⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠓⠶⠶⠖⠒⠛⣿⠁⠀⠀⠀⠀⢰⡇⣷⠀⠀⢰⠇⣀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⣾⠶⢾⡶⠶⣾⠋⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡏⢷⡀⠀⠀⣼⠃⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⡇⠀⠙⠆⠀⠃⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣠⡤⠟⠀⠙⡟⠙⠛⠛⠛⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡶⠛⠋⠉⢹⠁⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⢹⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣼⠋⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣻⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠀⠀⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠸⢷⡄⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡤⢀⡴⣂⡤⠀⣠⡤⢀⣠⡶⢂⣠⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⢣⣾⣿⡿⠛⡿⠗⣻⣯⣖⣁⡿⠛⠱⠿⠔⢚⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠿⠤⠈⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠂⠠⠤⠿⠶⠾⣿⣄⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠊⠉⠀⠀⠀⢀⠤⠒⣩⠏⠀⣀⣴⠖⠀⠀⢀⣀⠀⠀⣀⣤⡶⠋⠀⢈⣡⠬⠹⠓⠢⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠁⠀⠀⠀⣠⢆⡠⢂⠁⣠⠞⢁⠔⢊⠔⠋⣠⠔⡺⢛⡡⠔⡫⠖⠁⣀⣤⠾⠋⢁⣠⣴⠖⠀⠀⠀⡀
⠀⠀⠀⠀⢰⠀⠀⠀⠀⣠⠎⠀⡠⣾⠟⢩⡴⣣⠎⡡⠊⢁⠔⣡⠔⢉⣴⡾⠞⢉⠔⢊⡠⢔⠭⢊⡡⠔⡪⠕⠋⢀⡠⢔⡾⠛⠁
⠀⠀⠀⠀⢠⠀⠀⣠⡾⠁⡠⢊⠞⠁⡴⠋⣰⡗⠋⣀⡸⠿⠭⠐⠒⠺⠅⠐⢶⣥⡖⠁⠴⠧⠒⣉⠔⢊⡠⠔⢊⠡⠐⣁⠤⢐⡾⠃
⠀⠀⠀⠀⢸⠀⠀⡜⡠⠊⡐⠁⢀⠖⡠⢚⠟⢐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣘⠓⠊⠁⣤⣮⠵⠒⠉⡠⠖⠁
⠀⠀⠀⠀⠘⠀⠘⠉⢀⠎⠔⡀⠁⠎⡠⠊⣴⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠈⠙⠒⠦⢄⡀⢀⠔⠉⣀⠠⠤⠒⣺⠗
⠀⠀⠀⠀⠀⠐⣀⠀⠛⢁⢌⠔⢀⠔⡁⢰⣿⠇⠀⠀⠀⠀⠀⠀⠠⣾⡿⠛⠉⠉⠉⣉⡀⠀⠀⠀⠀⠀⠀⢹⡈⠉⠉⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠓⣦⠶⠁⢠⡾⠊⢰⢸⣿⣤⣤⣤⣄⠀⠀⠀⠀⠉⠀⣴⣾⣿⡿⢿⠟⠀⠀⠀⠀⠀⠀⢸⣧⠀⠠⡴⠯⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠀⠀⢸⣿⠛⣉⣉⣹⠇⠀⠀⠀⠑⠚⠀⠈⣉⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⠘⣶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣧⣝⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠀⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣇⣴⣤⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⡇⠀⠀⠀⢀⣀⢤⣠⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⡿⣄⠀⠀⠋⠉⠚⠛⠉⠀⠀⠀⠀⠀⢤⠔⠂⠀⠀⠀⠀⠀⢸⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⡿⣿⣮⠖⠒⠒⠂⡠⠒⠒⣶⠦⠀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠟⠁⡀⠀⠀⡐⠀⠀⣸⠻⠀⠆⠈⢦⠀⠀⠀⠀⠀⢀⣴⣾⣷⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠃⠀⠀⠀⠀⠀⠀⠀⢰⣯⡗⡶⣶⡀⠀⢇⠀⢀⣠⣾⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⢤⡀⠀⠀⠀⠀⠀⠀⠘⢛⠋⠻⣄⡇⠀⢨⣧⣴⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠃⡞⡼⠳⡤⣤⣄⣀⠀⠘⠞⠀⠀⠙⠀⠀⣾⣿⣿⣿⢿⣩⡴⠖⣁⢤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⢸⢡⠃⠰⠀⡟⠀⡏⠑⡶⠤⣤⠤⠖⠒⣏⠉⢈⠿⠛⡋⠤⠒⢉⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠇⡎⢸⢠⠁⢰⠁⡸⠀⢰⠁⢸⠇⣰⡇⡾⣿⣉⠤⠂⠁⢀⣴⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⠠⠃⠟⡎⠀⡞⢀⠇⠀⡜⠀⣸⠠⢻⡾⢿⡏⢀⠀⠀⠐⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⣌⠓⠀⠐⠃⢰⡇⢸⠀⠀⣧⠀⣇⠃⣾⠣⢾⠋⠀⠀⢀⡞⠀⢀⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣾⡏⠀⠀⠀⠀⠀⠀⠇⠀⠘⠃⠀⠛⠀⠋⣀⣾⢀⠾⠋⠈⡁⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢋⠔⢁⢠⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠊⠁⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣇⡀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣸⣤⡾⠻⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⢀⣴⣏⡾⠁⠀⡀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⣤⠶⠛⠉⠘⠷⣤⣤⡤⠖⠋⣡⣏⣀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣤⡀⠙⢦⣄⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⢾⡏⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠙⢷⣄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠛⠻⣾⣧⣀⣀⣀⣠⣶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⣧⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣿⠀⠀⠀⠙⣦⡉⠉⢩⡿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣿⡀⠀⠀⠀⣼⣇⣰⡟⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠋⣿⣏⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣾⣧⣤⠤⠤⠴⠶⢶⣶⡶⠶⠶⢼⡇
⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣧⡾⠉⢿⣆⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⣠⡿⠁⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⡟⠀⠀⠀⠻⣆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣾⣿⠟⠀⠀⠀⣠⡶⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢹⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⠁⠀⣠⡴⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⣄⣠⡾⠋⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣩⠟⢿⣄⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣀⣴⢟⣡⡾⠟⠁⠀⠀⠹⣷⡄⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠘⣧⠀⠀⢀⣠⣾⣯⡶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠙⣷⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠈⠻⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⡄⠉⠀⠀⠀⠀⠀⣠⣤⣬⣿⡀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠓



⠀⠀⣀⡀⠀⠀⢀⠀⠀⡀
⣿⡟⣉⣻⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣠⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣠⣴⣿⣿⣿⣿⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠘⣦⣤⣤⣄⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠙⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠁⠈⠘⠀⠙⣿⣿⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣴⣶⣿⣶⣴⣄⠀⢀⣤⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡀⣿⣿⣿⡿⠿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⢻⣿⣿⠀⠀⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠈⢻⣿⡀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠈⣿⡇⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣈⣿⣿⣀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡿⢙⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢁⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣿⠱⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠂⠨⡉⠓⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢧⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⢀⠚⠃⠄⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠆⠀⠀⠀⠀⠀⠀⠢⠀⠇⠀⠀⠀⠀⠀⣸⠀⢠⠐⠿⠤⠛⢢⡔⠤⣔⣓⠴⣷⡼⠲⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡄⠀⠀⠀⠀⠀⢀⡇⠸⣄⠀⠀⢠⡀⠛⠀⣨⠐⢁⠈⢄⢙⣋⣉⣉⠙⡘⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⢶⡞⠀⣕⡤⢤⢆⣁⣒⣁⡶⠴⣷⢚⣖⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠧⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠓⠒⣏⣀⣼⡟⠶⠾⠶⠮⠭⠽⠿⠿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠲⠛⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠁⠀⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢰⠶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠄⡐⠂⠠⠈⠀⠈⡉⠞⠁⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠒⠀⠀⠀⠀⢀⠀⣠⣤⡤⠴⠊⠉⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠀⢸⡀⠰⠂⠺⣟⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠁⠈⠀⣨⠀⠀⠤⡀⢤⠀⢤⣇⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠰⠁⠁
⠀⠀⠀⠀⠀⢰⠀⠃⠀⢹⠀⠀⠁⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠁⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⣠⢈⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⢐⣦⣀⠀⠐⠂⠀⠤⠀⠠
⠀⠀⠀⠸⡕⠪⢄⡀⡆⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠠⠃⠀⠀⠀⠄⢃⡀⠸⡆⠈⢠⡈⢂⠐
⠀⠀⠀⠀⢀⠀⠀⠘⠐⠢⠀⡁⠀⠀⠀⠑⠂⠀⠀⣀⠠⠀⠀⠠⠄⡤⠀⢀⢠⢀⠂⠀⠑⢰⡇⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣦⠄⢀⠀⠀⠐⠉⠉⠐⠀⠀⠁⠀⠀⠰⠀⠀⢐⡂⠀⠀⢰⠓⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣆⠨⡇⠀⠀⠠⣤⠀⠀⠀⠄⢦⠀⠀⠀⠲⡇⠀⠈⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠄⠀⠀⠙⡅⠀⠀⠀⠐⡀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡀⠀⠀⢣⠀⠀⠀⠐⢁⠀⠀⠀⢸⡄⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠇⡀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⣆⠀⠀⠀⠃⡀⠀⠀⢯⠀⠀⠀⠈⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣯⣦⣧⣾⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⡀⠂⠀⠀⠀⠉⠀⣤⠤⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠉⠉⣇⠀⠈⠁⠀⡅⠰⠴⢂⠀⡀⠈⠦⣀⣵⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠠⠀⠀⠀⠀⢰⠀⣀⡀⠀⠀⠀⢻⠟
⠠⣀⠀⠀⠀⠀⠰⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠙⠓⠀⠀⠈⠀⢀⠇⠠⠇⠋⠀⠀⣀⡀⠀⠀⠀⠀⠰⢮⠋⠽⠓⠀⠀⠀⠀⠀⠀⢀⣤⣼⠿
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⠶⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠈⠘⢏⣹⠂⠀⠀⠀⢡
⠀⠚⠁⠀⢙⡀⠀⠀⠈⠲⡄⠀⠈⠀⠀⠀⠀⠀⠐⠚⢁⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⠀⠁⠀⠀⠀⠀⠘
⠀⠆⠀⠀⠀⠑⠂⠀⠠⠄⠈⠒⠀⠀⠀⠀⠀⠀⠘⢏⣩⡙⠅⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⠀⠐⠀⣀⠀⠀⠀⠈⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢀⠀⠀⠈⠛⠉⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⡋⠁⠀⠀⠀⠘⣶⠯⠃⠂⠀⠰⠂⠼⢻⡾
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠳⠀⠀⠈⢀⣠⠀⠀⡗⠀⠀⡀⠀⠀⠀⠠⡟⠁⠀⠀⠀⠃⠀⠈⠀⠷⢦⣤⠾⠧⠔⠋⠀⠀⣀⡄
⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢟⣦⡀⢀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠈⠀⠀⢀⠀⠀⢁⠀⣢⡠⡆⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠠⠌⠀⢀⠀⠈⣸⣷⠄⠈⢦⣄⡀⠀⠀⠀⠀⠀⢰⣶⢀⡀⠉⠀⣆⡰⠀⠀⣰⠟⣁⡶⢀⣴
⠀⠊⠀⠀⠀⠈⠁⠀⠀⢉⣽⡷⣴⣁⠀⠈⠙⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣯⣄⠀⠀⠀⠀⠀⠠⠄⠀⣴⠊⠉⣹⣆⠀⠉⢀⡤⠚⢁⡴⠋⢠⡞⠁
⠀⠀⢄⠀⠉⠀⠀⠀⠀⠁⠹⠙⠆⠈⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠈⠀⣀⠠⣿⣥⣀⠀⠀⠂⠀⠀⠀⠀⢹⠆⢀⡡⠀⢀⡴⠟⠀⢠⡞⢁⣴⠏
⠈⣀⠀⠁⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢌⣉⠿⠐⠧⠀⠀⠀⠉⠃⠀⠸⡻⣧⣀⡀⠡⣀⡀⠀⠀⠀⠘⠓⢁⡴⠋⠀⠀⡴⠋⣠⠞
⠰⠀⠀⠠⡀⠐⢀⡀⢢⡀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠄⠀⢄⣀⠀⠀⠿⢿⣥⡀⠀⠀⠀⠀⠀⠠⠔⠉⠀⠀⣠⠞⣡⡾⠃⠀⠀⠈⢲
⠀⠀⠁⠀⠈⠲⡌⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠜⠁⢐⡡⠞⠁⢀⡆⢀⠈⣂⢀⣄
⠀⠀⠀⠀⠀⠰⣇⠓⢄⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⢀⠀⠀⠀⠀⠀⠠⢆⣿⠀⠠⠘⠃⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢠⡀⣰⣖⡛⠉⢋
⠀⠀⠐⠀⠀⠀⠀⠁⠀⠉⠂⡀⠀⣀⢴⡇⠀⠀⠀⡘⠿⢧⡄⠈⠀⠀⠀⠀⠰⣋⣳⠏⠀⠐⠆⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢊⠙⠃⠀⠅⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⢈⣦⣾⡟⠁⢀⣄⡀⠀⠐⠂⠀⠀⠄⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⠉⠋⠀⠀⠘⠿⠛⠀⠀⠀⠀⢢⠂⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⣤⣴⡤
⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣯⠀⣏⡅⢩⡅⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠓⠀⠃⠁⠑⠂⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⣉⠀⠀⠈⠀⡅⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠒⠈⠂⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⣿⠇⣿⣿⡏⣰⡏⢀⣠⣄⣀⣇⣦⠙⣿⣿⣿⣿⣿⣸⠀⠀⢸⣿⣿⣷⣾
⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⡁⠀⢿⡇⣿⣿⠃⣿⣾⠋⠠⢤⣹⡿⢻⠁⢸⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿
⠀⠀⠈⠠⣀⠉⠉⠁⠀⠉⠙⠓⠂⢸⣇⢿⣿⣅⣌⡿⢶⣯⡉⠉⠽⠏⠀⠸⠿⠿⠿⠿⠿⣗⠀⢸⣿⣿⡟⠿⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡆⠁⡉⠀⠀⠚⠂⠀⠷⠀⣤⣄⡿⣷⣶⣶⣆⠀⠒⠀⢠⠖⠚⠛⢉⣯⣿⣿⣿⣷⠀⣄⡰⠛⡅⠠⢀⠄⢀⡦⠄⠀⡼⠄⠸
⠀⡄⠇⠀⠉⠀⠀⠶⠄⠠⣦⡀⠀⠀⠀⡏⠛⠿⣿⣿⣷⣦⣶⣷⣮⣶⣿⣿⣿⣟⢋⣽⠀⠀⠙⠛⢣⠉⠁⢀⠈⡀⠀⠀⡀
⠀⠁⠀⠬⠓⠀⠀⣦⡄⢐⢤⡇⠀⠀⢀⣧⣤⣾⣿⣿⣿⡿⠿⠿⠿⠿⠋⢹⣿⣿⣿⣿⠀⠀⠀⠀⢸⠘⠊⠀⠸⠒⠉⠰⠗⠂
⠰⢰⣀⢀⣀⠀⠤⠤⠤⠐⠂⠁⠀⡀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠚⠛⢛⠛⣛⣛⢁⣀⠀⠀⠀⠀⡶⠕⠂⠰⠤⠂⢀⡖⠊⡀
⠀⠀⣀⣀⠠⠄⠐⠒⠂⠉⠁⡆⡆⣀⣆⢀⣠⠀⢀⣀⠀⡆⠀⠀⣄⡠⠀⢀⠀⡀⠀⠀⠀⠀⡆⠀⠰⠤⣈⣉⠉
⠀⢸⠀⠂⣠⠀⠐⡰⠀⡰⠆⡧⡇⢀⢀⠀⠙⡀⠈⠀⠀⡇⠐⠀⠁⠀⠀⠸⠊⠀⠐⠗⠁⠀⡇⠀⡅⢀⣀⢀⠉⠒⠢⠤⣀⡀
⠀⡞⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠙⠀⠰⠅⠀⠋⠀⠇⠰⠀⣴⠖⠀⣦⠒⠀⢠⡠⠀⢸⡇⢠⠁⠈⠉⠁⠤⠆⡀⢀⣀⡈⠉
⠀⡇⠀⠠⠜⠁⠀⠝⠀⠔⠉⠁⡇⠠⠄⠀⠐⠇⠀⡀⢐⣶⣶⣦⣤⣄⠀⠀⠀⠀⠈⠀⠀⢸⡇⠘⠐⠺⢍⠀⢤⡤⠄⠈⠑⠂
⠀⡇⠀⠠⢤⠄⠀⣠⠄⢠⠄⠀⡇⠠⠄⠀⠐⠎⠀⠰⢟⡙⠁⠘⣿⣿⡄⠘⠖⠁⢨⠞⠀⢸⠀⡇⢀⡀⠀⠀⠀⠈⣥⣄⠒
⠀⢃⠀⠐⠁⠀⠀⡀⣀⠀⠀⠀⠃⠒⠀⠐⠉⠁⠀⠀⠀⠉⠀⠀⢛⠛⠃⠀⠀⠀⠠⠀⠀⠘⢠⠉⠉⠒⠀⠳⣄⠀⠀⠀⡀⠀⢠
⠀⠈⡆⠐⡢⠆⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠙⠢⠀⠀⡈
⠀⠀⠇⠈⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⣀⠀⠀⠀⡇
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠊⢢⢀⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠉⠳⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡦⠀⠀⢄⠴⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣋⡥⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⢲⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠛⠁⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠾⣇⢀⣀⣤⣤⡿⠓⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⢀⡶⠛⠛⠳⢦⡀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⢶
⢸⠁⠀⠀⠀⠀⣙⣃⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠹⡀
⢸⠀⠀⢀⡴⠋⠁⠀⠉⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢣⡤⠒⠠⣀⠀⠀⠀⠀⡠⠞⠙⡆⠀⠀⢀
⠈⣇⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⠆⠀⢠⠞⠀⠀⠀⠇⠀⣠⡟
⣠⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠞⢠⣧
⢇⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠈⢻⠆⠈⠉⠐⠒⠤⠤⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠖⠊⠉⠀⢴⠞
⠀⢸⡆⢠⠒⠂⠤⠄⣀⣀⣿⠀⠀⣼⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⣷⠀⢰⣏⡠⠤⠔⠲⡄⢸
⠀⠈⡇⠘⡀⠀⠀⠀⠀⠀⠉⠲⠖⠋⠀⠒⠲⠶⠖⠒⠖⠒⠒⠒⠖⠒⠒⠛⠛⠉⣿⠀⣼⠁⠀⠀⠀⢰⠁⢸
⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⣸⠀⡏
⠀⠀⠸⡆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡏⢰⠃
⠀⠀⠀⢻⡀⢷⠀⠀⣠⠔⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠹⠆⠀⠀⠀⣼⢁⡟
⠀⠀⠀⠈⢷⡈⢧⠀⠘⣄⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⢀⢰⠇⠀⠀⣰⢃⡾⠁
⠀⠀⠀⠀⠈⢷⡈⢳⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣰⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠻⣆⠙⣄⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠈⠳⠤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣌⡑⠢⢤⣀⡀⠀⠀⠀⠀⢀⣀⡤⢖⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣷⠀⠀⠉⠉⠉⠉⠉⠁⠠⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣍⣒⣠⡤⠦⢤⣤⠤⠤⢤⡤⠤⠤⠤⠶⢶⣒⣫⡽⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣉⣉⣿⠠⢤⢀⣤⢸⣏⣉⣉⣉⣉⣿⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⢸⣿⡍⣻⠋⣿⠘⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿⠰⠧⠘⠛⢸⡏⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣬⣷⣦⣾⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠛⠿⠶⠶⠶⠶⠾⠟⠉⠉⠉⢹⡏⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣬⣭⣭⣭⣭⣭⣥⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠛⠛⡟⠛⢻⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣬⣭⢩⣭⣭⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⡇⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠛⠒⠚⠓⠒⠚⠓⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠛⠛⠈⠛⠛⠘⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠂⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⡀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠠⡀⠄⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⢀
⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠈⠠⢀⠀⠄⡠⠑⠄⠀⢀⠤⠈⠀⠀⣁⣤⡀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⠀⠀⠀⠀⠀⠐⢀⡠⠆⠁⣀⢰⣄
⠀⠀⠀⠠⠔⠁⠀⠠⠤⠄⠀⠤⠠⠄⠀⠀⠴⠀⠂⠆⠊⠲⠤⠐⠠⠀⠀⠤⠴⠠⠄⢄⣀⣀⢀⢈⠑⡤⠄


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠑⠢⡄⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⡀⣀⡀⠀⠀⡠⠒⠂⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⠎⡄⠩⣑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡠⠋⠀⠀⠀⠈⢠⠔⠢⠤⣈⠀⠀⢀⣀⣀⠼⠀⠀⠀⠀⠀⠀⠸⢠⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠢⠘⢰⠁⠀⠀⠀⠀⠀⠰⠀⠀⡠⠂⡠⠊⠀⠀⢠⠀⠀⠑⠆⠀⠀⠀⡆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⣠⠔⠒⠒⠚⢦⠀⠀⠀⠀⠀⠀⢀⣼⢀⡜⠀⠀⠀⠀⡇⣠⠀⠀⠸⠇⠀⠘⣱⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠖⡠⠚⠁⢀⣀⣠⠎⠀⠀⠀⠀⠀⢀⡇⠀⠀⠠⢀⠜⠁⠀⠈⠀⠀⠀⣀⠀⣶⠁⠀⠀⣸⠋⠀⠀⢣
⠀⠀⠀⠀⢀⠖⢁⠔⠉⠀⠀⡜⡩⠋⠀⢄⣀⣠⠤⠤⠐⠁⢀⡓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⢠⡏⠀⠀⠀⣿⢈⡀⢨⠀⠘
⠀⠀⠀⠀⡆⠀⣼⣦⡤⠚⡁⠐⠁⠀⠀⠀⠀⠀⣀⣠⣗⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠧⠄⠀⡾⠁⡀⣠⢲⡿⠈⠄⠀⠂
⠈⠀⡄⠀⠐⠀⠻⠽⠐⠠⠄⠀⠀⢁⣈⣩⣽⣛⡋⠍⠁⠀⠀⣓⣂⠀⠀⠀⠒⠈⠈⠉⢡⠀⠀⠀⠀⠀⣰⠃⡼⢋⡵⠏
⠀⠀⠄⠀⣀⣀⡀⠀⠀⣀⡀⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⢂⡀⠀⣠⠔⠰⠤⢼⡤⠤⠲⢖⣪⣥⣾⣿⣋⣀⣀⣀⣀
⠀⠀⠀⢀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⠫⠊⠀⠀⣀⣠⡀⡼⠀⠀⠀⢐⠀⠀⠘⠋⠉⠉⠉⠙⠛⠿⣟⡲⢤⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡥⠤⠴⠛⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⣀⠠⢄⡽⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠚⢲⢶⡉⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠁⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⢰⣃⡼⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⢀⡀⠀⣤⡄⠀⠀⢀⠀⢰⣶⠂⠀⠑⢶⡿⠼⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀
⠀⣴⠛⠙⠦⠀⢀⡴⢶⠀⠘⡿⢶⡄⢀⣾⡇⢠⣿⠃⣸⣧⢃⡀⡴⣿⡆⢾⡵⠊⢹⡆⣾⡇⢠⣶⠀⢠⣶⡷⣄⣠⡇⢀⣶⠀⠀⣾⣫⠏⠀⣰⠂
⠀⣿⣄⡤⢶⣆⢸⡇⠀⠀⢰⠃⢸⡇⡼⢹⣇⡞⣿⢀⣿⣱⢻⣿⠁⣿⠀⣿⠀⣠⠟⡼⣿⢁⢾⡇⣠⣿⠈⠛⡏⣽⣣⢾⡇⢀⣼⠋⢀⡤⠚⠁
⣄⣸⢓⡆⣸⡏⢸⣧⠀⢠⠏⠀⢸⡟⠁⣼⡿⠀⠿⠋⣿⠃⠘⠃⠀⠘⠃⣿⠚⠁⣰⠁⠿⠏⢸⣧⠇⠻⠤⠜⠁⠿⠃⣿⡴⢋⣿⠖⠉
⠀⠻⣉⡴⠋⠀⠀⠹⠶⠋⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⢰⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡴⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡵⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠛⢁⣤⠶⠶⠶⠶⣄⡈⠛⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠋⠉⠛⠻⣦⠀⠀⠈⠁⣠⠶⢦⣄⠈⠁⠀⢠⡾⠋⠁⠀⠈⣙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢰⡟⠙⢷⡄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⡶⢦⣾⣋⣿⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⠘⠷⠴⠟⠁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠻⠶⣿⠉⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⣦⣤⡾⠶⠋⠀⠀⠀⠀⣠⡾⢷⣄⠀⠀⠀⠈⠳⣦⣄⣉⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⣠⡾⠋⠀⠀⠙⢷⣄⠠⣤⣤⣤⣬⣭⣥⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠶⠶⠶⠶⠶⠆⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⣄⠰⠶⠶⠶⠶⠶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡶⠶⠶⡆⠺⣿⠶⣶⠶⠶⠶⠶⠶⠶⣶⠶⣿⠇⡰⠶⠶⢶⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣧⣤⣤⡿⠀⣿⠀⣿⠀⢀⣤⣤⡀⠀⣿⠀⣿⠀⣯⣤⣤⣼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣤⣤⣤⣤⠀⣿⠀⣿⢀⡟⠁⠈⢻⠀⣿⠀⣿⠀⣤⣤⣤⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⣀⣀⣿⠀⣿⠀⣿⠸⡇⠀⠀⢸⠀⣿⠀⣿⠀⣧⣀⣀⣸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣤⣭⣭⣭⣥⣤⣽⣤⣿⣬⣧⣤⣤⣼⣤⣿⣤⣯⣤⣭⣭⣭⣭⣤⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠈⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠐⠀⠀⠀⠠⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠠⣀⠀⠈⠣⡀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠁⡀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⡀⠀⢹⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⠛⠀⠅⠀⠀⠀⠀⢀⣠⡟⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⢠⠀⢇⠀⠀⠠⡀⠀⠀⣠⠀⠀⠀⡇⠀⠀⡇
⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠐⠒⢐⠈⠁⠀⢀⠞⠀⠘⠄⢀⣀⡀⠀⠀⠀⠀⠀⢀⣼⠠⠘⢦⡀⠀⠀⠀⠊⠀⠀⠀⠠⠁⠀⢸⠃
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⠃⠀⣠⠇⠀⠀⠀⠀⠁⠈⠁⠲⠂⠂⠀⠀⠉⠀⢿⣄⠀⠙⠲⠤⣄⣀⣀⡠⠖⠁⠀⣠⠏
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡟⠱⠀⠀⠐⠀⠀⣄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡿⠳⢄⣀⡀⠀⠀⠀⠀⣀⣠⠞⠁
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⣿⡋⠀⠐⢛⡍⠈⠉⠓⠒⠀⣹⠀⣼⠁⡄⠰⠒⣷⠀⠀⠈⠉⠉⠛⠛⠉⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣤⠟⣻⡥⠠⡸⣤⡇⠀⠀⠀⠀⠈⠀⢩⡗⠀⠀⣼⣽
⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡴⠋⠃⠀⠀⠋⠀⠈⢱⠆⠀⠀⣰⢀⣏⣤⠴⠇⠘⠻⣦⡀
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞⠀⠀⠀⠀⠠⠐⠛⠉⠁⢀⠔⠋⠅⠘⢀⠀⠀⠀⠈⠀⠼⠛
⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢀⡔⠀⠀⠀⠀⠘⣤⠴⠖⢳⡀⢱⡄⠀⢀⡀⠀⢁⡚
⠘⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⣠⣼⠿⣧⣀⠀⠘⠣⣀⠀⠀⠀⢜⠂⠀⢰⠀⠉⢁⡾⠀⠀⢐⣳⡾⠁
⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⣼⡟⠁⠈⠀⠉⠉⠉⠃⠉⠉⠲⢂⣬⡤⠀⢁⣠⠔⢋⣀⣤⣴⠿⠿⣷⣄
⠀⠀⠈⣿⣿⡄⠀⠀⠀⣸⡿⠶⠚⠂⠀⠀⠀⣀⠴⠚⠋⠉⠉⢀⡠⠞⠉⠡⠚⠋⠉⠁⢀⣀⣄⣌⣿⣧
⠀⠀⠀⢹⣿⣧⠀⠀⠘⢵⣆⠒⠁⡾⠁⠀⣸⣿⠛⡉⢱⡄⠀⠛⣷⠒⠖⠚⠉⠉⠉⢶⠟⡡⠠⢍⠙⣿
⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠙⣿⣅⣀⡀⠀⠸⣍⠉⠉⠉⠁⠀⠆⠀⠀⠐⠀⢀⣀⡤⠚⠳⠂⠀⠐⣻⣿
⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⣿⡋⢹⡆⣞⠛⠛⠓⠢⣄⠀⠈⣠⣤⣴⣍⠉⣀⣀⣠⢶⠀⢀⣴⡿⠃
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣧⣿⠶⠦⠤⣤⣼⡇⢸⣤⣤⣤⣭⣽⣭⣿⣷⡟⢰⡿⠋
⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⡎⠃⡀⠂⠀⠀⠘⠷⠾⠃⠀⠀⠀⠀⠀⠀⢿⣤⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⢾⣇⡀⠀⠒⠒⠶⠤⠴⠦⠔⠄⠖⠒⠒⠒⠒⣻⣿⠄
⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣧⠬⣿⣋⣻⣿⣒⣳⣶⣒⣲⡿⠿⠿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠈⣿⣆⠁⠄⣀⠀⠀⠀⠀⠀⠸⠄⣄⢰⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣻⡆⠀⠠⢏⣐⠦⣄⡀⠐⠂⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⡀⠀⠀⠈⠀⠬⠝⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠛⢄⢖⣠⢀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡌⢛⠳⢬⣿⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣬⣶⡿⠋

⠀⠀⠀⠀⠰⡄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⢤⢈⠛⠓⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠼⢿⠁⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⡐⣯⣼⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣀⡀
⠀⠀⠀⠛⠿⠆⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⣰⡀⠉⣹⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣶⡦⡧⠀⠀⠀⠀⠀⠶⣆⠈⠙⠁⡀
⠀⠀⠐⠷⠔⣛⡿⣅⠘⠁⠀⠀⠀⠀⠀⠸⣟⣙⣀⢥⡴⠟⠋⠀⠀⠀⠀⠀⣰⣤⣾⢿⡟⣿⣷⣐⣴⠀⠀⠀⢀⣀⠀⢾⣻⣀⠈⠋
⠀⠀⠐⣶⣋⡍⣴⡏⣁⣤⡀⠀⠀⠀⠐⠄⡿⢿⣧⣖⣯⣰⣿⡆⠀⠀⠀⠨⢿⣯⡿⣭⣯⡟⡳⠏⠁⠀⠀⠀⠈⠁⠺⣻⡏⠟⠷
⠀⠀⠰⣯⣻⣿⡿⢹⣿⡿⠀⠀⠀⠀⠐⢼⣿⡟⣿⣿⠶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠇⠁⠀⠁⠀⠀⠀⠀⠲⣛⣿⣿⣷⡀
⠀⠀⠀⠀⠐⠾⡿⠊⠉⠁⠀⠀⠀⠀⠀⠘⣿⣷⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣯⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣰⡆⣀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣰⣣⣾⡴⣀⡀⠀⠀⠀⠀⢠⣤⣄⣀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢨⣿⣹⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⡰⠆⢸⣿⣿⣿⠟⠛⠁⠀⠀⣠⣷⣬⠾⠛⣿⠚⣠⣦⣴⡄⠀⠀⠀⢶⣤⣿⡷⠞
⠀⠀⠀⠀⠀⣾⠷⣿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢀⣿⣄⣴⣾⡿⠉⠀⣴⣌⡟⠃⡇⠔⠁⠀⠀⠉⠛⠃⠀⠀⠐⢿⢯⣿⣽⡿⠐
⠀⠀⠀⠀⠀⠃⡞⣙⡾⢧⣤⣤⠭⠉⠀⠀⣤⣤⢀⠀⠘⡧⣀⣉⣩⠅⠀⠀⠀⠙⠷⢶⢠⡏⡰⠆⠀⣠⠆⠀⠀⠀⠀⢻⣿⡘⢦⣙⡁
⠀⠀⣠⡀⢠⣟⣩⡅⠰⣿⡟⠋⠀⠀⠀⠰⣤⡷⣛⣿⣾⣿⣿⠿⠛⠂⠀⠀⣀⣾⠛⣸⠏⠀⡅⣴⣶⡆⠀⠀⠀⠀⠤⢬⣥⡿⣿⣿⡛⠉⠁
⠀⠀⢿⠿⣿⣿⣣⣿⡀⡿⢿⣵⣆⠀⠀⠀⠀⣾⡗⣼⡗⡠⡀⢓⣤⠆⠀⠈⢙⣷⣆⡟⠇⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠈⣭⣿⣿⢧⡀
⠀⠀⠀⠘⢿⣭⣟⠻⠷⠤⡀⠀⠀⠁⠀⠀⠀⠛⠿⠿⠋⣷⣾⠏⠁⠀⠀⠀⠀⠁⠘⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⢻⠭⠓⠈
⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣄⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⠀⠀⣠⠤⠀⠀⠀⠀⠴⠛⡿⠿⠟⢿⣿⣷⣆⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠰⣷⢠⣴⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠳⣧⣮⣿⣷⣶⣖⠚⠀⠀⢀⣿⣿⣿⠙⣿⢫⣝⠏⠉⣥⣄
⠀⠀⠀⠀⣀⣸⡿⠿⠟⢶⣻⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⣘⣿⡓⠈⠃⣠⣠⣀⡀⠀⠛⠉⠉⢠⣶⢧⠰⡟⠂⢀⠈⠹⡇
⠀⠀⠀⠀⢩⣷⡿⣾⡼⣿⠯⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠨⣽⣿⣿⢷⡝⠧⠉⠉⠀⠀⠀⠀⠀⠀⣸⣯⠆⡞⠉⠓⠈⢡⣶⣄
⠀⠀⢀⣶⣮⣛⡸⣿⣿⡏⢯⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠦⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢻⣷⠇⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠚⠉⠁⠸⠇⢷⢾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛

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

⠀⠀⠀⠀⡀⣀⡀⠤⠒⠈⢈⠇⠀⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠀⠐⠀⠐⡄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠷⡤⠸⢗⡈⠁⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⡇⠝⠣⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠐⠈⠁⠀⠀⠈⠀⢀⠄⠀⠀⡇
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⡴
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣼⠗⡯⣄
⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠁⠀⠀⠀⣤⣷⣖⠅⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢨⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠿⡿⡔⠈⠀⠀⠀⠀⠀⠀⠠⠄⡄
⠀⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⢧⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠁⠇⠀⠀⠀⠀⠀⢸⣟⣿⣷⡃⠀⠀⠀⠀⠐⠈⠉⠊⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡅⠀⢘⡀⠀⠀⢰⡌⣽⣾⣿⣿⢫⢡⠀⠀⠀⠆⠀⠀⠀⠀⠐⠈⢠⡔⠠⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠄⢸⣻⣿⢿⠏⠀⠀⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠸⣯⡿⡟⢠⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⡀⠹⡷⠃⢸⠀⠀⠀⠈⠀⢠⠁⠀⠀⠁⠼⣄⠀⣀⡀⣀⠖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠏⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠀⠁⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠔⠊⠁⠀⠉⠒⢎⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⡠⠐⠒⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠉⣢⠠⠤⠤⢀⡀⠀⣂⠠⠤⢀⡀⠀⠀⠰⠄⠒⠚⠀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⠀⠈⢆⠀⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠅⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠢⠄⢀⠈⢄⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⣀⠔⠁⠀⡀⠀⠀⠀⠀⢀⠜⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠂⠉⠢⣄⡀⠀⣀⠤⠊⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠂⠤⠄⠐⠁⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠑⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠄⠒⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡐⠁⠈⢆⡀⠈⡩⠥⡄⠀⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁⠀⠀⠀⠉⠉⠀⠀⠈⠓⠒⠉⠈⠢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡶⠀⠊⠉⠢⠤⠴⡀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠾⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠱⢀⠠⠊⠀⠑⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⣀⠠⡎⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⣀⠜⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⡑⠢⡀
⠀⢾⠀⠪⣀⡀⠣⢀⠤⠤⠠⡀⠛⠠⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠑⠒⠢⠄⠤⠁⢀⠇
⠀⠀⠉⠑⢆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣉⡉⠁⠒⠒⠒⠒⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠒⠒⠒⠒⠂⠉⠉⣀⡀⠄⠀⠀⠀⠀⢀⠔⠊⠁
⠀⠀⠀⠀⠀⠉⠒⠒⠒⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣄⢀⡠⠤⠤⠀⢀⠜⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⡤⠴⠂⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⡉⠉⠉⠁⠒⠤⢀⣀⡀⠀⠀⠀⠈⠉⣲⠀⢀⣈⣁⠀⠄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠒⠒⠒⠒⠒⠠⢄⣀⣀⡀⠀⠈⠉⠁⡠⠔⠖⠐⠒⠂⠒⠀⠀⠒⠒⠒⠒⠒⠒⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠈⠉⠉⠁⠒⢒⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢒⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡜⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠜⢇⡀⠀⠀⠀⣦⠰⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⢀⣀⣀⠠⠤⢄⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⠀⠈⠑⣯⠤⡃⠀⠀⠀⠀⠀⠀⠨⠛⠲⠖⣚⡱⠢⣀⡠⠂⡂⢸⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠾⠍⣱⢊⠯⢭⡁⠢⡏⠀⠹⣖⡠⠄⢀⡀⠤⢞⢢⠀⠀⠀⠀⠀⠀⡤⠐⠙⠚⢿⡖⢄⡀
⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⢋⠼⢮⡉⠂⠀⠀⢱⠀⠀⢡⠈⠓⢦⢄⠀⠀⢇⣢⣀⣀⠀⠤⠊⠀⠀⠀⠀⡰⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⢸⢀⡝⢻⡄⠀⠀⢸⠀⠀⠈⡆⠀⠈⠶⢄⢘⡀⠀⠀⠱⡀⠀⠀⠀⠀⣠⠞⢀⡤⠶⠚⠋⡁
⠀⠀⠀⠀⠀⠠⣀⣾⠀⠀⡔⠋⠀⠈⠙⡄⠀⠀⡆⠀⡀⡇⠀⠀⡀⠀⠉⡇⠀⠀⠀⠑⠤⠤⠔⠊⠀⠀⠉⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠱⠀⣧⠃⠀⠀⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⡆⠀⠀⠀⠀⠈⡀⠀⠀⢣⡟⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⡀⠀⡸⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠷⡠⠃⠀⠀⠀⠀⠀⠀⠉⠗⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠴⠂⠀⠀⠀⠀⡰⠁
⠀⠀⠀⢠⡄⣀⠼⣦⣀⢴⠗⠁⠒⠒⠠⠤⠤⢼⣤⡀⠤⠇⣀⠀⣀⡀⠤⠐⠒⠂⠉⠁⠀⠀⠀⠀⣀⠠⠞
⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠀⠒⠂⠀⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠖⠒⠲⠶⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⠯⠥⠤⢤⣀⡀⠀⠀⢀⣀⣤⣤⣈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠋⡼⠁⠀⠀⡀⠀⠀⠉⠙⠉⠉⣀⣤⠀⠈⢦⠀⠀⠙⢦⣀⠤⠤⣤⢄⣀⡀
⠀⠀⠀⠀⠀⣴⣃⣀⣰⠃⠀⠀⠻⠟⠀⠀⠢⠔⠀⠀⠈⠉⠀⠀⠀⠳⣤⣔⠷⠐⠒⣈⠁⣠⡖⢉⣦⢄
⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠠⠤⠤⠀⣀⣀⣀⣀⣤⣄⣀⠀⠀⢺⠀⡔⠉⣥⠘⣧⠀⣬⠀⣩⠱⠮⢡⡌⢂
⠀⠀⠀⣼⠇⠀⠀⠀⣀⣀⠀⠀⡠⢊⡥⠞⠋⠉⠉⠓⠺⣵⡄⠈⣰⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢠⠏⡇⠀⠀⠀⠀⠀⠀⡼⢡⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢸⠀⢳⠀⠀⠀⠰⣆⢰⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⠀⢸⠂⠀⣀⡤⠉⠈⣇⣇⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠘⡆⢸⠀⠀⠁⠀⠠⣤⡜⢿⣆⠀⠀⠀⠀⠀⠀⠀⢉⡼⠃⢡⣀⠔⢄⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡄⠒⠈
⠀⠀⠀⢳⢸⠀⠀⠀⠀⢠⡀⠀⠀⠙⠳⠦⣤⣀⣠⠤⠖⠋⢀⣘⠀⠀⠀⢀⣀⡈⢇⡀⡠⠃⣀⡉⠂⠈⠀⡇
⠀⠀⠀⠈⢯⢧⡀⠀⠀⠀⠙⠀⠀⣷⠀⠀⡀⠀⠀⢦⡀⠈⢹⠻⡆⠀⠀⠘⠻⠃⠀⠴⠂⠀⠛⠃⠀⡆⢰
⠀⠀⠀⠀⠀⠳⡝⠢⢤⣀⡀⠀⠀⠁⠐⠛⠁⠰⣄⠀⠁⠀⡜⠀⢳⠀⠃⠀⠀⡀⠀⡄⠀⢀⠀⠀⢰⠀⡂
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠉⢢⡀⠀⠀⠀⠀⠀⡸⠋⠙⠾⠥⡖⠺⠋⠉⢢⠀⠁⠀⠃⠀⠈⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡙⢦⣀⣀⣀⡤⢧⠀⠀⠀⢀⡇⠀⠀⠀⣸⣀⠀⠀⠀⠀⢀⣀⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠳⠶⠶⠶⠟⠒⠒⠋⠉⠓⠒⠋



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣤⣤⣄⡀⠀⠀⠀⣀⣼⢿⡉⢹⢆⣰⠟⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⡿⡿⣼⣫⢻⣶⣜⣫⡀⠀⣾⡿⣟⠲⣁⠉⢠⣇⢐⣋⣀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠅⠒⠄⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⢠⠟⠟⠙⠙⠉⠈⠹⣿⣽⡇⠀⢿⣧⡙⠳⠾⢥⣭⣿⣿⠟⠋⠀⠀⠀⠀⠀⢰⣤⣀⠃⠄⠀⠀⠀⠇⣀⣧⠀⠀⢸⣿⢻⢿⡟⣿⡟⣿⡇
⠀⠀⠀⠀⠰⠀⠀⠀⠀⡈⢰⡄⠨⣬⡇⠀⠀⡽⠿⠷⠶⣶⣿⣿⣏⣀⣀⣀⠀⠀⠒⠄⠸⣿⣿⣿⣶⣦⣤⣴⣾⣿⣿⠀⠀⢸⡧⢸⠐⢡⣿⣱⡇⡅
⠀⠀⠀⠀⢸⠀⠀⠐⢉⠄⣄⡇⠀⣿⡧⠀⠘⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣸⣯⣸⣿⣠⣽⣿⣷⡇
⠀⠀⠀⠀⠰⢀⠀⠁⠘⠀⠉⠀⣠⡿⠁⠀⠘⠀⣀⠀⠀⠀⢻⣿⣿⣄⢀⣀⢀⡀⠌⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠘⠿⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⠖⠀⠀⠀⠀⠄⠀⠀⠀⢀⡰⣞⣟⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠴⠂⢀⣶⣂⣶⣶⡶⠤⠀⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⠉⠍⠉⠉⠻⣿⣿⡄⠀⠀⢰⠀⡀⠈⠀⠁⣼⣿⣿⡉⠈⡱⠚⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣿⣿⣧⣤⠄⠀⠀⡄⠴⠻⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⢽⣿⡇⠀⠀⠸⣄⡤⠂⠈⠉⣿⣿⣿⠀⠀⠀⠠⠈⠑⡆⠻⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢁⠀⠈⠀⡀⠀⡆⣸⡿⠁⠀⠀⠀⢹⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⢀⠟⠐⣌⣦
⠀⠀⠀⠀⠀⠈⠇⡀⠀⠘⣿⣿⣧⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠑⠀⠂⠃⠈⠴⠛⠁⠀⠀⠀⠀⠀⠣⢤⡀⣄⠀⢻⣿⣿⡀⠀⢠⠤⠊⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠛⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠀⣿⡟⣥⠶⣬⠹⣿⠀⢲⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣍⡻⠇⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠈⠷⣴⣶⣦⠾⠃⠀⠈⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣙⠻⢿⣿⣷⣦⣀⠀⠀⠀⢀⣀⣠⣤⠶⣀⣤⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⠉⠛⢿⣿⣿⣶⣿⣿⣿⠟⣡⣾⢿⣿⣿⣿⣿⣿⡿⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠙⠛⠉⠁⢀⣾⠟⠀⢸⣿⣿⣿⣿⣿⡇⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⡆⠀⠀⠛⠟⠁⠀⢸⣿⣿⣿⣿⣿⣧⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡏⠁⠉⠉⠉⠉⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⡀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⠁⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣤⠤⠤⠤⠤⢴⡟⠛⠛⠛⠛⠛⣷⠤⠤⠤⠤⢤⡄⢸⠀⢚⠆⣴⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡆⠀⠀⠈⠉⠛⠛⢷⣦⡀
⣿⣤⣤⣤⣤⣤⡇⢐⡳⢠⣶⠀⣧⣤⣤⣤⣤⣼⡇⢸⠀⠛⠃⠉⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⣿⣀⣀⣀⣀⣨⡇⠘⠒⠈⠉⠀⣇⣀⣀⣀⣀⣸⡇⠘⠛⠛⢻⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢈⣡⣄⠀⠀⣀⠀⢀⠀⠀⠀⢹
⢸⡏⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢁⣼⢇⡼⣯⠀⢸⡤⣤⠀⠈
⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⢠⣾⣥⡘⠓⣿⠓⢸⠀⢸⠀⢸
⢸⡇⠀⠀⠀⠀⣿⠉⠙⡏⠉⢹⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⢸⡇⠀⠀⠀⠀⣿⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⣀⣠⣾⠟⠁
⠘⠓⠒⠒⠒⠒⠛⠒⠚⠛⠒⠚⠓⠒⠒⠒⠒⠛⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉

⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠘⠻⣷⡀⠘⠀⠀⠘⠈⡽⠃⠀⠉⠁⠂⠀⠀⠀⠀⠜⠀⠠⠀⠀⠀⣄⠀⠄⠀⠀⠀⠀⠈⠆
⡀⠁⠉⠐⠰⠦⡀⠀⠀⠀⠀⢠⣎⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⡤⠀⠘
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⣼⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠛⠛⠒⠀⠠⠀⠀⠉⠁⠀⠀⠂⠐⠂⠀⠀⠀⠀⠤⠀⢷⡀⠄
⠠⠀⠀⢀⣠⠟⠑⠑⠞⠚⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠒⠃⡸⣇
⣴⣶⠶⠋⠁⠀⠀⠀⠀⠀⠀⣀⣄⣠⠀⣀⡀⠀⠀⠀⠀⠀⠜⣦⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢀⣌⡀⡖⣢⠄⠀⠀⠀⠈⠳
⡀⠀⡀⠀⠀⠄⠀⠀⠀⠠⠜⠁⠀⠀⠀⠉⣿⣄⣀⡀⠀⠀⠀⠜⠳⣥⡄⠀⢀⡰⢃⡄⠀⠀⠀⠀⠛⠐⠬⡗⠻⣖⣺⣇
⡴⣒⠟⠳⠶⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠁⠀⠀⠀⠀⠐⠶⠝⠳⠏⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠈⣿⡧
⡾⡃⠀⠀⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⠙⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠃
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⣤⠀⠀⢀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⣦⣠⣤⠶⠂⠁⠀⠠⣰⣤⣟⠒⡀⠒⠋⠀⠀⠀⠀⠡⢠⡟⠈⠁⠀⠀⢠⡀⠑⢤⠀⠀⠀⠀⠀⢃⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡶⠟⠁⠠⠃⠀⢈⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⢀⡄⠀⠀⠀⠀⠀⢻⡆⠀⡤
⢀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠃⠀⠸⠂⠀⠀⠀⠀⠀⠈⠲⢦⣤⠤⠶⠖⠛⠡⣈⠀⠀⠀⣱⣶⠊⠧⠄⠀⢸⠀⢀⣀⠁⠐⠂
⠈⠀⠀⠀⠀⠀⠛⠥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⢾⡿⠉⠃⠀⠀⠀⢸⡆⠀⠈⠉⠀⠐
⣀⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠀⠀⠀⠐
⠟⢠⡈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢷⣦⣀⠀⠀⠠⠠⠒⠦⣄⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣔⣀⣀⡤
⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⠀⢰⣡⢌⣠⣿⣷⡖⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⣤⡀
⠀⠀⠄⠠⣤⠇⢤⡰⠂⠀⠀⠈⢿⣂⠀⢡⡴⡷⣶⠋⠀⠚⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡖⠊⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠽⡃⢀⡀⠀⠀⠀⠀⠹⠿⣿⡶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠿⠃⠀⠀⠀⠀⣀⣾⡇
⠀⠀⠀⠀⠀⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡦⠴⠋⠋⠀⠀⠀⠀⠀⠉⠁⣼⢆⡀
⣀⢀⡀⡤⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠃⠺⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡝⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢀⠈⠁⠲⠉⠀⠀⠀⠀⠘⠃⣰⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠴⠂
⣀⣀⣐⣀⣀⣀⣀⣀⣀⣠⣄⣠⣀⣒⣀⣉⣛⣷⣠⣬⣃⣀⣁⣀⣀⣀⣀⣀⣀⣸⣋⣀⣃⣀⣂⣐⣃⣀⣀⣀⣀⣂⣸⣋⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣾⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⣀⣪⣔⠶⣿⣧⠂
⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣐⣿⣿⣿⣮⣿⣿⣿⣦⣿⣿⣯⡐⠂⠀⠀⠠
⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⡤
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠝⠙⠛⠙⠛⠋⠉⠀⠐
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢤⣠⣀⣀⣀
⠀⠀⡀⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⢿⣿⡿⣿⣿⣿⣧⣄
⠀⠈⠰⠶⠶⢶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣀⣀⡀
⠀⠀⠀⠀⠀⠉⠉⢉⣹⣟⣋⠙⣿⣍⠿⡿⢧⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋
⠀⠀⠀⠀⡀⠀⠛⡿⣿⣿⣿⡄⢙⣿⣿⡀⠀⠁⣤⣋⣙⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠅⠉
⠀⠀⠀⠀⠉⠀⠠⠀⠀⠙⠛⠁⠈⠉⠿⣿⢿⣶⣿⣿⠿⠟⠾⢿⣿⡟⠛⠙⠟⠉⣿⠉⠉⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⡀⠋⠊⣁⣠⣤⡴⢶⢦⠸⣿⣿⣤⣤⣠⣼⢿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠻⡟⢋⠙⠁⠀⢰⠿⣾⠟⠛⢹⡿⠷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠷⡀⠀⠐⠲⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣿⣷⢰⠾⡿⠿⠿⣿⣶⡒⢒⣦⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠘⣶⣿⣦⣠⣽⢿⣳⣸⣏⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣤⡏⠻⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠛⢻⣿⣿⡿⠿⠛⠁⠀⠈⠙⠻⡿⢿⡿⠛⠿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠳⡶⠀⢿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠉⠀⠈⠀⢀⣟⡛⠒⠦⣤⣄⠀⠀⢀⣀⣀⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠳⣶⣧⠀⠀⠘⠿⢦⣤⣽⠿⠂⢀⡄⣀⣉⣡⢳⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡍⠉⠁⢸⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀⠃⣀⣀⣸⣿⠃⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠠⠅⣿⡏⢀⡠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣍⡑⢤⡀⠀⠤⣭⣽⣯⡿⠋⠀⠀⠀⣠⣶⣾⡾⠇⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣠⢿⣎⠃⠈⠉⠁⠉⠀⠄⡿⠟⣁⣼⣷⣾⣶⣾⣏⠙⠻⣅⠀⠀⢀⣤⣸⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⠁⠈⣿⣿⣶⣤⣤⣠⠋⠚⢡⡾⠃⣿⣿⣿⣿⣿⠿⠛⢠⣿⠦⠐⠛⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢤⣠⡾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⣿⠊⠘⠀⠀⠹⢿⣿⣽⠁⠀⠀⠈⣿⡄⠀⢀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⠉⠟⠛⡖⠒⠒⠀⠀⠀⠑⠂⠤⠀⣀⠀⠈⠹⠧⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⢿⣿⣦⡘⠉⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⣀⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⠀⢿⣿⢿⡇⠀⠘⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣧⢘⡟⢸⣿⠀⠀⠸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄⣿⢸⡟⠀⠀⠀⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣄⠀⢹⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⢹⢸⡇⠀⠀⠀⠀⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣧⣀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡆⢸⡇⠀⠀⠀⠀⢻⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⡏⣿⣿⣿⣿⣿⣼⣷⠀⠀⠀⠀⣿⣿⣿⣿⣇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣦⣤⣤⣠⣴⣖⣩⣿⣇⣹⣿⣿⣿⡎⢻⣿⠀⠀⢀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠻⣧⡀⢸⣿⠁⢹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠻⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⠶⡾⠿⠿⠿⣿⡿⠉⠉⠉⣽⡿⠏⠀⠀⠀⠘⣿⡀⠛⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⢴⣬⣿⣤⢠⣼⠟⣩⣤⣝⢿⡏⣤⣤⡙⣿⢡⣤⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⠌⣿⣿⢸⣿⡀⢿⣿⡟⣸⡇⣩⣉⢰⣿⢠⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣾⣿⣿⣾⣿⣿⣶⣶⣾⣿⣷⣿⣿⣶⣿⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⢀⣤⣤⣼⡟⣤⣤⣤⡄⣠⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣿⢃⣤⣤⣤⡀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⣼⣿⣿⣿⢡⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⢻⣿⣿⣿⡀⣿⣿⣿⣇⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢰⣿⣿⣿⡏⣼⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⣿⡘⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢿⣿⣿⣿⠇⣿⣿⣿⣿⠀⣿⣿⣿⡿⠸⣿⣿⣿⡇⢸⣿⣿⣿⡇⢿⣿⣿⣿⠇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣩⣴⣦⣙⣛⣡⣶⣮⣙⣋⣥⣶⣌⣙⣋⣵⣶⣌⣛⣉⣴⣦⣍⣛⣩⣴⣦⣙⣛⣡⣶⣬⡙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠞⣡⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⡇⣿⣿⣿⡏⣭⣭⣭⣭⣭⣭⣍⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢛⣵⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢚⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⢿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣿⣿⣿⡇⣿⣼⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣸⣿⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⣴⣠⢄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠲⢒⣼⢿⣖⣾⣹⣷⢧⢼⠃⡘⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠶⢶⣳⣯⣿⡛⡷⣤⣍⣯⣉⣷⣞⣷⡾⠼⣅⠺⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢑⣧⡼⢯⡷⣿⡟⢯⣠⣤⣯⣿⣯⣉⣿⣱⣿⣿⣇⣔⣆⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⣷⡾⠿⣿⣉⣶⣿⣿⣯⣿⣿⣿⣿⣭⡿⣿⣿⢿⣹⡷⡞⠋⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⢾⡷⣾⣿⣿⣾⣿⣧⣽⣿⣭⣿⣿⣿⣶⣽⠶⠟⡳⠁⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣗⣶⢶⣿⣿⢿⣿⣿⣿⣿⣿⣹⡿⡿⣟⣷⡿⣡⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣻⣟⢙⣿⢷⣾⣿⣿⣿⣺⡟⣭⠿⡩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠿⡿⣿⣿⣿⣼⣿⣟⣿⣿⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡻⣿⣿⣥⣿⣿⣿⣯⣶⡎⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣻⣯⡿⠿⠇⢚⣽⣿⣧⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠃⠠⠀⠀⢘⣻⠝⠶⠗⠀⠀⠀⠀⡀⡠⠬⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⢊⡏⢄⡲⢢⢿⣤⠊⠣⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢘⣃⠿⠉⢟⣮⡘⢇⠼⣀⡀⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠿⢿⡿⣾⣻⣶⡿⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠈⠉⠉⠁⠒⢲⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢒⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡼⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠜⢇⡀⠀⠀⠀⣦⠰⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⢀⣀⣀⠠⠤⢄⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⠀⠀⠀⠀⠀⠈⠑⣯⠤⣃⠀⠀⠀⠀⠀⠀⡨⠛⠲⠖⣒⠹⠢⣀⡠⠂⡂⢸⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠾⠉⣱⢊⠯⢭⡁⠲⡟⠀⢹⣖⡠⠄⢀⣀⠤⢞⢢⠀⠀⠀⠀⠀⠀⡤⠐⠙⠛⢿⡖⢄⡀
⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⢋⠼⣮⡉⠂⠀⠀⢱⠀⠀⢡⠈⠓⢦⢄⠀⠀⢏⣢⣀⣀⠠⠤⠊⠀⠀⠀⠀⡰⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⢸⢀⡝⢿⡄⠀⠀⢸⠀⠀⠈⡆⠀⠈⠶⢄⢘⡀⠀⠁⠹⡀⠀⠀⠀⠀⣠⠞⢀⡤⠶⠛⠋⡁
⠀⠀⠀⠀⠀⠰⣀⣾⠀⠀⡜⠋⠀⠈⠙⡄⠀⠀⡆⠀⡀⡇⠀⠀⡀⠀⠉⡇⠀⠀⠀⠑⠤⠤⠔⠊⠀⠀⠉⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⢰⡀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠱⠀⣧⠃⠀⠀⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⡆⠀⠀⠀⠀⠈⡀⠀⠀⢣⡟⠀⠀⢀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡀⠀⡸⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⡷⡠⠃⠀⠀⠀⠀⠀⠀⠉⠗⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣤⠴⠂⠀⠀⠀⠀⡰⠁
⠀⠀⠀⢠⡄⣀⠼⣦⠀⢴⠗⠉⠒⠒⠠⠤⠤⢼⣤⡠⠤⠇⣀⠀⣀⡀⠤⠐⠒⠊⠉⠁⠀⠀⠀⠀⣀⠠⠞
⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣰⣞⠁⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠂⠉