Shoes Emojis & Symbols

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠈⢇⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢄⡀⠀⠂⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡤⢀⡀⠔⠆⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⢠⠀⠈⠁⠀⠐⢃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠄⣀⠀⠈⠁
⠀⠀⠤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⣀⠀⠀⠀⠠⠀⠀⣀⣀⣀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⢠⠂⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⢤⣤⣀⣀⣀⣀⣀⣀⡠⠤⠴⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢈⣉⣁⣀⣤⠤⠤⠒⠒⠒⠈⠉⠉
⠀⠈⠓⠲⠶⠤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠶⠤⠤

⣶⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣿⣶⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠉⠑⢦⡀
⠀⠀⢀⣀⣠⣤⢤⣤⣾⣷⣤⣀⠀⠀⠀⠀⠑⢤⡀
⢀⡜⠁⠀⠀⠀⢸⠀⡤⢦⠈⠹⣷⣀⠤⠖⠒⠦⢷⣀
⢸⠀⠀⠀⠀⠀⡟⠀⠀⡇⣧⠴⠋⠁⣀⡤⠴⠶⢶⣬⡇
⣸⠀⠀⠀⠀⠀⡇⠀⢴⡇⡧⣤⡶⠋⠁⠀⠀⠀⠀⣳⡀
⡇⠀⠀⠀⢀⡼⠁⠀⢀⠇⢷⣿⡁⠀⢀⣠⠴⠚⠋⠉⠉⢓⣦⡀
⡇⠀⢀⡴⠋⠀⠀⠀⣸⢸⡤⠽⣿⠟⠋⢀⣠⠴⠖⢋⣉⡭⠭⠷⢄⡀
⢹⣶⣏⣠⡤⠴⠒⠋⡇⢸⡀⢸⣷⣶⠊⡿⣷⡤⠖⢉⣁⡤⢤⣤⣤⣷⡀
⢸⠻⣿⣷⡀⠀⠀⠀⡇⣯⠟⠀⣉⡴⠊⢰⣣⣴⣾⣩⠔⠊⣉⡤⠤⣶⣿⣷⣄⡀
⢸⠀⠈⢿⣿⡀⠀⠀⢹⡰⡖⠋⠁⢦⠴⣄⠀⠈⣏⣀⣴⣏⡴⠚⣉⡭⠴⠶⠶⢭⣆
⢸⠀⠀⠈⢿⣷⠴⠚⠉⠱⣜⢦⡀⠀⠀⠘⠖⢄⠈⠁⢸⣃⠴⢿⣷⣤⡴⠒⠋⠉⣉⣉⡳⡄
⢸⠀⠀⠀⠸⣿⡇⠀⠀⠀⠹⡆⢳⡀⠀⠀⠀⠀⠑⠀⠀⣠⣾⡿⢿⣁⣠⡴⠚⠉⢉⣉⣭⣿⣦⡀
⢸⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⣿⠈⡇⠀⠀⠀⠀⢀⡤⣺⠟⠁⠀⢀⣽⣿⣷⣾⣿⣿⡿⠿⠛⠛⠙⠲⢄⡀
⣾⣤⣀⡀⠀⢹⣿⠀⠀⠀⠀⣿⠀⡇⠀⠀⢀⢔⡽⠊⠁⠀⠀⢠⡿⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄
⡟⠲⠬⣍⣛⠺⠿⢧⣤⣄⣀⣿⢠⡇⢀⣴⡷⠋⠀⠀⠀⠀⠀⢻⡣⣀⣀⣀⣠⣤⣴⢐⡀⣄⣠⣀⣆⡰⣴⡳⠽⠊⠱⡄
⠹⣄⡀⠀⠈⠉⠙⠒⠒⠒⠒⢧⠘⣷⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠉⠉⠁⠀⠉⠑⠒⠒⠚⠋⠉⢁⣀⣠⠴⢚⣽⠦
⠀⠈⠛⠷⢶⣦⣤⣤⣤⣤⣤⣌⣧⣈⡓⠮⣍⡓⠒⠦⠤⠤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠶⠒⠒⣛⣋⣩⡥⠶⠛⣉⣠⣴
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⣿⣽⣲⠭⣟⣯⣛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢛⣋⣉⣉⣥⣤⣶⣶⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣾⣭⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢁⡴⢢⠞⡴⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡴⢋⡴⣣⠞⠁⠀⣀⣀⠀⠀⠀⣠⠞⣉⢀⡼⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡞⢡⠞⡴⢋⣠⠴⠛⠁⣹⡄⢀⡾⣡⠞⣡⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⢠⢏⡼⠗⠋⠁⣠⡴⢚⣥⣇⡞⡴⠃⡴⣫⠞⠀⣠⠴⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣷⡟⡼⠁⢀⡴⠞⣡⠞⠋⣼⡟⣰⢁⡾⣱⣧⠖⠋⠁⣀⡴⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣼⢰⣇⡴⢋⣠⣏⠀⠀⢰⡿⢡⣧⡾⣱⠋⠀⣀⡴⢛⣡⠞⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣴⠇⠘⢋⡴⠋⠁⣿⠀⢀⡿⠁⠀⣿⢁⡇⣠⠞⢉⠔⠋⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⣠⠎⡟⠀⢠⠎⠀⠀⠀⣇⣠⠏⠀⠀⢠⠇⢸⠟⣁⡴⠛⡇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⢀⡴⠃⣼⠁⢠⠏⠀⠀⢀⡤⠛⠁⠀⢀⡔⡿⠀⢀⡴⠋⠀⠀⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣇⣠⣤⠴⠶⠛⠉⢀⡼⠃⢀⡟⠀⢀⠔⠉⠀⠀⠀⣠⠞⣰⠃⢀⡞⠀⠀⠀⢠⡇⢀⡟
⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠻⣄⣀⣀⣀⣠⠴⠋⠀⠀⣞⣠⡎⠀⢀⣀⣠⡤⠞⠁⣠⠏⠀⡾⠀⠀⠀⠀⢸⡇⣸⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⡠⠞⠉⠘⣷⠛⠉⠉⠀⠀⣀⡴⠋⠀⡼⠁⠀⠀⠀⠀⢸⢀⡏
⠀⠀⠀⠢⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠁⠀⠀⠀⠀⠈⠙⠒⠒⠚⠋⠁⠀⠀⡸⠁⠀⠀⠀⠀⠀⢸⣼
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠚⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠤⠤⣤⣤⣤⡤⠤⠴⠒⠋⠁



⣤⣤⣤⣴⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣬⣴⣬⣽⣴⣾⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢐⢦⡐⠉⠉⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡆⠹⠆⠁⠘⠒⣂⡤⠔⠀⠈⠓⠀⡀⠀⠀⠀⢀⣴⠟⣉⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠆⠰⣊⡥⠀⣀⠤⠖⠉⠁⠀⠀⢤⣀⠀⠀⠈⠑⠲⠶⠿⠛⠉⢁⡔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⠁⠃⠀⣈⠥⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⢀⠴⠋⠀⠈
⠀⠀⠀⠀⠀⠠⠤⠤⠒⠂⠀⡠⠂⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡠⠚⠁⢀⠴⠚⠉⡇
⠀⠀⠀⠀⣈⣉⣓⣒⣒⠂⠀⠐⢦⡀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠤⠚⠁⠀⠀⠐⣁⣀⠤⢒⠀⡄
⠀⠀⡇⠀⢀⣉⠉⠉⠛⠉⠂⠀⠀⠙⢂⣙⠲⠄⠀⠀⢀⣀⠤⠤⠤⠀⠒⢒⡲⠒⠒⠒⠒⣒⠤⠦⠒⠊⠅⠐⠂⠉⠁⠀⠸⡄
⠀⠀⢧⡀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠋⠉⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠐⠒⠒⠈⠉⠈⠃
⠀⠀⠀⠈⠑⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉





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

⠀⠀⠀⠀⠀⠀⠀⢐⣿⣷⣦⣠⣄⡀⣤⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣠⣴⣦⡀
⠀⠀⠀⠀⠀⠀⡔⢠⣿⣟⣽⣿⣿⡵⣶⣾⡗⢻⣆⠀⠀⠀⠀⠀⠀⣰⡿⣷⡆⣼⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠰⣿⣤⣿⣿⣿⠟⠁⠀⡀⠈⠋⠁⢸⠿⠳⡀⠀⠀⣠⢾⣿⣿⠦⠰⢿⣿⡛⠋⠻⣿⡆
⠀⠀⠀⠀⣾⢩⣿⣿⣿⣿⡄⡉⢻⣿⠂⠀⢀⡄⠀⠀⢸⣠⡞⣵⣿⠿⠧⣤⣦⡑⡘⣿⣷⡄⢸⣿⡀
⠀⠀⢠⠀⣭⡟⠿⠇⠹⡟⢳⣀⠀⠀⠁⢠⡾⠁⠀⢀⣾⣿⡧⣿⡇⢇⠀⠘⠛⠀⢠⣿⣿⡛⢾⣿⣧
⠀⠀⠈⠷⣟⣻⡶⣰⠿⠀⠘⢿⣿⣿⣿⡿⠁⠀⢠⡾⠻⣿⣧⠈⠻⣄⠁⠀⠤⠞⠓⣹⡿⣻⡆⢻⣿
⠀⠀⠀⠀⠈⣽⣿⣤⠀⣰⠓⢴⠞⢻⠟⡸⠃⣠⠟⠀⠀⢻⣿⡆⠀⣇⠀⠀⢀⣴⡊⣹⢿⣻⣧⠾⠋
⠀⠀⠀⠀⣰⣿⣿⡿⣧⠈⢷⣄⢄⢬⣼⠇⣰⡟⠀⠀⠀⠘⣿⡇⠀⠃⢳⡄⢧⡾⣣⣭⣼⣯⠁
⠀⠀⠀⢀⡿⢹⣿⣷⣌⣛⡟⣿⣿⣦⣌⡑⠻⣀⠀⠀⠀⠀⣿⡇⠀⣦⣼⠻⠾⠟⣿⣿⣼⢿⡄
⠀⠀⠀⣼⠇⢿⣿⡐⠛⠛⢛⣿⡍⢿⡏⢹⠇⠈⣤⠀⠀⠀⢿⡇⠀⢹⣿⣋⣁⣿⡶⢻⣿⡛⣧
⠀⠀⢠⡿⠶⢿⠿⣿⠻⣿⣿⡿⣿⣿⣦⣎⡀⠀⠛⠀⠀⠀⣿⡄⠀⣾⡿⡿⢛⣁⣴⣿⣿⡄⣿
⠀⢀⣼⡇⠀⠅⣶⠛⢻⣿⠃⢴⣯⣿⠙⣏⠙⠷⣄⠀⠀⣰⣿⣇⡴⠟⠋⣠⣿⠟⢩⣹⣿⡟⣾
⠀⣸⣿⠀⣴⣦⠬⠭⣿⣿⠟⠚⡋⡟⢀⣿⡀⠀⠈⠱⣴⣿⣿⠥⣶⣾⡿⠶⠿⠗⢻⣻⡟⢡⡟
⠀⣿⣿⣄⠈⠁⣠⣾⣿⣶⣦⠴⡿⡇⣸⠛⠙⠶⠤⢀⡼⢋⣠⠶⠿⢛⡓⠚⠛⠒⠛⠳⠇⢼⠃
⠀⣿⢹⣯⠷⠾⠿⠿⢿⣿⣿⣷⣄⢶⡟⠀⠀⠀⢰⡾⣷⡟⣛⣉⣩⣤⣿⣿⣿⣿⣟⣶⣶⡤⣤⢄⣀
⠀⣿⡎⣿⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠀⢀⡀⢰⢿⣿⣯⠄⣤⣝⠛⠋⠉⠉⠑⠚⠛⢿⡿⠀⠃⠑⢿⡆
⠀⢿⣷⡘⣧⡀⠀⠀⠀⠀⠀⢠⠞⠁⢠⣾⣿⣷⣾⣿⡏⣴⣾⣿⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠁
⠀⠘⣿⣷⡌⠳⢦⣄⣀⣠⡶⠋⡴⠀⠻⣯⠥⠋⠠⠙⣿⣿⣿⡏⠠⣤⣀⣀⣀⣴⣟⡄
⠀⠀⠸⢿⣿⣶⣦⣤⣥⣤⣴⠞⠁⠀⠀⠀⠀⣠⣤⠀⠙⢿⣿⣷⣤⣾⣿⣿⣿⡿⠛

⠀⠀⠀⠈⠉⠙⠛⠉⠛⠉⠁⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠈⢻⣟⠛⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠛⢶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠊⠀⠐⢌⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣠⠖⠁⠀⠈⢳⡄⠉⠀⠀⠀⠀⠈⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠳⡈⠀⡀⠤⣀⣀⠀⠛⠀⠀⠀⠀⢀⡴⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣄⣉⡙⠛⠒⠀⠀⠀⠉⠑⠂⠤⠤⠒⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠨⠦⠬⠍⠉⠀⣀⠀⠤⠤⠒⣁⠀⠀⠀⢀⣀⡤⠊⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⣋⠙⠂⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠉⠉⣩⠔⢋⡤⠊⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠹⣮⠈⠉⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡫⠔⠊⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⡠⠔⢊⠁⠀⠈⠆⢠⠈⠀⠀⡜⠁⡀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⣀⠤⠒⠉
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠑⢤⡀⠀⠊⠀⠀⡸⠀⠀⠈⠑⠦⡀⢠⡺⠛⠁⢀⡠⠔⠊
⠀⠀⠀⡀⠐⠤⣀⡀⠀⠀⠀⠈⢀⣀⠤⠚⠁⠀⠀⠀⠀⣠⠔⠉⠀⡠⠒⠉
⠀⠀⠰⡙⠦⣀⡀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢀⣀⡠⠔⠊⢁⡠⠖⠉
⠀⠀⠀⠙⠦⣀⡈⠉⠉⠒⠒⠒⠀⠐⠊⠉⣁⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⣾⣿⣿⡌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣿⣿⡽⣿⣆⠘⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⠟⠀⢰⢀⣿⣿⣶⢄⡀⠀⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢃⣿⣿⡏⠀⠀⠀⠸⢸⣿⣿⣿⠀⠙⢾⣾⣷⣤⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣉⣡⣠⣶⣿⣿⠟⠀⠀⠀⢠⢃⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⡿⠼⠦⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠃⠚⠋⣩⡭⠿⠛⠛⠋⠁⠀⠀⠀⢠⠃⣼⣿⣿⣿⠃⠀⠀⢸⣿⠋⠁⠀⠀⠀⠀⠀⡱⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⢤⢠⡞⢁⣾⠁⠀⠀⠀⠀⠀⠀⢀⢃⣾⣿⣿⡿⠃⠀⠀⢠⣿⢻⣇⢀⣄⣀⣠⣤⡴⢁⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⡟⠺⠷⣯⠟⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⠏⠀⠀⢀⣴⣿⡫⣜⠛⣨⢜⡭⡼⢶⣖⠀⡀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⢨⢿⠀⣗⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⢀⣴⡾⢻⠊⠀⢹⠓⢡⡏⢀⡠⠼⢿⣇⠀⠀⡠⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣸⠇⢐⠦⢇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⣴⠟⡉⠀⡇⡆⠀⢀⣴⢯⠁⡴⠄⠚⢿⣟⣆⠚⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⠖⢁⣴⡧⣾⢒⠆⠀⠀⠀⠀⠀⠀⣸⠇⠀⣰⡿⢻⣆⠹⣦⡙⠿⠓⠁⣹⠟⣰⠷⠖⠈⣛⣻⣿⣧⡒⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⣴⢫⣌⣣⡼⠾⠀⠀⠀⠀⠀⠀⢰⡟⠀⣼⡟⠀⠀⠙⢦⣅⢈⡢⠔⠊⡡⢾⣿⡶⠞⠓⠈⣛⣻⣏⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⢮⣀⠈⢄⣹⣿⠂⠀⠀⠀⠀⠀⢀⡿⠀⣼⡏⠀⠀⠀⠀⠀⡙⣋⡤⡶⠉⠀⠀⠿⣿⡟⢋⡁⠈⣭⣿⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢀⠸⢋⣛⢳⠋⠀⠀⠀⠀⢀⠀⣾⠃⣰⡟⠀⠀⠀⠀⠀⢠⠏⢘⣷⠸⡆⠀⠀⠈⢪⡫⢸⠗⠶⣿⠍⠀⢳⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣷⡾⣋⣿⠽⠉⠀⣀⠀⠀⢀⠎⣼⠃⣴⠋⠀⠀⠀⠀⠀⠀⠈⢰⣼⣿⠀⣧⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠈⢼⣿⣧
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠈⣀⠔⠊⣹⣿⣧⣬⣷⡾⣡⡞⠁⠀⠀⡀⠀⠀⠀⠈⠁⣿⣿⣿⡀⣿⣿⣷⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⡆
⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⣠⢞⣡⣾⣿⣿⣿⣿⡿⣋⣾⢟⣡⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⢸⣿⣿⣿⣿⣦⡢⡀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⣾⣏⠣⣀⣀⠤⢊⣵⣿⣿⣿⣿⣿⢟⣡⡾⠛⢋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⢻⣿⣿⣿⣷⣿⣮⣵⣢⡤⠄⣂⣰⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣷⣶⣶⣿⣿⣿⣿⡿⣟⣽⣾⣉⣭⣶⠊⠉⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏
⠀⠀⠀⠀⠀⠉⠛⢿⣿⣯⣿⣿⣿⣯⣿⣷⣾⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣍⡛⠿⠿⠿⠿⢿⣿⣿⣟⣿⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠾⠿⠿⠿⠛⠛⠋⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢁⡈⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠁⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⢀⡦⠀⠀⠀⠀⠀⠀⠀⣀⠔⢁⠄⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠠⠀⠀⠀⠀⠀⠀⢠⠞⠡⠖⠁⠀⠀⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠘⠀⢠⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠘⠃⠀⠀⠀⠄⢐⠈⡃
⠀⠀⠀⠀⠀⠀⢀⠈⠒⠈⠁⠠⡍⠀⠀⠀⠀⡠⠋⣠⠆⠀⠀⠀⠈⡀⠀⠂⠀⠂⢉⢑
⠀⠀⠀⠀⠀⠐⠀⠀⠉⡁⠀⡈⠀⠀⠀⢀⠜⢁⠔⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⢩⣀
⠀⠀⠀⠠⠤⠀⠤⢀⡀⠀⠉⠁⠀⣀⠔⠁⢠⠏⠀⡁⠢⣀⠀⠀⠀⠀⢀⠀⠈⢉⠁⠂⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡤⠔⠊⠀⠀⢰⠃⠀⠀⠑⠀⠠⠑⢄⠀⠀⠰⠄⢀⣉⠀⠤⠤⠈⠀⢥⣄⡀
⠀⠘⠤⠄⠠⠤⠤⠒⠊⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠸⠑⠤⢀⡔⢉⠀⠀⢀⣀⠠⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⣾⣿⣦⠈⠢⣀⣠⡴⣶⡟⠲⣄
⠀⠀⠀⠀⣸⣿⣿⣿⣦⡀⠈⠻⢿⣻⣿⣅⠈⠢⡀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣳⡀⠀⠀⠙⢿⣿⣆⠀⠘⢦⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠙⢿⡆⠀⠀⠙⣄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⢔⠠⡀⠈⠳⣄
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢻⡆⡀⠀⠀⠀⠈⠳⡙⢦⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣾⣿⡌⢢⡀⠀⠀⠀⠈⠢⡑⠄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⣿⣿⣿⣄⠹⣄⠀⠀⠀⠀⠈⠢⣄⣀⣀⣉⣲⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠻⣿⣿⣿⣿⣿⣦⡘⢦⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⣵⣀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⠿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠷⠶⠿⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡏⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⠖⠉⡩⠝⠂⠠⠴⣊⠁⠀⠀⣀⡰⠃⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠂⠀⣘⡁⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣠⠊⠉⢁⣀⡀⠁⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠒⡌⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠞⠁⠉⠉⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⠴⠂⠉⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠴⠈⠋⠀⢀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡴⠛⠂⡀⠀⠀⠀⠀⠈⠱⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢌⡁⡀⠤⠤⠤⠤⠣⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⡠⢊⠌⢠⡤⠐⠚⡉⠁⠉⠁⠒⠀⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢂⠄⠘⠀⠁⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡠⠊⠀⠊⠀⠈⠛⠀⠀⠀⠀⠤⠾⠂⣈⡉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⢤⠒⠈⠉⠉⢉⠉⠊⠀⠀⠀⠀⠀⠀⢀⠞⢁⠔⡠⠂⠀⠀⠀⠀⠘⠖⠀⠀⠠⠀⠀⠤⡌⠒⠚⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠗⢀⣀⢤⠤⠄⠀⣸⠇⠀⠀⠀⠀⠀⠀⣰⠋⠠⣢⠞⠀⠀⠀⠀⠀⠀⠀⠰⡧⠤⠀⠠⠤⠄⠀⠑⣯⡵⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠤⣈⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⠞⠁⣀⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣈⣁⠀⠘⠁⠠⢴⡆⡄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢨⠈⠙⠁⠁⠀⠀⠀⣀⡔⠁⠀⣨⠏⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠁⠒⢲⣈⣉⣉⣠⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠑⠢⢌⣆⠀⠀⠀⢀⡤⠚⠁⠀⣀⢼⠏⠀⠀⢳⣄⠀⠉⠢⣀⠀⠀⠀⠀⠀⠋⠃⠨⢟⣭⣿⠯⠥⠭⠭⠤⢬⡽⣦
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠴⠚⠉⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠙⠍⡓⠢⢌⠣⣀⠀⠀⠀⠀⢹⠈⢉⣉⣀⣤⣤⣤⣤⣤⣤⣽⣷⣷⣤⣀⡀
⠀⠀⢧⣀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠁⣽⠣⣄⡀⠀⠀⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠋⠈⠢⡀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠉⠑⠚⠒⠤⠤⠄⠐⠒⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠡⢄⣀⣀⣀⣀⣀⣠⡤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠂⠀⠀⠀⠐⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤⣠⣤⣄⡀⠀⢸⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠙⣿⣿⣿⣷⣼⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⢀⣀⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣄⣹⠀⠀⠀⠀⠀⠀⠘⡄⠉⠩⣶⣳⡶⠿⠛⠋⣁⠤⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⣿⠟⢇⠀⠀⠀⢀⣠⣴⡾⣆⠀⠀⣨⢷⣒⡮⠿⠒⢉⣠⣼⣳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠸⡌⠙⠛⠛⠁⢠⣼⣖⡲⠿⠓⢋⣁⣤⣚⢷⣀⠈⠉⣹⢤⣒⠯⠓⠋⢁⣀⣬⣳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠙⣄⠀⠀⠀⠀⠀⣼⣶⠾⠿⠛⢋⣩⢤⣾⠿⡙⢦⠉⠉⢹⡶⣾⡗⠛⠛⠉⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠧⣄⣀⠀⠈⠓⠤⣄⡀⠀⠀⢸⣶⡶⠿⠛⠋⣁⣠⣤⣿⣆⠳⡀⠀⠀⠀⠈⠁⠒⠒⠒⠋⠀⠙⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⠙⢦⡀⠀⠀⠉⠑⢤⠀⠀⢱⡶⣽⠟⠛⠉⠉⠀⠀⢱⡙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣳⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠦⣄⠀⠀⠳⡀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠉⠓⠲⠂⠔⠒⠁⠙⢦⡈⠉⡷⠊⠉⠉⠉⠙⠓⠒⠒⠚⠉⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠒⠦⣌⣦⡀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠈⠛⢷⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠉⠒⢲⠔⠊⠁⠀⠀⠉⠑⠒⠐⠒⠉⠀⠀⢳⠤⠤⠤⠤⠐⠒⠒⠊⠀⣠⣾⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣄⣀⣀⣀⣀⣀⣤⡀⠀⠀⠑⢄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡆⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠷⡄⠀⠀⠀⠉⠒⠒⠒⠒⠛⠲⢤⣤⣀⣀⣤⣤⣤⠤⠴⠋⠀⣠⢷⣶⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠴⣶⣶⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠋⢁⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠛⠛⠉⠉⠀⢀⣠⡤⠖⠋⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⡤⠤⠶⠖⠚⠋⠉⠁⣀⣤⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢳⡀⠀⠠⠴⠶⠚⠋⢉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢳⡀⠀⣤⠤⠶⢚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⣀⣤⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣄⣀⣀⣠⡼⠁⠘⠀⣀⣤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⢻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠛⣿⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁⠀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁⠀⣀⣀⣤⣤⠶⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠀⢀⣀⣀⣤⡤⠶⠖⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠶⠶⠶⠶⠶⠶⠖⠛⠛⠋⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⠔⠒⠒⢤⡀⠀⠀⠀⠀⡜⠁⣀⣤⣤⡀
⢠⣇⠀⠀⠀⠀⠈⠑⢀⡤⠞⠀⠾⢛⡛⢻⠄
⣾⢎⠲⠤⠤⢴⢖⠊⠁⠀⠀⠀⠀⠉⣚⡛⣐⣓⠦⡀
⣿⠀⠉⠉⠉⠁⠠⠀⠀⠠⢕⢄⠀⠀⠈⠱⠿⠟⢁⡿⠖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢀⡠⠖⠲⢤⡀
⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠣⡱⡄⠀⠀⠉⢐⠛⣋⡜⠙⣀⡀⠀⡀⢸⠿⠿⣶⡄⠐⢄⡀⠀⠐⠉⠀⠀⠀⠀⣿⡄
⡿⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠢⡀⠀⠀⠀⠑⠚⠉⠁⠀⠀⣨⡙⣦⣔⠲⠀⠀⠀⠀⠐⠀⠤⢤⣤⠤⠞⡸⣧
⡇⠀⠀⠀⠉⠉⠒⠂⠄⡀⠀⠀⠀⠀⠑⠜⠄⠀⠀⠀⠀⠀⢀⣔⠩⣶⣶⡰⠖⠀⠀⢀⠔⡂⠀⠀⠀⠀⠐⠒⠉⠀⢻
⢧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠄⠀⠀⠀⡀⣠⣍⢩⣥⡈⠭⠁⠀⠀⡠⢫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⠉⠙⠛⠓⠒⠢⠤⣀⡀⠀⠈⠑⠢⠀⣀⡠⠔⠀⠦⢤⣐⡲⠄⠄⠀⠀⢀⠔⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣲⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⢊⠊⠀⠀⠀⠀⠀⡀⠄⠒⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠁⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠑⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣎⡁⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣥⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡴⠶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠚⠛⠛⠻⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⣴⡟⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢧⣄⣠⡾⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣼⣟⣵⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢠⡿⢻⣅⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣤⡀⠀⢀⣤⣴⣶⣦⣄⠀⠀⠀⣠⣶⡄⠀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⢸⡇⠀⠈⠉⠁⠀⠀⡄⠀⠀⠀⠀⠀⢺⣿⣄⣀⠙⠃⠀⣿⡏⠀⠀⠈⣿⡇⠀⢠⣿⠙⣷⡀⠀⠈⣿⡀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣾⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣀⡉⠙⠛⢿⣦⠈⣿⡇⠀⠀⠀⣿⡏⢀⣿⣧⣤⣽⣷⠀⠀⣿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⡾⠏⠀⠙⢿⣦⣤⣾⠟⠁⣼⡟⠉⠉⠉⢿⡧⠠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⢸⡿⠚⠶⢦⣄⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⢠⣿⠂⠀⠀⠀⢹⡆⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠤⠤⠤⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠶⣦⣿⠇
⠀⠸⣎⠁⠀⠀⢀⣼⣥⣤⣀⠀⠉⠛⠻⠷⠶⠶⠶⠶⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠈⢿
⠀⠀⠉⠛⢻⠟⠉⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⠀⠀⠀⣠⠟
⠀⠀⠀⢀⡏⣼⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠤⠤⠤⠤⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⠟⠋⠁
⠀⠀⠀⠘⣷⣝⠃⠀⠀⠀⢀⣰⣷⣶⣴⣶⣶⠶⠶⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠷⠶⣶⣶⣶⣶⣶⡶⠾⠟⠋⠁
⠀⠀⠀⠀⠈⠛⠿⠶⠶⠶⠛⠁
⠀⣀⣀⡀
⠀⡃⠀⡁⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣴⡦⢠⣤⣔⣒⣲⣦⣴⣯⣭⣤⣤⣤⣤⡟⠙⣧⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢩⢤⢷⠶⢿⣿⣿⣯⡿⠟⠛⠙⣉⡉⠩⠭⠭⠭⠇⣸⠧⠤⣬⣅⣀⠀⢀⣁⡛⣷⣶⣤⣀⠀⣀
⠀⠀⠀⠀⠐⠸⢴⣊⢙⣩⢗⣛⠛⣋⣩⠤⠒⠚⣉⡩⠤⠄⠔⢒⣒⡂⣺⡁⠀⠈⠒⠒⠤⠭⣙⡒⠤⣝⠩⢝⡻⣭⣛⠍⠒⢀
⠀⠀⠀⠀⣠⠞⠃⠐⡐⡀⠀⢀⡊⠋⣀⡴⠞⠉⠁⢒⡈⠉⣉⣉⣉⣁⠃⢉⠉⠉⠑⠒⠢⢤⣄⠈⠁⠂⠄⠀⠈⠑⠉⠑⠢⣀
⠀⣰⢃⡞⠁⠀⠄⠀⠀⢀⡀⠀⢀⡾⠉⠀⡠⠀⠀⣴⣶⣾⠿⡿⠕⠁⠀⠀⠽⣿⣷⣶⡦⢄⡀⠓⢤⣠⣀⠀⠀⠀⠀⠐⡆⠈⠂⠀⠀⠀⠠⣄
⠰⠃⣸⠐⠀⠘⠀⡀⠀⡏⠈⠋⠿⠀⡂⢸⠀⠀⣶⢸⠇⠁⠀⠀⠀⣀⣀⣴⣮⣮⣿⠈⠂⠀⠀⠀⠀⣈⣿⣷⣤⠀⠀⠀⠈⢣⠀⠀⠀⠀⠛⡌⢦
⠘⠀⢀⢰⢀⢰⢡⢡⠀⣇⢀⣀⡀⠀⢇⠀⠀⠀⠙⢇⡀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢁⡠⠆⠀⠈⠀⠀⢨⣽⢿⣛⠄⠀⠀⢀⠈⡷⠀⠀⠀⠀⢸⠈⣇
⠀⠀⠀⠈⢎⢧⢻⢧⠱⡈⢮⡻⣿⣦⡀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠈⠉⠁⠀⣀⣀⡤⠤⠶⠀⢀⡾⠉⠀⣠⣾⠏⠀⠀⢀⡄⠀⠐⢸⢄⣷
⠀⠀⠀⠀⠈⢦⠳⣙⣴⣌⠂⣙⠪⣝⡷⣦⣀⠀⠀⠐⠢⠄⠀⡀⠀⢈⢩⠉⠉⠉⠉⠉⠉⠀⠀⠀⢠⠴⠋⢀⣤⠾⠋⣀⠴⢋⠤⠋⠀⠀⢀⠎⣼⠃
⠀⠀⠀⠀⠣⣀⠑⢌⠳⣗⠑⠢⣔⠠⣙⠻⢭⣟⡶⢤⣤⡀⠀⠀⠀⠀⠬⡭⠭⠭⠄⠀⣀⣀⣤⠤⠶⠚⣋⣉⠤⢖⣫⠵⢚⣡⠔⢠⠄⠀⠂⠚⠁
⠀⠀⠀⠀⠀⠀⠙⠦⠈⠀⠑⠂⠈⠙⠲⢭⣒⡬⢽⡓⠲⠬⣭⣽⣛⠓⠚⠛⠛⣛⣛⣩⠭⠥⠖⣒⣛⡩⠥⠖⣊⡡⠄⠚⠁⣀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡁⠀⠀⠈⠻⢡⡀⠀⡄⠀⠀⠒⠒⢈⠉⠩⠥⠴⡒⠊⠉⠀⠀⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠈⠑⠈⠑⠊⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠒⠂⠀⠀⠰⠀⠀⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⣀⠠⠔⠒⠉⢹⣻⠆⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⣀⠄⠒⠉⢀⣠⠴⠂⠉⠀⠀⠀⠀⠀⡞⠁⠓⢄⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⣀⠄⠒⠉⠀⣀⠤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢆⠀⠑⢄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⣀⠔⠊⠁⡀⠤⠖⠀⠀⢀⢀⢤⠠⠄⠀⠀⠀⢀⣤⡴⣶⢶⡀⠀⠱⡄⠈⢦⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⡀⠀⠈⠀⡠⠔⠊⢀⠀⢄⠠⢐⠢⠉⠀⠀⠀⠀⠀⠘⣯⠁⡆⣨⣿⠇⠀⠀⠘⢄⠈⠇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⠄⠊⣀⠤⠂⠁⠀⠀⢀⠘⠢⠈⠁⠀⠀⠀⠀⢠⣤⡀⠀⠀⠘⢷⣀⣟⠁⠀⠀⠀⠀⡈⠀⢸⠀⠀⠆
⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⡞⡁⠀⠉⠀⠀⠀⠀⠀⠜⠂⠁⠀⠀⠀⠀⠀⠀⠀⢸⡷⣼⣷⣄⠀⠀⠻⣿⡆⠀⠀⠀⠀⠓⠐⠃⠀⠀⢸
⠀⠀⠀⢀⣴⠏⠀⠀⠀⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣋⣙⢓⢄⠀⢸⠛⣰⣿⢾⣭⣶⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⢠⡾⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⡄⠀⢾⠄⡇⠈⠳⣬⠆⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡑⡆⠀⠀⣸
⠀⢠⣏⠀⢹⠀⠀⠀⡏⡍⢳⠀⠀⠀⠀⠀⣼⠁⠀⢈⣁⣀⡘⣧⡘⠤⣀⡿⣦⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡴⠁⢀⣾⡟
⠀⡞⠀⠀⠀⡆⠀⠀⡇⠈⠘⣆⠀⠀⠀⠀⠻⠾⠉⠓⠒⢀⣻⠈⠛⠶⠾⠟⠁⠀⠀⠀⠀⠀⣀⢠⠲⠒⠂⡠⠔⢊⠔⠁⢀⣴⣯⣿⡇
⢸⡇⠀⠀⠀⠸⡀⠀⠹⡀⠀⠘⡄⠀⠀⠀⠀⠀⢀⣠⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⣰⢅⠩⠑⠙⢀⠤⠊⢁⠔⠊⢀⣤⣾⣿⣿⣿⡿
⠈⡇⠀⠀⠀⠀⠱⡀⠀⢣⠀⠀⠘⣄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢀⣠⠤⠋⠀⣁⡠⠌⢁⠄⠀⢀⣤⠾⣽⣹⢿⣾⣿⡟⠁
⠀⢧⠀⠀⠀⠀⠀⠹⡄⠀⠳⡄⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠄⠐⠉⢀⠤⠊⢁⣤⢾⣿⠁⠜⣵⣱⣾⡿⠋
⠀⠈⣆⠀⠀⠀⠀⠀⠙⢆⠀⠈⠢⣀⠀⠭⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠊⠁⣀⠔⠊⢁⣠⢾⣿⣛⠛⣋⣿⢿⢷⡿⠋
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠳⡀⠀⠈⠙⠂⠁⠀⠀⠀⢀⠀⡄⠘⠁⢀⡠⠐⠀⣀⣤⢶⣿⠏⣴⢧⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠒⠈⢁⣠⢶⢛⡿⣏⡨⣃⡜⣸⣣⣳⠿⠋⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣗⣢⢾⣿⣽⣉⣻⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠐⠠⠀⣼⢫⡫⠋⢯⣽⣿⣿⣿⣻⣿⣿⣯⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⡀⢀⣾⣱⡰⢫⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠪⢶⣄⣜⣳⣆⣼⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀⡈⣠⡀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢾⡠⠄⠊⣡⠞⠁⠀⠈⠀⠀⠀⠀⠀⢧⡄⡀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣔⠀⠏⠀⢈⡶⠁⠀⠀⠀⠀⠀⠀⠐⠒⢦⠀⠀⢳
⠛⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣿⠁⠀⡸⠂⡼⣁⡀⠀⠀⠀⣴⠂⠀⠆⠀⢄⣠⡄⠸
⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠉⠁⠀⠀⢡⣴⣿⣿⠗⢀⠙⡄⠊⠉⠀⠀⠀⠀⠀⠀⠁
⣷⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡂⠀⢫⣿⣷⠛⣣⡛⠈⠀⠀⠀⠀⠀⢀⣀⣆⠀⠈
⢼⠗⢄⠀⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡾⠟⠀⠀⠀⠈⠁⠀⣿⣿⣶⢾⢽⣷⡇⠀⠀⠀⣀⣠⡟⠉⡈⠀⢠
⣾⣷⣾⣷⣤⣤⣄⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡹⠃⠀⡰⠂⢠⠀⠀⠀⢠⣿⡿⢡⡟⣼⣽⡇⠀⠀⠀⠀⠹⣧⢽⢣
⣿⣿⣿⣋⣿⡿⠿⠿⣧⣾⣿⣿⡗⠠⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣤⠟⠀⠀⠀⠀⢰⣯⡇⠀⠀⠀⢹⣿⣿⣆⣽⡿⣿⡁⠀⠀⠀⠀⠀⠘⠶⢧⡀⡀
⣿⡿⠛⠉⠀⠀⢲⣶⣿⣿⣿⣿⡇⣀⡨⣿⢿⣶⣬⣯⢶⣾⡿⠋⢋⣀⣀⣀⣾⢟⣟⣮⡖⠀⠀⠀⠈⢿⣿⣿⣿⣧⡈⠷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣿⣿⣾⣿⣇⣀⡉⠻⠿⢿⡦⠰⢯⣉⡿⠿⡿⢋⣾⣿⣿⡇⠀⠀⠀⠀⠈⢻⣏⣻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣆⣿⣿⣿⣿⡿⣿⣇⡈⠁⠀⠤⣀⠒⠿⣞⠛⣾⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣧⣿⣿⣏⡳⢶⣶⠮⣯⣷⡴⠶⠏⣲⣿⠿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠙⠯⣭⣀⠈⠻⢷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⠶⠿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣤⢞⣛⣡⣿⡳⠻⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣶⣷⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⢿⣿⣿⠿⠛⠫⠭⢭⣿⣿⣟⠚⠛⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢿⣿⠟⠒⢀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡋⡳⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠻⠿⡿⣿

⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⡀⠘⢈⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣽⠋⠕⠀⠀⣞⢱⠀⠀⠂⠀⠐⡌⠛⠋⠠⠂⠍⠐⡿⢛⠛⢿⠅⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠉⠱⢹
⣿⣿⣿⣿⣿⣿⢻⣿⡟⢿⢛⣽⣯⣀⣀⠀⣰⣿⣼⣧⢰⣦⣠⡀⠀⢀⠀⠀⠄⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠐⢸
⣿⣍⣿⣿⡿⢯⡈⡾⡆⠃⡠⡿⢾⣫⡁⠘⡛⠟⠛⠃⠚⠛⠋⠁⢀⡼⠄⠆⠀⣠⣴⣶⣄⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠰⠀⠀⠐⠆⢸
⣿⠋⢧⡿⡇⠊⠄⠃⠀⠀⠀⠀⠈⠟⣣⠛⣿⢷⠄⠤⠿⢿⠻⠶⠟⠁⠀⠀⣾⣿⣿⣿⣿⣶⠀⠐⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⢸
⣿⠀⠨⠉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠁⠀⠀⠀⠀⢀⠠⠀⠠⣶⠾⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣸⠙⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢀⣼⣿⣿⣷⣤⣶⡤⠠⡀⣀⠀⠀⢨⡟⡀⠀⠀⠀⢼
⣿⠀⠀⠀⠀⠀⢰⣿⠀⠪⠄⠀⠀⢀⣰⣄⠀⡀⢀⣄⠐⠀⠀⠀⣄⠒⠁⠀⠰⣾⣿⣿⣿⣿⠿⠿⣥⣤⣤⡀⠙⠀⠼⣷⣯⠀⠀⠀⢸
⣿⠀⠀⠤⠀⣸⣿⡿⣆⠂⢀⣾⠀⢸⣯⣽⡧⣱⠀⠀⠐⣦⣶⢲⣴⡿⠀⠀⠀⠀⠁⠀⠀⠀⠰⢿⣿⣿⡿⠓⠀⣀⣨⣽⣿⣶⠀⣠⣾
⣿⠀⣸⠇⠑⣯⣿⠁⢻⣀⣠⣽⣷⣏⣉⣴⣻⠏⠀⠀⠀⠈⠿⣿⣾⣒⣒⣊⣁⠐⢀⡀⠀⠀⠀⠀⠴⢦⣶⢂⡿⢿⡿⣿⣿⣷⡇⣿⣿
⣿⢀⣿⡀⡄⣷⣿⣿⣿⣿⣿⡟⠉⠙⣷⡿⣥⢾⠀⢴⣿⡗⢻⠒⠳⠂⠢⢤⠤⠀⠋⠀⠀⠒⣾⣗⣶⡯⠟⠉⢠⣾⣿⣿⣿⢟⡟⣹⣿
⣿⣸⣿⣷⣄⣿⣿⣿⠙⠈⠽⠓⠠⠤⠴⠛⠛⠒⠜⠈⠉⠁⢁⠁⢀⡂⠀⠈⠊⠁⠀⣀⣀⣨⠭⣤⠟⠉⠤⢀⣿⡿⣾⣿⣿⣿⡷⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠚⠂⠀⠀⠄⠀⠐⠊⠀⠀⠀⠀⠤⠄⠀⠁⠀⠀⠀⠀⠰⠀⠒⠀⢽⠿⣿⣀⡏⠀⣠⣮⣺⣿⠇⣻⣿⣿⣿⣏⠘⢻
⣿⣿⣿⠟⡉⠁⠂⠀⠀⢀⠀⠁⠀⠀⣀⣀⣠⠶⠲⠂⡤⠶⠀⠤⠀⠀⠀⠀⠀⠈⠁⠂⠈⢛⣿⠥⠀⣹⣿⣿⡟⡸⣿⣶⣾⣿⣯⠀⣿
⣿⣿⡦⠦⠠⠤⠀⠀⠀⠀⡀⠀⠀⠀⠘⠍⠀⣤⠄⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠐⠠⣤⣤⣌⣿⣧⣴⣾⣼⣿⡇⢧⣛⣶⢿⡙⣎⠐⣿
⣿⠁⠀⠒⠀⠀⠓⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠄⠀⠀⠀⣀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⡿⣷⢏⠀⠶⠎⠸⠇⢸
⣿⠀⠀⠀⠳⡀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⢀⣤⢴⣶⣿⣿⣿⣿⣿⣿⣧⣀⣧⣴⣾⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠐⠤⣄⡀⢀⣀⣠⡤⠤⠷⠶⠶⠒⠲⠒⠳⠶⠤⣤⣀⣀⣀⡤⠊⠀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⣀⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⡀⢀⣀⠄⠀⠀⠈⠳⣄
⠀⠀⠀⢀⡴⠋⠀⢀⣀⣀⣀⣀⣠⠊⠁⠀⠀⢀⣤⠶⠶⠀⣠⡴⠆⣄⠀⠀⣠⣤⡀⠀⢠⡴⢦⡀⠀⠀⠀⠙⢯⡀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⢹⠁⠀⠀⠀⠀⠘⠳⢤⡄⠀⣏⠀⠀⣿⠀⣼⠷⠾⢷⠀⢸⡗⠛⠁⠀⠀⠀⠀⠀⢷⡤⡤⠤⠄⠀⠀⠀⣷
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⡬⢧⡀⠀⠀⠀⠀⠶⠞⠁⠀⠈⠛⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⣟⢧⡀⠀⠀⠉⠁⠀⠀⠀⠉⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠛⠦⡀⠀⠀⠀⠀⠀⣠⠞⠁⡇
⠀⠀⠀⣷⠀⠙⢦⡀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠉⠙⠓⢶⠲⠶⠶⠶⠶⠶⡶⠶⠒⠒⠛⠉⠉⠱⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⡤⠞⠁⠀⢀⡇
⠀⠀⠀⣿⠀⠀⠀⠙⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠛⠋⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⣛⢟⣉⠛⣛⢛⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄
⣤⣤⣤⣤⣶⣬⣤⣥⣬⣤⣥⣤⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠛⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣄⠀⠀⠀⣀⡴⠃⠀⠀⠈⠳⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢀⠔⠋⠀⠀⠀⠙⣷⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠸⡿⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠀⣙⣥⣄⣀⠔⠒⠒⠲⠦⢤⣀⠁⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⣧⣀⡀⡹⠋⠙⠛⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠒⠒⠋⠁⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢹⣤⣭⣉⡛⠛⠓⠀⠀⠀⠀⢀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⣷⡀⣨⣉⠉⠉⠈⠀⣀⡴⠒⠉⠁⠀⠀⠀⠒⠶⠶⠦⠶⠤⠴⢖⡶⠛⠁⣠⠎⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄⡸⣧⢤⣈⡔⠈⠑⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣠⠴⠋⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠹⣷⣍⠈⠑⠃⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣉⡤⠖⠋⠁⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⢦⠀⠀⠈⠳⠅⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣫⠖⠋⠁⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⢦⡀⠀⠀⠀⠃⢸⡇⠀⠀⠀⡼⠁⠀⠲⢄⡀⠀⠀⠀⠀⠀⣠⢴⡯⠞⠉⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠋⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠳⢤⡀⠔⣫⠕⠋⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠁⢤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⡴⠚⠉
⠀⠀⠀⢀⠰⡄⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢀⡠⠞⠁
⠀⠀⠀⠘⣆⠉⠳⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠛⠉⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠉⠉⠙⠛⠒⠒⠂⠀⠒⠊⠉⠉⠀⢀⣀⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠚⠿⠶⠶⠒⠒⠒⠒⠒⠒⠛⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠑⠚⠆⠄⠀⣀⠐⠂⢄⠠⠄⠀⠀⠀⠀⠌⠂⠀⠀⣢⣠⡤⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣴⣯⣶⡄⣷⣸⢿⣄⣤⣴⣷⠆⠊⣛⣍⠱⣿⣶⡘⡒⢢⢤⣄⡆⡤⠀⡀⢁⢺⣁⣴⣹⡇
⠀⠀⠀⠀⠀⠀⢠⣴⣦⣊⣶⣷⣻⣷⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣶⣿⣽⣿⣿⣿⣿⣯⣦⣤
⠀⠀⠀⠉⠈⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠙⠙⠋⠉⠁⠁
⠀⠀⠀⠀⠐⠀⠘⢁⣠⣴⣖⣀⣠⠀⣦⠀⠀⢠⡀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣿⣧⣦⠈⣳⣴⡆⣯⣦⣶⢸⣯⡀⣤⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠿⠿⣿⣟⣛⣙⣿⣿⣿⠀⢀⣰⣦⣆⢀⣾⢿⡇⢰⢼⡄⠀⠀⠸⣄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠿⠉⢉⡛⠻⠆⠀⠀⠏⣿⣿⣿⣿⣷⡠⠼⠇⠀⠀⣆⣿⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠂⠀⠀⠀⠀⢳⡶⢖⠪⡿⠿⠶⠶⣿⣁⣈⣛⣻⣦⣤⠤⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣄⢄⡀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠁⠉⠉⠉⠙⠛⠒⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⡜⠿⢷⠦⠴⣠⣴⣦⣶⣾⣿⣿⣦⠀⠈⠉⠉⠙⠛⠓⠒⠒⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠄⠹⣿⣿⣿⣿⣿⠿⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠥⢄⡉⠂⡇⣑⣒⣆⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠹⠃⠳⠆⡿⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣒⠵⢒⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡯⢚⣡⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⡡⠖⣋⠵⠚⠉⡕⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠴⣫⢶⠏⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢟⣋⠥⠔⡺⠁⠀⠀⠸⠁⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠔⡡⠞⠁⡞⢸⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠀⠀⢰⠃⡏⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⠁⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠃⠀⢀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡠⡾⠀⢀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡾⠀⠀⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⣰⠋⢀⠇⢠⣳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⠃⠀⢰⡇⣿⡇⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢰⠃⠀⡞⢀⢿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⣠⠃⠀⠀⢸⢠⡏⠁⠀⠀⠀⢀⠀⢴⣉⡀⠀⠀⠀⠁⣀⠜⠀⡼⡞⣼
⠀⠀⠀⢀⣠⠤⠒⠉⠉⠈⠉⠉⠁⠀⠀⠀⣼⢸⠸⠀⠀⢀⠖⠁⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢠⢳⠁⠟
⠀⠰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣫⠃⠐⠃
⠀⠀⠈⠙⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠶⠋⠀⠙⠂⠀⠀⠀⠐⡂⠤⠤⠤⠤⣤⣤⣶⠾⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡾⠀⠀⠈⢳⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠒⠒⠲⢤⡀⠀⢳⣷⣀⡀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠉⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠙⠛⠷⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡴⠂⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠁⠀⠀⠀⠈⠓⠦⠴⠄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢠⠆⠀⠠⠭⠷⣄⠀⠸⣷⣤⣀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡤⠒⠚⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⡀⢿⡆⠀⠀⠀⠀⡌⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢠⠀⠈⠙⡆⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠤⠤⠄⠒⠉⠀⢦⡀⠀⠙⢦⠙⠶⠦⠔⠊⠀⣄⠈⠙⠀⠖
⠀⠀⠀⠀⠀⠘⠷⠤⠊⠀⢀⡎⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠁⠀⠀⠈⢧⠀⠀⠠⠤⠤⢌⡁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣾⣰⡇⠀⠀⠽⠃⠀⠀⢀⣠⡄⠀⠀⣸⢿⡄⢀⣶⡶⣶⣦⡀⠀⢸⡆⠀⠀⠀⠀⠀⠘⠄⠙⠂⠁⣤
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢻⡄⠀⠙⠛⠛⠟⠛⠷⢶⣄⢰⡿⠛⠻⢶⣤⡏⠀⣿⡀⣿⣠⡤⢻⡇⠀⠀⡇⠀⠀⠀⠠⠐⠲⡄⠀⢀⣤
⠀⠀⠠⣇⣈⡇⡄⠀⠀⠀⠈⡇⠀⠀⠀⣠⠺⣶⠀⠀⢹⣿⡁⠀⠀⢸⣿⠗⠶⢾⡇⣿⠟⠛⠉⢠⠒⢺⠗⠶⣤⠀⠀⠀⢠⠜⢤⡉⠁
⠀⠀⠀⠈⠸⠟⠹⠆⠶⠀⠀⢸⡀⠀⠀⢿⣦⡀⠀⣀⡼⠛⠷⠶⠔⠋⣹⡥⠀⢸⡧⢼⠤⠀⢀⠸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣜⠦⠄⠀⠀⠀⠀⠀⠀⠀⡤⢛⣆⣀
⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠰⠙⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠉⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠉⠉⠛⠻⠿⢷⣶⣾⣿⣟⣟⣓⣚⣋⣩⡭⠽⠖⢿⠈⠓⠂⠀⡔⡆⢠⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁
⠀⠀⠀⠀⠳⡀⠂⠀⠀⠀⠘⢦⣂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠳⠖⠐⠀⠙⠦⠼⣆⡠⠤
⠀⠀⠀⠀⠀⠈⠓⠒⠀⠂⠀⠀⠈⠙⠓⠒⠂⠀⠀⠀⠈⠛⠒⠒⠛⠓⠒⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠈⠁




⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠘⡎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⢳⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡀⠐⡆⠀⠀⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠙⢦⣿⠴⠚⠛⠛⢲⣋⣁⣤⣄⣀⣀⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⢉⡿⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣲⠶⡟⠀⠀⠀⠀⢀⣠⢾⣟⡲⠶⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠳⠤⠤⢤⡖⠋⠘⣇⠈⠉⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡴⠋⡇⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⡇⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡇⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⣾⣿⡄⠀⣿⣿⣿⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣭⣽⣯⣍⠀⠀⠀⣿⣿⡅⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⣼⣿⣧⣄⣀⣄⠀⠀⠀⢀⣿⡯⢿⣿⡇⠀⣿⣿⣿⣤⣧⠀⠀⢸⡀⠀⣰⣆⠀⠀⣿⣿⣿⣯⣀⡀⠀⣿⣿⡇⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣿⣾⣧⣾⣿⣄⠀⣤⣼⣿⣯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣏⡇⢀⣿⣿⡁⣦⢀⣿⣿⣿⡀⠀⠀⠀⠀⠠⣿
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣟⡇⢸⣿⣿⡇⣿⢸⡟⣿⣻⡇⠀⢀⣀⣠⣼⣿⣧⣄⣀⡀
⢻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⠿⠿⠿⢿⣿⣿⡿⠻⢿⣯⣭⣭⣭⡍⠹⠿⠿⠿⠿⠟⢻⣿⣿⡿⡿⠯⠟⢿⢿⠛⠛⢻⣿⣿⣿⣿⣿⣿⠿⠏⠛
⠀⠉⠉⠉⠱⡿⣿⣷⠿⠇⢉⣹⠛⠛⠛⠛⢓⠀⠀⠀⠀⢸⣿⣿⡇⠀⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠁⠰⣀⢠⣼⠀⠀⠀⠀⠀⠈⣯
⠀⠀⣀⠀⢀⡀⢀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠂⠀⠀⠀⠾⠿⠀⠃⠀⠚⠩⢿⡿⠍⠃⠀⠈⠀⠀⢀⠀⠀⣽⣿⠀⠀⠀⢸⢤⣼⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⠾⠼⠀⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠄⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⣤⡄⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠨⠽⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡇⢀⣀⣀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠃⠀⠀⠈⡷⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠒⠓⠲⠦⣄⠀⠀⢹⣹⣄⣀⡀⠔⠁⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠙⠿⢷⡶⠶⠖⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢹⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣄
⠀⠀⠀⠀⠀⠺⣤⡀⠏⠀⠀⠀⠀⠻⣄⣀⠀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡤⠒⠒⠲⢤⡀⠀⠀⣾⡅⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣭⠤⠤⠤⣤⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⡏⠀⠀⠉⠉⠉⢹⠀⠀⠘⠿⠿⠀⠈
⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⢀⡴⠷⠖⠒⠲⢤⡈⢿⣄⠀⠀⠀⢀⡜⠀⠀⠤⡄
⠀⠀⠀⣴⠀⠀⢈⠇⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠋⢁⠀⠈⠱⡄⠀⠀⠘⣦⠉⠛⠛⠛⠁⠀⠰⣀⠀⠉⠘⠁
⠀⠀⠀⠘⠓⠒⠈⠀⠀⡾⠀⠀⢀⠀⣠⡤⢴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠦⠄⠀⠁⠀⠀⠀⠘⣇⠀⠀⠠⠔⠰⠦⢄⡀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⡇⣾⡁⠀⠀⡨⠏⠀⠀⠐⢀⣠⡄⠀⠀⢠⡿⣷⡀⢠⣶⠶⢶⣶⣄⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⢹⠀⠓⠂⠁⣤
⠀⢀⠀⠀⠀⠀⠀⠒⠺⡇⠀⠈⠛⠿⠿⠶⠶⠶⢶⣤⡀⢴⠷⠚⠻⣶⣄⣾⠁⠸⣷⠀⣿⣀⣤⣹⣿⠀⠀⢸⡆⠀⠀⠀⢠⣄⠶⢦⡀⠀⢀⣄
⣔⠉⢻⠀⡔⠀⠀⠀⠀⢿⠀⠀⠀⠀⣠⢶⣦⠀⠀⠙⣿⣿⠀⠀⠀⢈⣿⣿⠤⢤⣿⡀⣿⡿⠾⠚⠁⡠⠲⢾⣡⣄⣀⠀⠀⠀⠀⣀⠧⣀⠛⠊
⠉⠻⣟⠆⣧⣀⣀⡀⠀⠸⡄⠀⠀⠰⣿⡀⠋⠀⠀⢀⡿⢿⣦⣀⣠⠞⢹⣇⠀⠀⢹⡇⣿⣀⠀⠀⠐⣧⡄⠁⠀⠀⠉⠁⠀⠀⠀⠁⠀⠈⢳
⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠙⠻⠶⠶⠖⠋⠀⠀⠉⠉⠁⠀⠊⠉⠁⠀⠛⠉⠉⠉⠀⢀⡎⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀
⠀⠀⠸⢷⠄⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠚⠲⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠗⠲
⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠛⠷⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡴⠶⢶⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⣧⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⣯⣿⣭⣭⣭⠭⠶⠖⠛⠋⢹⡀⠈⠉⠁⢰⣽⠇⢰⠁⠀⠀⠀⠀⠀⠌
⠀⠘⢧⡀⠂⠀⠀⠀⠀⡳⢮⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠈⠙⠲⠼⢧⣤⠤⠄⠀⠀⡀
⣤⣤⣤⣭⣷⣶⣶⣦⣥⣤⣤⣬⣭⣷⣶⣶⣶⣶⣬⣥⣬⣷⣶⣶⣿⣷⣶⣶⣬⣷⣶⣦⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠖⠛⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠛⠋⠁⠀⣀⣀⣤⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⣏⢏⢷⣀⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⢿⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⡾⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠞⣛⣫⣭⡭⠭⠥⠆⠀⠀⠀⠀⠀⠚⠛⠛⠛⠿⠿⠿⠿⠿⠛⣿⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣷⢤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣯⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠲⠾⠿⠭⠭⠭⠭⠍⠙⠛⠛⠉⠩⠭⣭⣭⣭⣭⡭⠭⢩⡏⠀⢀⡟⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⡾⠀⠀⣼⠁⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣤⠶⠖⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⣾⠃⠀⢰⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⡟⢛⣶⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠲⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⡤⠶⡾⠛⠋⢩⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣽⠁⠀⣸⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢠⡟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣼⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢰⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⡟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡾⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⠈⠉⠛⠲⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠞⠋⠁⠀⣸⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠙⠶⣭⣳⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⢖⣚⣩⡵⠞⠋
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠲⠶⠾⠿⠿⠿⠿⠿⠿⠷⠒⠛⠛⠉⠉
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠠⠄⢤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⡘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠁⣀⡘⢀⡄⠀⠀⠀⠀⠀⢀⠜⢃⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⡄⠀⠀⠀⠀⢠⡠⢫⡌⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⡀⠀⠀⠀⢀⡀⡔⢁⣵⢃⡈⠁⡆⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠀⠁⠀⠀⠀⢨⠏⢠⣪⠋⡌⠐⠂⠀⠸⢃⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠃⠀⠁⠀⠀⠀⣠⠃⠠⢳⣧⡀⠀⢃⡀⠀⢈⠦⠬⢩⣅
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠏⠀⠃⠀⠀⣠⠞⠁⣠⢡⣰⣿⣇⠀⠀⠰⠂⢀⡄⠠⠨⢽⣶⣤
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠠⠴⠂⡠⠞⠁⠈⠔⣡⣿⣿⣿⣍⡀⠀⠀⡈⢰⡇⠀⠀⠀⠛⠛⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⠊⠀⠀⠀⣠⠞⠁⠉⠉⠉⠉⢻⠢⢤⣃⣾⠁⠀⣀⣀⣀⡠⠤⠤⣚⣢
⠀⠀⠀⠀⠀⢀⢀⡠⠔⠪⠃⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠘⡏⠒⠚⠭⠭⠭⠑⠒⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⠤⠴⠶⠒⠛⠛⠉⠁



⠀⣀⡀⠀⢀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣦⣾⡟⣿⠿⠂⣸⣧⣤⠦⡱⠄⡶⠉⠉⣛⠐⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣄⡘⠶⢤⠰⣈⠵⠟⠛⣿⣿⡶⠖⠒⠓⠄⠂⠃⠀⣹⠏⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠀⠂⣤⡀⢨⣔⠁⠶⠆⣼⣿⣿⣃⣿⠀⢀⠰⡄⢦⠙⢱⡆⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⢰⡋⠛⢷⡀⠉⠉⢸⣧⣸⣿⣿⢉⣫⣀⣀⡚⢱⢯⠐⡈⠁⢀⡀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠄⠀⡉⢰⡽⢋⡀⠀⣽⠃⢸⣿⣿⣉⢛⠋⠉⠙⠈⢢⠀⠃⢻⡈⠀⡆⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⠆⠀⣡⠈⠁⢠⡦⣤⠌⢀⠀⢿⣿⣿⣥⣠⠀⠈⡹⠛⠀⡗⢸⣧⠀⠀⠘⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣧⣤⣤⣄⠀⠵⣇⠀⠀⠘⢇⡀⢘⣁⣼⣿⠁⢠⡄⠀⢻⠁⢀⡁⠹⢡⡄⢰⣤⠀⢦⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢂⡀⠀⠘⡤⢐⢢⡈⠑⠂⣤⡀⠉⠋⢹⣿⣧⣮⡔⠛⠓⢾⣶⠋⠀⠡⠼⢃⢴⣄⠁⢩⣝⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⡦⢹⣆⢂⣄⡀⠘⡇⠀⠰⡌⠙⢺⣦⠟⣻⣿⠷⡞⠀⡀⠈⣿⡀⢠⡶⠂⠁⠠⠛⠄⠁⠹⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠱⣀⡏⠑⠺⠁⡴⠆⣵⡀⠐⢳⡴⠞⠁⢀⣼⣿⠘⣧⠴⠀⠀⣸⢟⡼⠋⣿⠃⠀⠠⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⡞⠛⢉⢀⡆⠀⢠⡶⠹⣟⠂⠀⢠⣧⠀⢸⣿⡿⠤⠻⢦⡀⠀⢃⠜⢃⠀⠏⣉⣹⠉⠈⠀⠴⠃⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣤⣤⠂⠀⣇⠀⢸⠤⠀⣽⡀⠀⠛⠓⢢⡹⣿⣿⣶⡤⠞⠉⣀⡁⠀⠀⣤⣈⣉⡉⢀⠀⠀⠠⡤⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡏⠈⢻⠁⠀⠉⣠⣿⡃⠀⢹⡄⠀⠁⠈⢻⡅⢿⣿⠿⠟⠛⠚⣟⢀⡀⠉⠴⢭⠈⠁⠘⠇⢠⣤⡤⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠊⣦⣈⠂⣄⠀⠏⢹⡇⠀⠀⣷⡀⠰⠄⢀⠛⣿⣧⡀⣀⣀⣀⡉⠉⠀⠀⠀⠋⢀⠀⢀⠐⠟⠃⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠞⡉⠫⡙⢧⡀⠘⠋⠉⠀⠹⠟⣑⠐⠰⣷⣿⣿⣿⣿⡋⠿⠀⡷⠤⣤⠄⢠⠈⣦⣤⡤⠤⣄⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠸⠂⠙⣦⣉⣀⣲⠶⣶⢄⣾⣯⠀⠀⢸⣿⣿⡏⠶⢭⠖⢈⣳⡾⣏⡀⠀⣁⡜⠛⢠⡀⠈⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠰⣾⡮⣁⣀⠀⢹⣅⠈⠻⢯⣵⠤⣼⣿⣿⣿⡂⠛⠂⠉⠀⠁⣽⠛⡿⠏⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢛⡀⠓⠁⠐⠈⠉⢀⢼⡍⠉⣴⣤⣿⣰⠟⣿⣿⣿⡿⠶⠆⠀⠀⠾⡿⠗⠀⠀⠀⢀⡀⠶⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡄⣀⠀⣸⣦⠰⠶⢂⠀⠀⣉⠉⠉⠁⠘⣿⣿⣿⣴⣦⠄⠀⠐⠚⠁⡀⠀⢹⡄⠀⠈⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⢿⡍⠸⠑⡶⣽⠋⣷⣍⡒⠒⢾⣿⣿⣿⣏⡙⣈⡉⠀⠀⣴⡾⠃⡰⠛⠙⢦⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣿⣿⣶⠧⡌⣸⡿⢿⠡⢄⣀⣨⣿⣿⣿⠋⠁⠁⠀⠀⡈⣉⠛⣇⠈⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣽⣔⢩⣁⣂⣴⠂⢼⡛⣿⣿⣿⣉⡛⠁⠐⢀⡴⠟⣡⡇⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⣿⡀⠀⢀⡿⢾⣿⠻⣿⡿⡖⠰⠋⡀⢻⣟⣥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢖⣋⣀⡼⠃⠀⠙⠛⠿⠥⠾⠥⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣤⣶⣾⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠻⠿⢿⣿⠟⠉⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠈⠉⠉⠛⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⠀⠀⢀⠀⠀⢀⣠⣶⣿⠿⠋⠉⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠙⠳⣦⡙⣿⣦
⠀⠀⠀⠀⣀⣤⣤⣄⣀⠙⠻⢿⣿⣿⣿⢿⣷⣶⣿⠟⠋⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠈⢷⡘⣿⡇
⠀⠀⣠⣾⠿⠛⠛⠛⢿⣷⡀⠀⠀⠀⢠⣾⡿⠛⠁⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦⡀⠀⠀⢿⡀⠀⢸⡇⣿⣿
⠀⠀⣿⡏⠀⠀⠀⠀⠀⣿⣿⠀⢀⣴⣿⠏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠘⣧⠞⠁⠀⠀⢸⡇⠀⣸⠇⣿⡏
⠀⠀⢿⣷⡀⠀⠀⠀⣠⣿⡟⢠⣾⡿⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⣿⢙⣷⣄⡘⠷⠀⠀⠀⣾⠁⠰⠟⣸⣿⠃
⠀⠀⠈⠻⢿⣷⣶⣾⡿⠋⢠⣿⡟⢀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣾⠉⠀⠈⢻⡄⣿⠋⠀⠈⠁⠀⠀⠀⣼⠃⠀⠀⣴⣿⠃⣠⣾⡿⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢠⡟⠀⣸⠃⠀⠀⣴⡋⣁⡀⢻⣄⣀⣀⡼⠁⠈⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣾⡿⠃⣼⣿⠋⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⠀⠀⢻⡀⠀⠀⠈⠉⠉⢹⡆⠈⠉⠉⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣴⣿⣿⣅⠀⢿⣿⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⡄⠀⠘⢷⡀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⣀⣴⣿⠟⠉⠙⢿⣷⡌⢿⣷⣤⣤⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⠻⣄⠀⠀⠙⠶⣤⣄⣀⣀⣀⣀⣤⣤⠶⠞⠋⠁⠀⣀⣴⣾⡿⠋⠁⠀⠀⠀⠀⢻⣿⠀⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣍⠛⠆⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⣀⣤⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣴⣶⣾⣷⣤⣀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠛⠿⢿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⡀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣞⠉⣯⠱⠞⠙⠛⣣⣴⡞⡹⠉⠻⣷⡄⢦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣛⠛⣇⠘⣭⡤⠶⠰⠞⢢⣾⣿⣻⢦⣠⣤⣿⣴⠟⢥⣼⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡄⠽⣏⡿⠘⣿⡀⠴⢒⣯⣭⣿⣿⠛⡀⣈⠓⣯⠙⣿⠀⡿⠠⡟⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⡆⣀⣀⣏⡇⢀⣇⣅⠀⢋⣀⣬⣿⣿⡄⢻⣿⠟⠻⡆⢡⠞⠁⢀⣧⣾⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡿⢁⠈⠉⠛⠁⣠⠿⢛⣋⣉⠀⠀⣿⣯⣉⣿⢁⣀⢠⡇⠘⢧⡀⠘⣿⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠁⠘⢳⣶⡟⠛⠁⣲⠾⠿⠭⣄⣴⣿⣿⣿⠃⢈⠉⠟⠻⣄⣸⣧⡀⠈⠦⣼⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⣼⣄⣴⠋⢠⢿⡶⠛⠁⢠⠆⠀⠀⠈⢻⣿⡻⣧⢸⡇⠀⡀⣿⡏⢈⢷⠀⠀⠙⡆⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⢶⡌⢋⣓⣿⢴⡀⠘⢿⣉⣻⠿⡇⠀⣸⣿⣷⣿⣄⠳⣤⡛⠛⠳⠄⠻⣷⣴⠶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠂⣿⡿⠶⠦⠆⠘⢛⠳⣦⠃⠘⠘⠃⠚⣿⣿⣿⣷⠾⠳⡌⠓⢰⡖⠄⠀⣼⠁⢀⡾⣷⠁⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡻⣧⣘⣉⣒⠒⢓⠒⠲⢿⣦⡹⢦⡤⠞⠛⢷⡌⣿⡏⠳⣄⣼⡟⠚⢻⡟⠋⠀⠉⢈⡈⣷⡟⢈⠿
⠀⠀⠀⠀⠀⠀⠀⣿⡧⣈⣟⣉⡍⠹⣤⠀⣶⠞⣛⣻⣆⠠⠤⠬⣝⢷⣿⠇⠀⢻⡙⣷⣤⢾⡀⣠⢴⢒⣛⣓⢤⣀⣼⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠹⢿⠞⠙⡿⢿⡅⢿⠀⠃⢰⡇⠛⠨⣷⠤⣤⣶⣾⣿⡆⠀⠸⣿⠋⠙⢮⡛⠿⣆⡞⠁⡄⠀⣿⣵⡏⡀
⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⣿⣧⠀⡴⠈⢻⡿⠿⢧⣼⣷⢿⣋⠝⢦⣿⣿⣛⡾⠳⣬⡙⢦⣄⣀⣜⠁⠁⠐⠃⠀⡏⢩⣛⣇
⠀⠀⠀⠀⠀⠀⠘⡧⠪⢻⣿⡙⡾⣅⠀⠚⠀⣤⠀⢋⠙⣿⣄⣤⠞⢿⣿⡿⢀⡉⣰⡷⣜⣿⣩⠟⠉⣠⣞⣡⣾⡇⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⣵⡆⠘⢋⣷⢉⣈⠳⣤⡖⢨⣷⡶⠿⠃⠹⡇⠁⣸⣿⠀⠘⡇⢈⡷⢿⡜⣧⢐⣩⣭⣽⡿⣿⠀⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣇⡈⢦⡘⠂⣿⡳⣦⠤⠼⣏⣴⢋⢩⡝⠃⢰⢻⣿⠀⣖⣴⠏⠂⠀⢱⢤⣟⣏⣳⢛⣷⡟⠀⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢉⡛⠛⡿⢿⣄⣚⠉⢷⡑⢃⣠⡴⢃⣼⣿⠀⣿⣯⣢⣤⣴⣿⣾⠀⢰⣿⡶⢻⡧⠠⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⠉⢧⣀⣿⣁⠉⠭⣄⠙⠳⠦⠾⢿⣿⣿⣇⣩⡾⠿⠋⢁⡀⠈⠛⣿⠏⣠⣈⡇⢀⣜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣧⡴⢯⣉⡏⣧⠀⢈⡿⠒⠂⠤⣼⣿⣿⣿⡯⠔⣠⠔⣛⣷⡿⢦⡁⣪⠾⣩⢛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠈⠉⣇⢹⠟⠛⠛⠲⠾⡄⢹⣽⣿⣥⣴⣋⠉⢉⣉⠉⢙⣆⣻⣦⣄⣟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡜⠛⠛⢂⡉⠓⠂⣤⣉⠘⠾⣿⢻⣯⣽⡿⠛⠁⠄⣀⠉⠀⢈⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⣈⡁⠰⣎⡀⢻⣿⡿⢿⣶⣽⣈⠐⢦⡁⠒⢚⠕⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⣶⣤⣤⣤⡾⠛⠁⠘⣿⣈⣉⣁⣤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠓⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠒⠂⠈⠁⠀⠉⠁⣀⡀⠀⡁⠀⠑⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠤⠴⠀⠀⡀⣀⠹⠿⠄⠈⢀⣠⠀⣤⠤⠁⡙⠁⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⢆⣀⡀⠀⢀⣤⠖⠀⠙⢚⣙⠀⠀⠄⠀⠠⣤⣀⡁⠀⣀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⣠⢤⣾⠁⠀⠁⠯⡿⠀⠀⠀⠀⠀⠲⢂⣾⣶⣤⠄⢠⣽⡀⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠀⠀⠀⢐⠘⠃⣹⢷⡄⠀⠀⠀⣻⣧⠀⡀⠀⠂⠉⠱⡀
⠀⠀⠀⡀⠀⠀⠀⣠⡀⡸⠮⠲⡇⠒⠼⣷⣿⠏⠀⠉⣰⣦⣺⢿⣯⢏⠛⠰⠆⠤⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣠⡀
⠀⠀⠠⠀⠀⠀⠀⡙⠈⢡⠄⠈⠈⡒⠄⢈⣻⠇⠀⠀⠊⠉⢼⣾⠟⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠆⡈⢹⢿⢿⡗
⠀⠀⠀⣀⠀⠚⠁⠙⠚⠣⠇⠀⡀⠷⠌⠋⢉⣇⠀⠀⠀⠀⡼⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⣤⠄⣀⡀⡀⠠
⠀⢀⣍⣻⣿⡏⢀⣓⣶⢷⣶⡏⣯⣤⣤⣶⠂⣤⢶⣾⣷⣾⣶⣀⣔⡀⠒⠀⣀⣀⣀⡀⠀⣀⣀⠀⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠈⠉⠁⠈
⠀⠸⡷⢶⠄⠻⠻⣿⣿⠏⡟⠿⠐⢚⡷⠶⣿⣟⠙⠛⠀⠛⠻⣟⣩⣐⠂⠀⣩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⠤⢄⣀
⠀⠀⠤⠤⠤⠥⠤⠭⠝⠛⠛⣁⣘⣥⠖⣖⣵⠀⠁⠀⠁⠀⢀⡘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠁⠉
⠀⠀⠤⠤⠦⡄⢀⠀⠀⠀⠊⠁⠀⠀⠛⠠⠉⠁⠂⠀⠀⠀⠈⠃
⠀⠀⣀⡠⠎⠁⠀⢉⣤⡍⠀⠤⠢⣀⣀
⠀⢈⣍⠁⠚⠀⠀⠘⠓⢢⣤⡴⢠⣬⡍⢉⡂⠀⠄⠀⠀⠀⠈⠉⠁⢀⠄
⠀⠈⠁⠰⠄⠀⠢⠀⠈⠁⠀⠂⠀⠒⠘⠉⠀⠉⠁⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⢿⡀⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢀⣀
⠀⠀⠀⠀⠀⡀⣴⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠼
⠀⠀⠀⠀⢯⠟⣴⢦⠀⢀⡤⢄⠀⠀⠀⢠⣦⠀⠀⢀⡠⠴⠒⠒⢶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠳⠊⠀⠀⠀⠀⣁⠴⠚⠉⠀⢀⡀⠀⠈⢧⠀⠀⠉⠳⡀
⠀⠀⠀⠾⠇⠀⠰⣋⠇⠀⠀⠀⢀⡠⠖⠋⠀⠀⢀⡀⠔⠉⠀⢱⠀⠈⡆⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⡠⠐⢤⡁⠈⠳⡄⢰⠉⠀⠀⠸⡄⠀⠀⠀⣧
⠀⠀⠀⢰⡋⢳⠘⠷⠀⡏⠀⢀⠎⠩⣶⡁⠞⢨⡧⠟⠒⠉⠉⠀⠀⠀⡠⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠉⠁⠀⠀⠀⢳⠀⠀⢑⠆⢀⠗⠒⠁⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢼⡆⠀⠰⠔⠊⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠀⣀⠔⣋⡀
⠀⠀⠀⠀⣠⠊⠉⠁⠀⠀⢱⡀⠀⠀⣀⣀⠤⠒⠉⡀⣀⠴⠖⠒⠐⣎⠁⠀⠙⢿⠆
⠀⠀⠀⡞⠉⠀⠀⠀⠀⠐⠉⠉⠓⠁⠀⠉⠒⠊⠉⢆⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⡹⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠒⠒⠒⠒⣒⣦⠤⠤⠤⢄⣀⡀
⠀⢀⣸⠤⡄⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡶⠤⠤⠤⣄⣉⣒⠆⠀⠀⠀⠀⠹⡀
⢮⣁⣀⠀⠉⠈⠈⠀⠉⠉⠈⠉⠉⣀⡬⢭⠉⠁⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡩
⠀⠀⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠘⠤⠦⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠂⠉⠁
⣀⣀⣈⣓⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣒⣒⣒⣒⣒⣚⣉⣉⣉⣉⣉⣣⣤⣴⣒⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⣛⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣥⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠬⢭⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣛⠳⠄⠀⠀⣤⣤⣾⣯⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀⣤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠒⠒⠒⠒⠒⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⡖⠀⢰⠇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢀⠀⠀⢀⣭⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡾⠁⠀⠋⢠⠆⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠆⠸⣇⠀⠶⠀⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⢿⡆⠀⠀⠘⠈⠃⠀⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢞⣯⠉⠁⠀⠀⠀⣰⠃⠀⡆⠀⢀⣴⠀⠀⠀⠀⠀⢉⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣌⣋⣀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁⠀⠀⢀⣀⣠⣤⠴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⡀⠀⠉⣉⣉⠐⠒⠓⠒⠒⠒⠒⠓⠛⠛⠉⠉⠉⠀⠀⠀⢸⡿⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⣀⣈⣻⠛⠃⠀⢰⡇⠠⡄⢠⣆⠀⠀⠀⠀⠼⢫⡿⠀⢸⡇⢠⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠏⠉⠙⢢⣤⠤⡄⠹⡄⢀⡄⠉⡇⠀⣠⠶⢶⡄⠀⠀⢸⣷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣨⠴⠶⣄⠀⠀⠐⠃⣠⠇⠸⠁⣼⢁⡾⠀⢈⣸⠇⠀⠀⢸⣿⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠺⣧⡶⠂⠘⣷⠀⠀⠐⠋⠀⠀⠀⣉⡴⠃⠰⠟⠁⠀⣰⠆⢸⡏⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⣸⠏⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠰⠖⠛⠁⠀⢸⣇⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠻⠆⠀⠀⠀⠀⣠⡾⠏⠀⠀⠈⠉⠁⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⣸⡆⢸⣿⡛⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⢠⡾⠋⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⠛⠳⣦
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣰⡟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⢧
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣦⣤⣴⠏
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢸⣿⠁⠀⠘⡄
⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠤⠦⠞
⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡇
⠴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠈⠀⠒⠚⠋⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠀⠉⠙⠲⠶⢤⣤⣍⣉⣙⣛⣛⣀⣀⣬⣤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠜⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠁⠐⠂⠠⠀⠤⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠐⠂⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡈⠠⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⣠⠖⢁⠴⠁⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠤⠀⠠⠁⠀⠀⠀⠀⠀⢀⠔⠁⠀⠁⡄⠀⠂⠀⠁⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡴⠁⢀⠀⠀⠀⢠⡀⠀⠀⠈⠀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⡀⠆⢈⣠⠄⠀⡰⠀⠀⠀⠀⢀⠎⢀⠔⠁⠀⠀⠀⠀⠰⠀⠀⠀⠈⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡐⠀⠀⠀⢀⡐⠁⡰⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣉⠀⠲⠄
⠀⠀⠀⠐⠒⠀⠐⠂⠤⢐⡀⠀⠀⣀⠔⠉⠀⡼⠁⠀⡄⠁⠠⡀⠀⠀⠀⠐⠀⠀⢀⠄⠀⠀⠈⢙⢀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠔⠈⠀⠀⢀⡜⠁⠀⠀⠈⠁⠐⠈⢢⡀⠀⠀⠃⢀⡄⠀⠤⠤⠤⠤⠀⠲⢤
⠀⠈⠂⠀⠀⠰⠐⠒⠉⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠒⠤⠴⣉⣀⣀⡀⠀⠤⠄⠐⠂⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠉
⠀⠀⠀⠂⠀⠀⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠂⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠉⠁⠀⠁⠈⠀⠈⠁⠀⠀⠀⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠑⠁⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⣸⣧⣤⡤⠀⠀⠁⠋⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⡀⠀⠀⠀⠀⢶⣿⣿⣿⠁⠀⠀⠛⣿⣿⣿⡄⠀⢀⣄⠀⠀⠑⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡫⠀⠀⣀⣿⣶⣶⠆⠀⠀⠻⠛⠙⠃⠀⠀⠀⠘⠁⠈⠁⢤⣼⣿⣷⡟⠀⠀⠁⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠑⠀⠀⠈⠙⣿⣿⣷⠀⠀⢀⠠⠀⠒⠀⠉⠁⠀⠒⠀⠀⡀⠀⢹⡿⠛⠧⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⣤⡀⠀⠉⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣶⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⠀⠠⣴⣿⣿⡿⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⣆⠐⢷⡄⠀⣿⠀⠀⣾⣏⣿⣄⠀⢻⣆⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠈⡿⠛⠻⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⢸⡿⠛⢻⡆⠀⢿⡀⠈⢻⣤⡯⠀⠀⣿⠋⠉⠻⠆⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠘⣏⣉⣹⡇⠀⢻⡾⠫⣅⠀⠘⣇⠀⠀⠛⠋⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⣤⡄⢶⡀⠀⠀⠀⠀⣿⣛⣶⡀⠀⢿⡋⠙⣧⡀⠸⠇⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽
⠀⠀⠀⠀⠀⢀⡀⢰⣶⠾⠟⠀⠸⣧⣿⣿⣾⡇⠀⠀⠀⠀⣿⠛⠉⠻⠆⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣶⠀⠀⠀⠀⡶
⠀⠀⠘⣷⣤⠈⣧⠀⢿⡾⠇⠀⠀⠹⣿⠄⢻⡧⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⣽⣿⣿⠷⠀⠀⢱⠇
⠀⠀⠀⢿⡉⢻⣿⡄⠸⣷⡶⠾⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⢈⠉⠙⠿⠀⠀⢀⡎
⠀⠀⠀⠸⠇⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⣤⣴⡆⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣿⣀⠀⠀⠀⢄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡠⠀⠀⠀⣸⣿⣿⡿⠒⠀⠀⢀⡀⠀⠀⠀⢀⣀⣠⡆⠀⠀⠠⠿⢷⣿⠛⠁⠀⣢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡀⠉⠈⠻⠀⠀⠹⣿⣿⣧⣀⠀⠀⢘⣿⣿⣷⣤⠀⠀⠀⠀⠁⢀⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣀⠄⠀⠀⠀⠸⠟⢿⡏⠉⠀⠀⠛⠉⠻⠇⠀⠀⠀⠀⠀⣂⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠺⠷⠾⠿⠛⠒⠒⠋⠉

⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠈⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲
⡰⠒⠢⡄⠀⠀⣀⠀⠀⠀⠀⠸⢱⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠒⡄⠧⠴
⠑⠤⠠⠎⠀⡘⠂⠃⠀⠀⠀⠀⠀⣤⡀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣩⠆⠰⠅⠜⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⢎⣠⠇
⠀⠀⠀⢠⡏⠉⠑⢦⡤⡀⠀⠀⠀⠂⠣⡀⠀⠀⠘⢍⢧⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⠁⠀⠀⠀⠀⢀⠴⠤⢔⡺⠛⢉⡭⠝⡩⠿⠽⢦⠀⡠⢤
⠀⢀⠀⠀⠙⠛⠛⠲⣄⠙⣄⣀⣀⡼⠆⣈⡉⡒⠤⠒⠃⠉⠁⠀⠈⠉⠉⠢⠴⠊⠑⢒⣁⡴⣤⠤⡝⣯⡛⠒⢒⣉⣰⡴⠋⠀⠀⡿⢀⡾⠔⠊⠉⠁⠀⠈⠉
⠀⠈⠀⠀⠀⢀⡴⠒⠈⢳⣉⠲⢷⡖⠲⣆⣏⣁⣠⠦⣀⣀⡤⠀⠀⠒⠲⠴⠂⠀⠀⠀⠠⠀⠀⡜⢵⠋⠙⠒⠋⠀⡜⠀⠀⠀⣠⠇⢸⠁
⢀⣀⠀⢠⠒⠉⡠⢄⠤⢌⡳⣧⡀⠉⠓⠏⠙⠿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠉⠢⠤⠦⠶⠤⠀⠀⣸⠁⠀⢸
⠣⠔⠁⠈⠁⠋⠀⠠⠀⠀⠳⢌⣻⣦⡀⠀⠀⠀⠀⠙⠓⢦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠦⣶⡦⣄⠀⠀⠀⠀⠙⠦⣤⡤⠤⣄⣀⣄⣠⠖⠶⠃⠀⠀⠀⠀⣀⡀⠀⠀⣸⡇⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃⠀⠁⢿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣖⠈⠓⠶⠛⠛⠋⢩⠉⠛⠉⠅⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠙⠶⠤⣤⠴⠋⠳⠦⠴⠒⠐⠦⠖⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡆⠘⢆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⣄⠀⠀⠁⠒⠂⠤⠤⢤⡀⠀⠀⠀⠀⠀⠤⠤⠒⠒⠉⠀⠀⠀⠀⠀⠀⣸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠖⠂⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠂⠤⠤⠤⠤⠤⠤⠴⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣌⣠
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⡰⠞⣿⣿⡿⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠂⢰⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⣿⣿⣿⣿⠿⠿⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣶⣾⣶⣰⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⠆⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⢲⣄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⠟⠀⢀⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀⣤⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⠋⣸⣿⠀⠀⣽⣿⣦⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣤⣤⣬⣽⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⠀⠐⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⢠⣶⣿⡇⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⣿⣿⣿⣷⣦⣤⣦⣶⣤⣤⣶⡆
⠀⠀⢀⣤⡾⢿⣿⠇⠀⢹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⡰⠛⠿⡀⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠁⢠⠶⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡾⠇⠀⠀⠀⠀⢻⡂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⠀⣺⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢸⣇⡄⣻⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣷⣄⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣿⣟⠢⡄⣱⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠘⣿⣆⠈⠻⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉
⠀⠘⣿⣦⠀⠘⢿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢹⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⢿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⡟⢿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⣿⣷⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⣿⣷⠀⠹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣧⡀⢠⣾⣿⣿⣿⣿⣿⣿⣧⣅⠀⠀⠀⠀⠙⣿⣧⠀⠘⣷⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡄⠀⢄⡀⢿⣿⣷⣦⣽⣵⣰⣮⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣀
⣶⣀⠐⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⣆⠀⠛⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠠
⣿⣿⣷⣾⣿⣿⣿⣿⣿⣇⠻⣿⣿⣿⣿⡂⠹⣿⣿⣿⣿⣦⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠠⣿⣆
⣿⢿⣿⣿⣿⣿⣿⣿⡏⢿⣦⡄⣿⣿⣿⡏⡓⣻⣿⣿⣿⣿⣧⡀⠉⢃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠈⡛⢏⣦
⣿⣿⣿⣿⣿⡿⣿⣿⣷⠈⢻⣿⣝⣿⣿⣿⣼⣻⣿⣿⣿⣿⣿⣷⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠂⠘⠻⢷⣎⣠⡄
⣿⣿⣿⡯⠙⢿⡝⢿⣹⣷⣄⠙⢻⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣄⠀⠀⢉⣦
⣿⡟⣿⣷⣦⣀⠙⢮⠻⣴⠙⠷⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣾⡿⠛⠃⣸⣿⠂
⣿⣿⣾⣿⣿⣿⣷⣤⣃⣙⣦⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣃⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢄⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠞⣰⡇⠀⠀⣼⣆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠛⣡⣾⠟⠁⢠⣾⣿⣿⡄⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣐⣛⠁⠀⢰⣿⡿⠟⠉⠀⢀⣈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⣀⡿⠋⠀⣀⣤⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣋⡁⠙⢿⣿⡿⣻⣄⣠⣾⠛⠛⠻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣆⠉⠂⠨⠆⠀⢾⣯⣺⠿⠿⣟⣻⡭⠖⣋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⣤⣾⠟⡅⣭⠈⠀⢀⣴⣿⣷⣮⣭⣿⣿⣭⡥⣶⣿⡏⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠩⠿⠛⠁⠀⣀⣷⢀⡀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⣿⣿⣻⣿⣿
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢡⣴⣶⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⣾⣿⣶⣶⣤⣶⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⣻⣿⠟⣿⡏⠁
⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣿⣿⣿⣿⣿⣤⡿⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣾⣭⣽⣿⣿⣿⣿⣿⣭⣿⡿⠟⠋⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠄⠬⠀⠀⠀⠀⠉⠉⠉⠉⠿⠋⠁


⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣣⣴⣾⠿⢛⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢣⣾⣿⡟⣡⣾⣿⡿⠟⢛⣛⣓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⡿⣴⣿⡟⣡⣾⣿⣿⠿⠿⠿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣶⣄⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠷⠿⠿⣿⣶⣦⣥⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⢟⢻⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣏⡽⣿⣷⣶⠾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣒⣒⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢿⠸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣟⣯⡗⢾⠀⠹⣿⣽⣿⣿⢛⣿⣛⡟⣯⢞⡷
⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⣛⣿⣷⠿⠛⠉⠀⢸⡆⠀⠈⠻⠿⠟⡟⠿⢿⠟⠋⣸⠇
⠀⠀⢀⣤⣶⣿⣿⣿⡿⠟⠻⡆⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡿
⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⠅⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⡆⠀⠀⠀⣸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣷⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢿⠀⠀⢀⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠴⠶⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⣶⣿⣝⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⠚⠉⢡⠶⢦⡸⣧⡴⠋⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣶⣟⠉⢠⡟⠉⢰⡄⢸⡗⠋⠓⠈⣃⣤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠀⠸⣧⣤⣤⡘⠳⠦⠞⢁⣀⡥⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡇
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠶⢞⣣⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⡇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⢸⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⢸⡇⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠓⠲⠦⢤⣤⣀⣀⣀⣠⣤⣤⠤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉
⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣄⣀⣀⣀⣠⣤⠤⠶⠚⠋⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣏⣏⣼⣩⣽⣥⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠈⠀⣠⠔⠈⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠆⡀⢂⠠⠤⠈⠀⠋⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠰⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠀⠒⡀⠊⠀⠁⠀⠃⢀⡴⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣀⠀⠀⢀⠘⢤⡀⠀⠢⠀⠈⢠⠀⠀⠀⠀⠰⡃⣀⠤⣤⣤⣶⡎⡁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠧⣀⡅⠀⢀⣅⠐⠠⠒⠣⠤⡰⠀⠀⠀⠞⢡⠿⠆⠛⣘⢋⣅⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠠⠁⠐⢀⣀⠀⡀⢺⢄⣤⡶⠃⠠⢀⠀⣀⣀⡀⢀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢦⠀⠢⠄⠐⠒⠒⠛⠫⠛⠁⠀⠈⣉⡉⡡⠔⢁⠴⣿⣦⡥⠤⠅⠈⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠤
⠀⠴⠒⠀⠂⠂⠐⠀⠀⣀⠀⠀⠀⠴⠤⠀⣐⠒⠀⠰⠦⠶⠶⡴⠖⢚⠋⠁⠀⠀⠞⠂⠁⠙⠙⠃⠀⠀⠀⠐⠀⠐⠒⠐⠐⠒⠒⠀⠀⠁
⠀⠀⠀⠀⠂⠂⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠠⠂⠀⠀⠀⠀⠀⠐⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠦⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡩⠷⠒⠒⢼⣏⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠊⠀⠀⠀⠀⠀⠀⠱⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡄
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⠳⣄⠀⠀⡎⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢧
⠀⠀⠀⠀⠈⠓⠬⣓⠢⢄⡈⢣⡈⠓⢶⣁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀
⠀⠀⠀⢀⡤⠤⠤⠀⣉⣦⠈⠉⠁⠀⠀⠙⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⠌⡃
⠀⠀⠀⠀⢀⣉⣉⠉⠠⠦⠀⠀⠀⠀⠀⠀⠘⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇⡟⠛⠛⠶⡒⢤⡀
⠀⠀⠀⠀⠙⢒⣒⣐⡒⠂⡄⡴⠒⠒⠒⠒⠒⠛⠒⣲⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⡇⣧⣠⣤⣴⠡⠾⠇
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢰⠋⠉⠛⠛⠛⠛⠛⠉⠉⣩⣿⡇⣯⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡐⠷⣿⡟⢏⠉⣲⠛⠦⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⠈⣿⠁⠀⡰⠋⠲⢄⡀⠀⠀⠈⣧⠤⠤⠤⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠞⠀⠀⠀⠀⢘⣦⠞⠉⠀⠀⠀⠀⠀⠀⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⡜⡇⠀⢀⡤⠤⠄⠀⠤⠤⣄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣠⡄⢰⡇⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⡖⠒⠤⠤⠄⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣠⠎⠀⢠⠘⠇⡇⠀⢻⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⠁⠀⠀⢸⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣸⠁⠀⠀⠀⢸⠀⡄⡄⠀⢸⠀⠀⠀⠀⠀⠀⡸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇⡇⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡆⠀⠀⠀⠀⡌⠀⢰⢁⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡁⠀⠀⠀⢠⠃⠀⢸⢸⠀⠀⢣⠀⠀⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢇⣀⣀⡠⠋⠀⠀⢸⠘⡀⠀⠀⠙⠒⠒⠋⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⢫⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠛⠋⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠂⠠⠄⣁⠀⣀⠜⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠐⠒⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢈⠁⠀⣨⠂⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⠔⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠃⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠔⢁⠀⠤⠀⠤⠀⡘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠘⠀⠠⠀⠀⠀⠀⠀⠀⢀⠔⠁⠂⠀⠀⠻⠀⠀⠀⠠⠆⣐⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⠈⠁⠁⡍⠁⠀⠀⠀⠀⡰⠃⢀⠔⠀⠀⠀⠀⢃⠀⠀⠀⠀⠆⢃⣑
⠀⠀⠀⠀⠀⠀⠠⠉⠐⠒⠃⠀⠐⠃⠀⠀⠀⢀⠜⢀⡴⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠠⠄⢋⣃
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠁⠒⠋⠀⠀⢀⠔⠃⢠⠏⠀⠢⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣄⣉⣁⣀
⠀⠀⠀⠈⠀⠀⠀⠈⠉⠐⢧⠀⢀⡤⠒⠁⠀⢤⠏⠀⠈⢦⢀⠙⠢⡀⠀⠀⠀⢀⠀⠡⠞⠀⠀⠐⠐⠂⠡⡀
⠀⢰⠀⠀⠀⠀⠀⠀⣀⠠⠔⠋⠁⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠑⠘⡦⡀⠀⠈⢀⠖⠒⠀⠉⠉⠁⠀⠈⣙⡳⠀⡀
⠀⠀⠉⠁⠀⠊⠉⠁⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠒⠃⠀⠀⠀⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠁⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠤⠄⠀⠀⠠⠤⠄⠀⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠙⠋⠀⠀⠈⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡖⠁⠀⢠⢤⠀⠀⠀⠀⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢚⠀⠀⡜⢀⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣭⠃⠀⠙⠋⢁⠀⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠸⣦⣀⡼⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀⠀⡀⠀⡉⠑⠒⡄⢀⠀⠀⠀⡰⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢒⠏⠻⠤⠕⠀⢾⣿⣿⣿⢖⠝⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣴⣶⣤⣴⣿⣿⣿⡷⡍⣴⡁⠀⠀⠀⣀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣯⢟⠞⠱⡄⠈⠓⣖⠉⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⢿⣿⣿⣿⡿⡣⢯⠶⠚⠙⠦⣤⡼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣹⠊⠀⢀⢞⠞⡔⠛⠿⣬⡉⠁⠀⡶⠒⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠰⣇⢀⡰⡻⠃⠀⢸⠀⢀⣨⣿⡆⣸⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠙⢦⠌⡐⣟⠀⠀⢠⠃⠀⢻⣿⡿⠙⠋
⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⣢⠾⠁⠀⡰⠁⠠⣾⣿⡟
⠀⠀⠀⠀⢠⡏⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠜⠁⠀⢀⠜⠀⠀⣤⣾⣿
⠀⠀⠀⠀⢸⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡡⠋⠀⠀⢠⣾⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠘⣇⠀⢸⠀⠀⠀⠀⢀⠤⠒⠤⣾⠝⠀⠀⠀⠐⠛⠛⢻⠉⠙⣯⠉⠙⣇
⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⢀⠔⠡⢄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⡀⠀⡇⢇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢀⠄⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢣⢀⡇⠘⡄⢸
⠀⠀⠀⠀⠀⠠⠴⠚⣉⠄⢀⠅⠀⡠⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⢣⢸
⠀⠀⠀⠀⠀⠀⠠⠭⠒⠭⡀⢄⣪⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠈⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⣤⣤⣀⣀⣀⠁⠰⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠚⠉⠉⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠁⠒⠖⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠒⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁⠠⠄⠒⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣙⣦⣀⣀⠀⠀⠀⠀⠀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⠂
⠀⠀⠀⠀⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠐⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠠⠴⠀⠀⠀⠀⣀⠠⢀⣀⠀⣀⡀
⠀⠀⠠⡀⠀⠈⢄⠨⡒⢄⡠⢀⠃⢱⡀⠀⠀⠀⠀⠀⣀⠠⠤⠲⣀⣀⠤⠒⠩⠔⠁⠀⠂
⡤⠀⠀⠀⠀⢀⠈⢂⠑⠒⠠⠤⠐⠂⠀⢈⠀⠀⠀⠅⠀⡀⠀⠀⠀⠐⠒⠄⠃⢄⡀⢀⣀⣀⠄⠀⠀⠀⣀
⠀⠠⡌⢁⣀⡡⠤⠤⠗⠒⠒⠦⣄⣀⡳⠚⠃⢄⣄⡠⡆⢧⠀⠀⡀⠠⠠⢤⣀⡠⢀⢀⣭⡤⠄⠈⠙⠀⠐
⠀⠀⠈⠠⢅⣀⣀⠀⠀⠀⠀⠈⠀⠀⡀⠤⢴⣆⣀⠔⡁⠀⠀⠰⠔⠒⠀⠐⠂⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠐⠒⠒⠁⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠀⠈⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠀⢀⣤⣿⣿⠀⣀⠀⠀⢰⣿
⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⢀⣸⣿⣿⢀⣾⣿⣿⣿⢸⣿⣇⠀⢸⣿⣇⣶⣿⣦⣴⣤⠀⢠⡀⠀⠀⣀⡀⠀⠀⣀
⠀⢀⠀⢸⣿⢠⡆⢠⣾⣷⣄⣶⣾⣧⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⣿
⠀⠼⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠄




⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣿⡤⠤⢤⣶⣶⣶⣶⡶⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⡼⠓⣛⣿⣯⡙⡍⣉⠉⡍⢍⠙⣓⠺⣝⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⣸⠿⢭⣤⣈⣏⣀⣉⣔⣲⣌⣭⡾⠤⢗⣫⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣰⣯⣍⣙⡒⠒⠲⠶⠶⠶⠶⠖⠒⠒⣋⣉⣤⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⠏⣇⠙⢮⡉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠀⡟⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡞⠀⢻⠀⠀⠉⠲⣄⣀⠀⠀⠀⠀⠀⢀⣠⠼⠗⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢾⡁⠀⠘⡇⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠺⠿⡶⠚⠁
⠀⠀⠀⠀⠀⠀⡄⠀⢀⣤⣤⣀⠀⢠⣞⣉⣙⠺⡀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⣀⠀⢙⡶⣫⠶⠦⣌⣳⢚⣹⢹⡟⣿⣷⠦⣤⠼⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠂⠀⠀⣯⣍⡭⠞⡥⠖⠶⢤⡼⢋⡡⢫⣷⣿⣅⡠⢬⡛⣩⠴⢭⣳⡀⠀⠀⠀⠀⣀⡼⢣⡄⢀
⠀⠀⠀⠀⠙⢦⡤⠞⣱⠚⣹⡏⣰⢋⡶⢡⠋⡏⣽⡖⠲⠭⠗⣲⡶⠏⢝⢟⢛⡛⣫⠝⡴⡢⠢⠀⠑⠂
⠀⠀⠀⠀⠀⢀⣝⡻⢥⣞⡴⢧⣹⣼⣿⣜⣦⡳⢝⠻⣏⠙⣻⡥⣀⠀⠀⠐⠉⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠐⠂⠁⠀⠒⠆⠉⠙⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠻⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⡀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠉⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠘⢷⡄⠀⠈⢿⣶⣶⣿⣿⣿⣿⣿⣷⡶⠟⠉⠀⠀⠀⠀⠀⢀⣀⣈⣿
⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⡀⠀⣿⠀⠀⠈⠻⣦⡀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣤⣶⡛⠋⠉⠉⢻⣷⣄
⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠉⠉⠛⠻⠿⣦⣄⡀⠀⠈⠻⣦⡀⠀⣹⡿⣿⡟⢁⣀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣤⡀⠀⢹⣿⢷⣄
⠀⢀⣾⠋⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡈⠛⣿⠏⢠⡿⣰⣿⣿⠂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⡟⠀⢙⣷⣄
⠀⣾⣧⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⡿⠿⠷⠿⣧⡻⠿⢃⣾⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣠⡾⠃⠙⠻⣦⡀
⢸⡏⠹⣧⡀⠀⠙⣷⣀⣀⣤⣤⣤⣤⣤⣤⣀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠈⣿⡶⢿⣥⣀⡀⠀⠀⠉⠉⠉⠉⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠈⠛⢷⣤⡀
⣾⠇⠀⠘⢷⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣀⣤⣴⠶⠶⣿⣄⠀⠈⠉⠛⠛⠷⠶⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⠀⠀⠀⠀⠻⣷⣄⠀⠈⠻⣿⣿⣿⡟⠁⠀⠀⠀⢀⣴⣿⣿⣷⣄⡀⠀⠈⢻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⠀⠀⠀⠀⠀⠀⠙⢷⣄⣼⠏⣻⠏⣴⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⣿⠉⠻⣿⡷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣷⡀
⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢰⡟⢸⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⡿⠻⣦⣈⠉⠛⠻⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟⠋⠀⠀⠘⣷
⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⣧⣀⣉⣴⡟⠁⠉⠙⠛⠛⠿⠿⠿⠛⠛⠉⠀⣠⣼⠟⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣦⡀⠀⠀⠀⠀⢸⡏⠀⠀⣿⣏⡉⠉⠉⠛⠷⢶⣤⣤⣀⣀⣀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡏⠛⢷⣤⣀⠀⣿⠁⠀⣸⡏⠉⠛⢶⣤⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾
⠘⠷⣦⡀⠈⠙⠿⣿⣀⠀⣿⠁⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣷⡶⣦⣤⣤⣤⣤⣤⡶⠶⠟⠛⠋⠉⢠⡿
⠀⠀⠈⠻⢶⣄⡀⠈⠙⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠶⠶⠶⠶⠶⠶⠟⠛⠋⠁⠀⠀⠀⠀⢹⡷⠶⠶⠶⠶⠶⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠈⠙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠉⠙⠛⠷⢶⣤⣤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣤⣤⡶⠾⠛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣰⡎⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠠⢄⣤⣤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡄⣀⣀
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠠⠤⠤⠤⠀⠀⣀⠀⠈⠀⠋⠉⠉⠙⠛⠋⠛⠂⠙⠒⠒⠲⠶⠶⢶⣮⣉⣉⠉⠉
⣥⣤⣤⣄⣷⣤⣤⣶⣿⣿⣿⡿⠿⣛⣙⠃⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠋⠍⠉
⠭⠭⣽⣯⣭⡉⠿⠿⠿⡿⠯⠽⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣄⣀⣀⣀⣀⢀⡀⠀⣀⣀⣸⣶⣷⣶⣶⣶⣶⣶
⣶⣶⣾⣿⠿⢭⣭⣭⣭⣥⣀⣀⠀⠤⠤⠤⠤⠶⠶⠿⠛⠛⠓⠒⠚⠛⠛⠛⢽⠽⠿⠿⠷⠖⠲⠶⠶⣾⣿⣏⣉⡉⠡⠤⠤
⠛⠉⠓⠂⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣤⣶⣖⣒⣉⣭⣤⣄⣠⣤⣴⣶⣶⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣀⡀⠀⠉⠭⣽⣿⣿⣟⣛⣛⣉⣉⣀⣀⣁⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠛⢛⡛⠿⠻
⠛⠛⠩⠭⠭⠥⣤⣤⡄⠀⠶⠶⠾⠿⠿⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠤⣼⣤⠿⠭⠵⠶⠶
⢖⣶⣶⣿⣿⣿⡶⣶⠶⠶⠶⠒⠲⠶⠶⠶⢶⡖⢂⡀⠐⠂⠀⠀⣀⣀⣠⣤⡄⠁⠀⢀⣀⣉⣉⣉⣉⣙⡛⠓⠒⣒⣲⣶⣶
⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣶⠶⠶⠶⢾⣿⣿⣛⡛⠿⠿⣿⣿⣭⣍⣀⣀⠀⣀⣀⣀⣀⣈⣉⣉⣩⣤⣴⣶⣲⣶⣶⡶⠶
⣤⣤⡤⠤⠤⣴⣦⣤⣤⣤⠴⠶⠒⠒⠶⠶⠤⠀⠀⠐⠒⠒⠲⠶⠖⢺⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣭⣭⣭⣤⣤⣤⣶⣶
⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠿⢿⣷⠶⠶⠶⠶⠾⠛⠟⠛⠾⠿⠗⠒⠂⠀⠐⣚⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠥⠤⠤⠤⠤⠤⠤⠤⠴⠶⠾⠿⢟⣛⣛⣛⣛⣛⣿⣿⣿⡿⠯⠭⠽⠟⠛⠛⠛⠛⠉⠉⣉⣛⣉⣉⣀⣈⣉⣉⣀
⠿⠿⠿⠿⠿⠿⠾⠿⠿⠶⠾⠛⠛⠛⠋⠉⠉⢉⢁⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠉⠉
⣒⣒⣂⣠⡤⣄⣠⣤⡤⠤⠤⢴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠲⠒⠒⠒⠒⠂⠛⠋⠀⠒⠀⠈⠙⠛⠓⠂
⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣄⣤⣤⣤⣤⣤⣤⣀⣀
⣀⣀⣀⣤⣤⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣭⣭⣭⣽⣿⣿⣭⣥⣬
⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⡀⠀⠈⠉⢉⣩⣭⣭⠭⠭⠴⠶⠚⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠙⠉⠛⠛⢛⣛⣛⣛⣛⡛⠻⠿⠷⢶⣶⣶⡶⠶⠶⠶⠶⠂⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣻⣿⣿⣿⣭⣭⣍⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⠿⠟⠛⠛
⣀⣀⣀⣲⣀⣈⣭⣭⣭⣿⣿⣿⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣯⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠠⢄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⡈⠀⠀⠀⠀⠈⠁⠀⠚⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠁⠀⠅⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡀⣀⠀⣤⠦⠐⣄⠤⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠌⠳⡄⡀⠀⠀⡕⠊⠀⠀⠀⠀⠀⠀⠀⠐⡢⠀⠀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠘⠃⠀⢀⠀⠀⠈⠛⡠⠀⠀⠀⢀⠄⠤⢈⠴⠫⢀⠔⠢⠤⠁⢀⠀⠀⠀⠰⠆⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⠀⠀⡀⠀⠀⠀⢠⠣⡈⠢⢀⢠⠐⠁⠀⠀⠀⠤⡀⠐⠃⠀⠲⢿⠁⠂⠄⡌⠀⠠⠒⡂⠑⠃⠀⡘⠤⠃⠀⠀⣀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠉⠌⢊⠢⡀⠀⠀⠀⠑⢄⢡⡀⡀⢀⡞⢞⣳⠀⠀⠀⠐⢄⠱⡀⡆⠨⢰⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠁⠜⢀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢸⡀⠄⠀⠀⠂⠀⠀⠺⠓⠂⠉⠀⠢⡠⠴⠀⠀⡃⢀⠃⡝⢑⠂⡰⠈⠀⠐⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠰⢀⠰⣀⡐⠁⠀⡠⢠⡟⡏⠅⠀⠀⠠⢈⡤⡁⠂⠄⠀⠰⠖⡐⠋⠀⡀⠔⣡⡮⠀⡑⠀⠀⠀⠠⠄⠠⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡣⠄⠠⡄⠕⠐⣬⡂⡊⡤⠋⢈⠄⠨⡐⠪⡴⠛⣁⣤⣄⡀⢤⢲⠿⠤⠤⢤⣆⣁⣼⣀⢨⣥⠀⣉⠉⠠⠔⠄⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢜⢯⡑⠞⠫⠒⠀⠐⢁⣭⡈⢀⡙⢹⡆⠀⠈⠓⢓⠈⡀⡀⠀⠠⢌⠀⢨⡼⠀⠈⣣⣰⢁⣾⡷⢎⣡⠁⡰⠀⢂
⠀⠀⠀⠀⠆⠆⠀⠀⠀⠀⠑⠩⠑⢤⣀⠀⢠⡟⠄⡽⠿⣉⡉⠀⠀⣠⡤⠗⠛⠲⣤⡤⠋⠷⠔⡉⢳⠀⠉⠈⠡⠈⡋⠀⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⣤⠀⣎⠆⠀⠆⠐⠂⠀⠰⡙⡖⠫⠉⢉⣤⠴⠃⠂⠐⠑⢀⡤⣐⡒⠖⠠⠤⠐⠒⠀⠂⠉⣀⠀⢄⠁⠉⠠⡩⠂⠀⠛⠀⠀⠀⠀⠀⠀⣀
⡀⠀⠀⠀⣀⡆⢠⠒⠀⠀⠀⠀⠀⠀⠀⢰⡈⠀⠘⠚⠑⠲⠓⠉⠙⣻⣮⢔⣲⡭⠁⢠⠒⢒⡂⢁⠀⠂⠐⠀⠡⠈⠀⠀⠂
⠀⠀⢀⠀⠀⠀⡄⣡⠴⢄⠀⠀⠂⡠⢀⠆⠀⠂⠀⠀⢀⡄⠰⢆⢬⡁⠉⠀⠠⢀⠀⢗⠀⡆⢀⢀⠀⠀⠀⠀⠐⠀⠀⠔
⠀⠀⠀⠁⡄⢠⣅⡨⡗⠀⠦⡭⣤⠴⠻⠄⠀⠀⠀⣄⠴⢀⡾⠞⠛⠁⠒⠒⠂⠁⡀⠀⢇⡱⠈⠊⠀⣤
⠀⠀⠀⠂⠁⠪⡉⢫⡀⠀⠀⠀⠠⢄⡁⠀⠀⠀⣊⠡⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠈⠜⣆⠈⠀⠀⠑⠈⡠⠔⠂⠉⠀⠀⠀⠘⠀⣀
⠀⠀⠠⠀⠀⠀⠀⠠⣨⢗⡂⠀⠀⠀⡁⠀⠀⠀⠣⠃⠀⠀⢀⡀
⠀⠀⠀⠑⠀⠀⡠⠚⠉⠋⠐⠀⡀⠀⠐⠂⠠⠤⠎⠬⠄⢒⠄
⠀⠀⢀⠔⠰⠶⡇⠀⠒⠀⠒⠂⠀⠂⠠⠆⠒⠨⠄⠒⠠⢣
⠀⠀⠈⠉⠀⠀⠐⠈⠀⠀⠘⠄⠐⠐⠠⠄⠉⢀⣘⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⡠⠋⠈⢢
⠀⠀⠀⢀⡴⠊⠁⠀⠠⠊⠀⠀⠀⠀⠁⢓⢲⡄
⠀⠀⠀⠊⣀⠤⠤⠤⠤⠐⠒⠈⠉⠉⠉⣉⠴⢻
⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠐⠒⠀⠉⠁⠀⠀⠸
⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠤⠤⠔⠂⢴
⠀⠀⢸⢀⠀⠀⠀⠀⠀⣀⠔⠀⠀⢀⠆⠀⡜⡀⠀⠥⣹⠆⣄
⠀⠀⢸⠀⡇⠀⠤⠒⠊⠁⠀⣀⠀⢸⡀⠀⠀⠙⠂⠀⣠⡤⣀⠸⠆⢠
⠀⠀⢸⠐⣇⠒⠒⠒⠒⠉⠁⠀⠀⣀⠉⠉⠉⠉⠉⠒⠒⠤⣉⡀⠖⢨⡄⢶⡦⣀⣀
⠀⠀⢸⠀⠀⠙⠒⠦⣄⣀⡀⠐⠋⠀⠀⠀⢀⠔⡠⠂⡠⠀⠀⢈⠁⠒⠄⠀⠀⠁⠈⠉⠉⠉⠉⠉⡲⠒⠄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠶⣤⣤⣁⡈⠀⠊⠰⠋⢠⡞⠀⠀⠀⠐⢄⣀⣀⣀⡀⠤⠒⠉⠀⠀⡠⠘⡄
⠀⢀⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠒⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉
⠀⠈⢆⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠒⠒⠒⠒⠒⠀⠀⠀⠤⢀⣀⣀⣀⣀⣀⡀⠤⠤⠒⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠙⠲⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠔⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠉⠉⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣚⣋⡉⠉⠉⠉⣉⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣯⡟⢻⣶⠏⠀⠻⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠁⠀⣀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠖⢻⣧⠘⢦⠀⠀⢀⣴⣿⠙⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠀⣿⠐⢧⡙⣦⣤⣤⡴⠟⣹⠏⠀⣷⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢿⠀⣿⠀⠀⣧⣘⣿⠤⣠⡾⠋⢠⡴⠿⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⣼⠧⠾⠦⡄⠈⠉⢻⡷⠯⠶⠾⠟⠀⠀⢀⣤⠄⠀⠀⢹⡇
⠀⠀⠀⠀⢀⡾⠋⠀⢠⡞⠁⠀⠐⢚⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠘⣧
⠀⠀⠀⢠⡟⠀⢠⣴⠋⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣿⡤⢶⡟⠁⠀⠀⣠⣴⢶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⢀⡿⠁⠀⢸⣷⣀⣴⣿⣿⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠆
⠀⠘⡇⠀⠀⠸⣿⡿⢹⠏⢹⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⢣⡀⠀⠀⣀⠔⠁⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠇⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠸⣿⠀⢿⣄⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡟⠛⠂⣠⣤⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡧⠾⠗⠚⠉⠁⠀⠈⣿⡄⠀⠀⠀⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠀⠀⠀⠀⢀⣤⣴⣿⡇⣀⣤⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⣀⣴⠟⠉⠉⠛⠿⠿⠿⠟⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⣴⣿⠟⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠉⣿⠀⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⠀⠀⣼⠃⠹⣇⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⠀⢹⡆⢰⡏⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⠀⢸⣇⡿⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⡇⠸⣿⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣾⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣿⣿⣿⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣯⠞⣹⣿⡇⠀⠀⠀⠀⠀⠀⡴⠚⣷
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⢰⡏⣰⣿⣿⣷⣶⣶⣶⣶⣶⡞⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠇⠀⠀⠀⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⡿⠛⢛⣿⣆⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⡶⠟⢻⣿⣿⣿⣟⣛⣛⠛⠛⣿⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⠇⠀⢺⣿⣿⡀⠀⠀⠀⠀⠀⡾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣉⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⠶⣶⣾⣿⣿⡷⣄⠀⠀⠀⠀⢳⣶⣶⣶⣤⣤⣤⣤⣤⣉⣉⣉⣿⣧⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣟⣮⠳⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣿⣿⡇⢹⡟⣿⢹⣿⣿⠸⣧⢹⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣼⣿⡇⢸⡇⣿⡘⣿⣿⡇⣿⣾⣿⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣿⣿⣿⡏⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⢸⣧⢸⡇⠿⢹⡇⣿⢻⣿⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⡿⢿⣿
⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠇⢸⡿⢸⣿⢰⠺⡇⣿⢸⡏⠀⢹⣿⣿⡟⠋⠉⠙⠛⠛⠛⠛⠿⣿⣿⣆⠾⠛⠁⠀⠈⠙
⠻⠿⠿⠿⠿⠿⠿⠛⠻⠿⢿⡟⣠⣼⠇⣸⣿⣾⡇⣇⣻⡘⣧⠀⠈⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣾⣥⣿⣾⡿⠿⠿⢿⣿⣿⣷⣿⡧
⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠊⠉⠁⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⣄⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⣥⠶⠲⣆⠈⠛⢦⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⢴⠳⣤⡙⢷⣴⠋⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄
⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢋⣁⠀⢸⠛⢷⡀⠸⡟⠉⠙⠆⠉⣀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠹⡆
⠀⠀⠀⣠⠋⣇⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⢿⣀⣤⣜⢧⣄⡽⠀⠉⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⣿
⠀⠀⢠⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣤⠼⠃⣀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⢀⡴⣿
⠀⠀⢸⣇⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⣠⠴⠋⣰⠏
⠀⠀⠸⡏⢧⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⢀⣠⠴⠋⢁⣠⠞⠁
⠀⠀⠀⢳⡀⠹⣦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⢀⣠⡴⠞⠋⢀⣠⠖⠋
⠀⠀⠀⠈⢳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠙⠒⠤⢤⣤⣤⣤⣤⠴⠶⠛⠉⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠙⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠉⠛⠲⠶⠶⠒⠚⠋⠉⠀⠀⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠉⠁

⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠛⠉⣠⠴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⣉⣀⣠⠤⠶⠚⠉⣡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣅⠀⠠⠤⠴⠒⢋⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠸⡄⠠⠴⠒⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⣸⠀⠇⠀⢒⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢿⣿⣿⣿⣿⣥⣤⣶⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡛⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣯⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⢻⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⢉⣹⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⣀⣀⣸⣿⣿⣿⠿⠿⠛⠛⠋⠉⣁⣀⣤⠤⠤⠔⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣈⣉⣉⣀⣀⣠⣤⠤⠶⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⡴⢁⣴⢂⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠠⠔⠂⣸⢡⠏⣈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢿⣿⠀⢁⡉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⣿⡄⠀⠁⣎⣷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠘⢿⣤⡀⠀⠳⠞⢉⡿⣶⣰⣿⠖⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡀⠀⠀⠀⠀⠀⠈⠛⠷⠦⣤⣤⣤⡼⠟⠁⣠⠞⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⠀⠀⠘⣆⢳⡀⠀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢉⡤⢲⠋⠀⠀⠀⠀⠀⠀⠙⠄⡠⢄⣠⢤⣀⡴⠖⠦⢄⡀⢀⡠⣄⢀⠥⣀⠔⠤⠋⠉
⠀⠀⠀⠀⠀⡖⢁⡠⠤⠐⡞⡴⠃⡃⣿
⠀⠀⠀⠀⠀⠙⢇⠀⠀⠸⣷⡇⠈⠁⢻⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢿⣇⠀⠉⣩⢳⣄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⢻⣦⡀⠈⠸⡥⠟⢒⣦⡄⣴⡦⠤⠀⣀
⠀⠀⠀⠀⠀⡿⢄⠀⠀⠀⠀⠀⠉⠹⠶⣤⣤⣄⣩⣬⣿⠟⠁⣠⠊⠉⠱⡄
⠀⠀⠀⠀⠀⢷⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⡞⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠈⢇⢉⣄⡀⣀⡀⢀⡤⠤⣄⡀⠀⢀⣀⠀⢘⡂⢀⢆⡰⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠉⠉⠀⠀⠀⠉⠀⠉⠈⠁⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⢆⠀⠀⠁⢱⠀⠀⠀⠀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⠀⠀⠀⢘⣀⢸⡀⠀⠀⠀⠘⠃⠀⠁⡆⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⢠⡇⠀⠀⠰⣍⠀⠀⠀⢸⠀⠈⠃⠀⣦⠀⠀⢠⠀⠀⡀⠀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠲
⠀⠀⠀⠀⡄⡀⠀⠲⠀⣧⠀⠀⠀⠁⠀⠀⡀⠛⡉⠀⡆⢸⠀⠀⠀⠀⢠⠀⠀⢸⠀⠐⠃⠄⠩⠆⡀⠀⠀⠀⠀⠤⠄⠀⢀⠀⠀⠀⡄⣹⡇⠠⠄
⠀⠀⠀⡀⠀⡇⠀⠀⠀⣻⠀⠘⠀⠐⡇⠀⠃⠈⠃⠀⣷⠸⠀⢀⠀⢤⠀⣀⠀⣿⡇⠁⠀⠀⡀⠀⠀⢸⣦⠀⢸⠀⠀⣇⠀⡄⠀⣀⠣⠈⠃⠀⠂
⠀⠀⠀⠉⠀⠋⠀⠀⠀⠁⣄⣀⠀⠀⠁⠀⠃⣤⠀⠀⡟⠉⠀⠚⠗⠘⠀⠉⠈⠋⠰⣀⠐⠀⠓⠀⠀⣸⡍⠀⢐⠐⠂⠛⠀⢀⡈⠓⠰⣀⡙⠀⠀⠀⠂
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠶⢦⡀
⠀⠀⠀⠀⠀⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⣿⠉⠛⠳⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⠞⠛⠛⠉⠁⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⢸⡇⣀⣠⡴⠶⠞⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠳⠶⢦⣤⣀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢿⡇
⠀⠀⠀⠀⠀⠘⡇⠈⠙⠳⠶⠦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉⠀⣼⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠉⠛⠶⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠞⠋⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⠚⠛⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣬⣽⣥⣬⣩⣯⣥⣿⣹⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢦
⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⡇⢰⠆⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠱⠗⡠⠊
⠀⠀⠀⠀⠀⠀⣰⠳⢦⣨⠇⠀⠀⠀⢳⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣀⠴⠋
⠀⠀⠀⠀⠀⢀⡏⠀⠀⢧⣀⠀⠀⠀⠘⡆⠀⠀⣇⢀⡞⠉⠉⠙⠓⠒⠶⢦⣀⡴⠊⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠉⢦⠀⠀⢹⡀⠀⢹⡈⢳⠀⣠⢤⣤⣄⣀⡸⠊⠀⣀⡴⠋
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠀⡀⠈⡆⠀⣀⠷⠚⠺⣇⡏⢠⡟⠾⣄⡴⠋⢀⣴⡚⢧⡀
⠀⠀⠀⠀⠀⢸⡀⠀⡎⠀⠀⠈⢂⠹⡋⠁⢀⠴⠒⠋⠀⠸⣧⡾⢋⣀⣜⡧⠤⠽⠔⠛⠲⡄
⠀⠀⠀⠀⠀⠀⢧⠀⢣⠀⠀⠀⠈⡄⢳⠀⡎⡤⠀⠦⠤⣀⠈⢱⠉⠀⢀⣀⣀⣀⣀⣀⠀⢻⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⡆⠈⢆⠀⠀⠀⡀⠀⢿⢰⠁⠀⠀⠀⢀⠀⢸⠀⡎⠁⠀⠀⠀⠀⠈⡆⢸⠋⠁⠀⠈⠙⠲⣄
⠀⠀⠀⠀⢀⡔⠒⠻⡀⠈⠳⠤⠴⠃⠀⠈⠇⠀⠀⠀⠀⢸⠀⡽⠀⢰⠀⠀⠀⠀⠀⠀⢣⠈⡆⠀⢀⣄⠀⢠⠘⡄
⠀⠀⠀⠀⠀⢳⡄⠸⠥⣀⣀⣀⣀⣀⣀⠀⠈⣆⠀⠀⠀⡇⢰⢦⡆⢸⠀⠀⠀⠀⠀⠀⠘⡄⣧⠜⡅⠈⡇⢸⠀⢹⡀
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠠⠤⢀⣀⣀⣀⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⠔⠁⠀⡆⠀⢧
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⢢⠀⠀⣇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⡟⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠳⡤⠇
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠖⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⣇⠉⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠳⠋⢴⣢⠀⢠⠖⡄⠀⠀⠀⢶⠄⠀⣀⡤⠖⠚⠙⢻⡓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠈⠛⠁⠀⠀⢀⡠⠖⠋⠁⠀⣀⠀⡀⠀⢣⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠥⠃⠀⠀⣀⡤⠚⠉⠀⠀⡠⠤⣐⠀⠀⣸⠀⠀⢇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⡴⠊⠁⣀⣄⢠⢊⡐⣆⢀⣈⠧⠸⠀⠀⠀⠘⠆⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠘⠧⠼⠉⠉⠀⡇⠀⠸⣀⠘⢺⣈⡡⠟⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡜⢁⠜⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠞⠉⠙⠆⠀⠈⠀⠀⠀⢀⡠⠔⠈⠀⣀⣀⣀⡠⠞⠁⢶⢦
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠠⠼⠦⡤⠐⠒⢎⡡⠠⢆⠐⠁⠀⠀⠀⠱⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢹⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣳⣀⣀⣀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⡀⢀⣀⠐⠪⢍⠉⠉⠉⠉⠓⡄
⠀⠀⠀⢠⡒⠉⠉⠑⠀⠒⠉⠒⠒⠑⠂⠂⢐⣒⡒⠒⠤⠔⠒⠒⠊⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⢒⡄
⠀⠀⠀⠀⠉⠉⢳⠄⠀⠀⠀⠀⠀⠀⠀⠸⡩⣀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠳⠤⠤⣤⣄⣀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠴⠶⠒⠒⠒⠋⠉⠙⢦⡤⠤⠔⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡮⠓⠒⠐⠫⢕⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⢶⡶⠰⣶⣶⠆⠰⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣔⡗⠁⠀⠀⠀⠀⠀⠀⠑⢕⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠚⠒⠒⠒⠛⠚⠒⠒⠓⠚⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡅⠀⠙
⠀⠀⠠⠊⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠋⠙⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠷⢲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠖⡎
⠀⠀⠐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠇⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⡇
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇
⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣅⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠠⢤⡤⠀⠀⠀⢤⠤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣝⣢⣄⣀⣀⣀⣀⣀⣀⣤⣞⣵⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⢍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡦⢄⣀⠀⠀⠀⠀⣀⠤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠉⠉⠉⠉⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⣁⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⣉⣉⣉⣉⣉⣉⣉⣉⣁⣉⣉⣹



⣿⠿⠿⠿⡿⠟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⡴⠋⡠⠤⠀⠀⠀⡀⠀⠀⠀⠀⢠⢤⠀⠀⢀⡤⢤⡈⠳⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠘⣇⣀⣀⠀⢸⠁⠀⢸⡆⠀⣏⣈⡇⠀⡎⠀⢀⡇⠀⢳⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣈⡇⠘⢆⣠⠜⠁⠀⠁⠀⠀⠀⠉⠈⠉⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠑⢤⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣠⠤⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠒⠶⠤⣄⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⣒⣛⣫⡭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠐⠂⠤⢄⡀
⠀⠀⠀⣠⠊⠁⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠘⠒⠤⠤⢤⣄⣀⣘⣤⣀⣀⣀⣀⣀⣀⣀⣤⣴⣖⣚⣋⣉⣉⣉⣉⣩⣉⣉⣙⣳⣶⣤⣤⣤⣤⣤⠤⠤⠤⠤⠶⠤⠶⠶⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣏⡉⢻⣿⣿⣷⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⡛⢷⣷⡀⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠁⠀⠀⠀⣾⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡏⠈⠙⠒⠦⢤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁