Coco Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡾⢛⣿⣿⡷⢀⠄⠐⣺⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣥⣷⣶⣿⣦⣄⣻⢃⡔⣠⣤⣭⣭⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⢀⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢠⣾⣣⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⡀
⠀⠀⣼⡿⢛⣱⣌⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢳
⠀⠀⠉⢶⣿⣿⣿⣿⠿⠛⠋⠀⠛⠟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⢹⡶⣄⡀⠀⠀⠠⠖⠛⠷⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣘⠉⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢃⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⡷⣟⠻⣿⣿⣿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣷⣯⣠⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠂⠲⠰⠄⠄⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡈⠱⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⣄⠀⠈⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⣸⣿⡆⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠟⠉⣩⣄⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⠴⠊⢉⣁⡴⠶⠞⠛⠛⠟⠿⠛⠛⣋⣉⣤⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣠⡤⠊⢉⣤⣤⣴⣶⣶⣤⣌⣙⣛⡛⠛⠛⠟⠛⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⢀⡀⡄⠠⣍⣉⣛⡛⣛⣛⣛⣋⣁⣤⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀⠀⠀⠀⣀⣠⣤⣽⣄⢳⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠁⣰⠞⢉⣭⠟⠫⣿⢿⣦⠻⣶⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢂⠞⣡⣾⢟⣩⣾⣎⣴⣿⣿⣧⠹⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⢠⠳⢰⠟⣱⣿⠿⣻⣿⣿⣿⣿⣿⣷⡙⣿⣷⡌⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠃⠐⠫⠞⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡌⢻⣿⣦⡘⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣦⣀⡀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣶⡈⠙⠻⠿⠟
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠾⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⣉⣻⣷

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢀⠔⢲⣤⣄⠋⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠑⣆⠀⠀⠀⠀⢀⣴⣒⠿⠛⣦⡀
⠀⠀⠀⡞⠀⢨⡇⣽⣇⠀⠠⣐⣇⣀⠀⠀⠀⢳⣶⣿⣄⠀⠀⠀⡹⠀⠀⠀⠀⢻⡧⠑⣀⢀⠀⣳
⠀⠀⠀⠁⢀⣼⣁⣶⣄⣾⣟⣿⡿⠋⠀⠀⠀⠀⠙⠛⠛⠷⠶⠞⠁⠀⠀⠀⠀⠘⠿⣿⣶⣤⡾⠁
⠀⠀⠀⠐⠛⠛⠻⠽⠿⠼⣿⣿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠔⠁⠀⠀⠀⢠⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⡼
⠀⠀⠀⢀⣔⢈⣽⣟⣿⣧⡾⠋⠀⠀⠀⠀⠀⠀⣰⠖⠒⡻⣶⣄⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠟⠁
⠀⠀⠀⢻⢃⣽⣿⣿⡿⠟⠿⣶⠾⠟⠉⠀⠀⠀⡿⡀⢀⠐⠹⣿⡄⠀⠀⠀⠀⣀⣠⣤⣀
⠀⠀⠀⠈⠻⢷⡾⣿⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠙⢾⣀⣥⣴⡟⠁⠀⠀⢠⣿⠃⠀⠐⢠⣲⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠀⢀⠈⠀⠀⠀⠠⠤⠤⣀⡈⠉⠉⠀⠀⠀⢀⣸⣭⣔⠆⠀⣲⡟⣽⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠁⠀⠀⢠⣀⠀⠀⢀⣀⡼⠀⠀⠀⠀⠀⠀⠙⢿⣟⣷⣌⣹⡁⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⡉⣩⡡⠃⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠺⣽⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠶⢄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠄⠒⢢⠐⢲⣴⣷⠂⠄⠀⠈⣿⡄⠀⠀⠀⢀⡀⠀⠀⠀⢠⡾⢿⣽⡿⣶⡀
⠀⠀⠀⢀⠀⠀⡏⠀⢰⡇⡽⣧⠀⣘⣯⣽⡧⠀⠀⠎⠁⠀⠀⠀⠀⢸⣷⣜⢺⢻⡟⠁⠀⠀⢠⡀⠀⡀
⠀⠀⠀⠘⠢⠴⠀⠀⣼⣅⣼⣿⣾⣯⣿⠟⠀⠀⠀⢀⠀⠀⢀⡰⠀⠈⢿⣦⣅⢸⡄⠀⠀⢀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠐⠚⠻⠿⠷⠛⠛⠻⠛⠷⡀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠙⠛⠋⠙⠲⠶⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⠿⠿⢿⣽⣟⠿⠿⣿⣷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣤⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣠⡴⢁⡨⠔⠊⠉⠉⠤⣤⠭⢍⡛⠪⢕⢯⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠀⠀⠈⠓⢝⣦⠞⠋⠉⠻⣿⣷⢦⡀⢊⣠⣞⡵⢶⡿⢋⣙⡛⠛⠶⠘⠂⠈⠑⠲⣽⣿⢌⣷⡆
⠀⠀⠀⠀⠀⠀⠀⡴⡫⠋⢀⣠⠤⠴⠢⢤⡀⣠⡾⢡⠞⠑⢦⠀⠸⣿⣝⢿⣿⣯⡥⣶⠿⠫⠵⠶⠤⠴⠶⠒⢒⣀⣀⣀⠈⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣹⠁⢰⠃⠀⠀⠀⠀⠀⣿⠟⣠⠏⠀⠀⢸⡄⠀⣿⡗⠄⠻⢿⣿⣧⢴⣒⣫⠭⠭⠉⠛⢀⠀⠀⢀⣠⣬⠶⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⠀⠀⠀⣰⡟⣰⠃⠀⠀⠀⠀⡇⠀⣿⡗⠦⣀⢄⣙⣿⠛⠓⠶⠒⠒⠒⠊⣁⡴⢚⡽⣋⣴⡲⣿⣿⢿⣤
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⢦⣄⣀⠀⢀⣿⢁⡏⠀⠀⠀⠀⣸⠃⢸⣿⣍⠑⢮⣦⠇⣿⣿⣦⣄⠀⠉⠀⠩⠵⣿⡽⠾⢛⡩⢞⠋⣸⣼⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢸⡏⢸⠃⠀⠀⠀⢰⠃⢀⣿⡟⠈⠛⠶⡙⢧⠽⠻⣳⠤⢉⠀⠀⠀⠈⠥⣒⣾⣏⣼⣡⣿⣿⣋⣀⣀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣲⠤⠤⣄⣿⠃⠘⠀⠀⠀⠀⠁⠀⣼⡿⠉⠉⠁⠀⣉⢲⣅⣜⠹⡗⠐⣶⣶⣶⣾⣿⡟⢿⡏⢿⢟⣻⣯⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣿⡀⢸⡀⡀⠀⠀⢀⣼⣿⣧⣤⠤⠔⠒⢺⣿⣿⣿⠟⣷⣻⣿⣿⣿⡏⠴⠷⣏⣷⠞⣩⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢇⠀⠁⠀⠀⣠⣾⣟⣒⣭⣖⣫⣭⣴⣿⣿⣿⣷⣤⣾⡿⣿⣿⣿⣃⣰⣶⣿⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣕⠶⣶⣿⣿⣭⣿⣿⠿⣟⣿⣟⡻⠓⢉⣽⣿⠄⡰⢋⢻⡳⡶⣿⣻⣿⣟⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠗⠛⣿⣿⣿⡿⣭⣿⣧⢠⣳⣿⣾⣿⣥⣷⣾⣿⣧⢳⣼⣭⣝⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠀⠈⠉⠳⠯⣯⣿⣻⣿⣿⣟⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠿⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠁⠀⠀⠀⠈⠫⠍⠉⢼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠈⠈⢙⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢄⠀⠀⠂⠛⠋⠀⠀⠀⠀⠀⠉⢿⡿⣿⣿⣿⣻⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣑⠂⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⠍⠳⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣀⣠⡴⢟⣼⣧⠐⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡤⠶⢛⣩⣧⣷⣾⡿⠿⢛⣡⣆⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢋⣡⠔⣭⣽⣶⣶⣬⣿⣟⠻⠛⡛⠉⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⢉⢈⣩⣴⣶⣶⢤⣳⣶⣿⣶⣷⣶⣿⣿⣿⣿⡌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⣸⡿⣿⣿⣿⣿⣧⣳⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢋⡾⣫⣿⣿⣿⣿⣷⡹⣦⡹⣿⣿⣿⣿⣿⣿⣿⣷⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠘⣙⣽⣾⣿⣿⣿⣿⣿⣜⢿⣮⠻⣿⣿⣿⡿⢛⣉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣻⣶⣭⣭⣴⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⠿⢿⣿⣿⠟⠻⠿⠿⠿⠿⠿⠉⠙⠿⠯⠔⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇


⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿

⠀⣀⣀⣤⣄⣠⣤⢠⣤⣀⣠⣄⣀⣤⣀⣠⣤⣀⣤⣀⣤⣄⣄⣤⣠⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣠⣤⢠⣤⣤⣤⣤⣤⣠⡄⣀⣄⣀⣀⡀
⠀⣟⠉⠈⠁⠉⠉⠉⠈⠀⠁⠁⠉⠈⠈⠉⠁⠀⠈⠈⢁⠇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠣⡈⠈⠀⠉⠈⠈⠀⠀⠁⠉⠈⠈⠉⠉⠈⠉⠛⡟
⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠿⠀⠀⠀⠠⡄⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⢠⠀⠀⠀⠘⠇⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⣄⠀⠠⡧
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⢀⠀⠠⠚⠀⠉⠈⡈⠀⠑⢄⣥⢰⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖
⢀⣝⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂⠀⠀⠀⢾⣿⡆⠀⢀⣠⡁⠘⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡷⢀⠆⠀⠀⠀⠀⠂⠀⠀⠁⠠⠀⠀⠀⠀⡀⢣⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⢰⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⣟⠁⠠⣄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⣕⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⡀⡿
⠀⢿⠀⠀⠀⠀⠢⡀⠀⡠⠀⠀⠀⡀⠀⠀⠀⢀⣄⣀⠒⠨⣴⠢⣀⠀⠙⠒⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⣀⠄⠈⠁⣶
⠠⣯⡄⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⠐⠖⠂⠈⠀⠀⠈⠑⢤⠀⠀⠀⠙⠖⠲⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⣶
⢀⣗⠀⠀⠀⠀⠀⠀⠐⠈⢾⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠂⢀⠀⠀⠀⡽
⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⡏⣿⣾⢩⣸⡆⡿⣿⠁⢸⡆⠱⠀⠈⣿
⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠒⠒⢢⠔⠄⢠⠂⠀⠀⡀⠀⢀⠀⠁⠄⠀⠘⠀⠈⠀⠜⠁⠘⠃⠛⠉⠛⠉⢳⠁⠛⠊⠛⠛⠁⠀⠀⣿
⠐⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠠⠽⠇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠠⣶
⠠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠄⢤⠅⠀⠀⠀⢠⠄⠀⠀⠒⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣯
⢀⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢰⠶⢤⣀⡀⠀⠀⠀⠀⠈⠀⠀⠠⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠀⡞⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛
⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡗⠀⠀⠀⢗⠐⠂⠀⠀⠀⠀⠀⢹⠒⠊⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠰⡟⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡇⠀⢨⡁⠀⠀⠀⠈⡆⠀⠀⠀⠐⠂⠉⢁⠁⠀⠀⠹⡌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿
⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠇⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⢀⡆⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭
⢀⣆⠀⠀⠀⢀⠀⠀⠀⡴⠺⠉⠉⣻⠀⠀⣾⠃⠳⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢛⡙⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩
⠀⡱⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡧⠀⢠⡏⠈⠀⠀⠘⡄⠐⠀⠀⠀⢰⡄⠀⠀⠘⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠸⢏⠀⠀⠀⠀⠀⠠⣆⠀⠀⠂⣠⣁⣀⣸⠃⠀⠀⠀⢀⡇⠠⠀⠀⠀⡀⢁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠸⡷⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⣿⣿⣿⣿⠀⠀⡀⠀⣸⠀⠘⠀⠀⠀⡇⡘⠁⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢰⣧⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠙⠻⠟⠋⠀⠀⠁⠀⠂⠀⠐⠀⠀⠀⢰⡇⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣩
⢐⣿⠀⠀⠀⡀⠜⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠩⠀⠘⣄⠀⡖⠀⠀⠀⠀⠃⠀⠀⠈⣦⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣼
⠨⣛⠀⢀⡞⠁⠀⡐⠀⠀⣀⣄⣀⣈⠁⠀⢀⠄⠀⡀⠘⡀⡓⠀⠀⠀⢠⡄⠀⠀⠀⣞⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣛
⠘⠏⠀⢸⠁⠀⠘⠁⠂⠀⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠙⠀⠈⠉⠬⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⢾
⠨⡷⠄⠸⣇⠀⠀⠀⠘⠀⠀⠀⠀⡄⠀⠰⠆⠂⠀⠀⠂⡼⠔⠒⠒⠀⠀⣸⠄⠠⣤⢷⣄⣀⣠⣀⠀⢠⠀⡀⠀⡀⠀⢀⡀⢀⠀⢄⠀⠀⣿
⢰⣞⡀⠀⠈⠳⣤⡀⢂⠉⠀⠈⠀⠀⠠⠄⠀⠀⢠⠞⠊⠁⠀⠈⠀⠀⠀⡀⠀⠀⠈⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⢐⡍⠀⠀⠀⠀⠈⠙⠛⠶⢤⣤⣄⡀⣀⢀⠠⠐⢚⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣘
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠒⠒⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛
⢰⣷⢶⢶⠴⠵⠶⠰⠶⠶⠶⠿⠶⠾⠆⠲⠷⠺⠼⠶⠶⣾⣟⣾⣋⣷⣾⣶⣾⢹⣦⣦⡄⣤⡦⣤⣦⣤⢰⣤⢤⣤⣤⣤⣤⡄⣶⡄⢴⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠐⠲⠖⠶⡦⠴⣦⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠛⢡⠐⢀⡪⠔⣒⡀⠂⠐⠐⠒⠐⠶⣾⣦⣭⣼⣳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠆⢀⠀⠀⣀⢀⡀⣈⣘⣉⠥⠤⠔⠒⠲⠶⢤⣬⣉⢉⣛⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢀⠀⠞⠛⠴⠓⣃⣌⣶⣻⣷⣶⠾⠥⠤⠾⠴⠯⠽⠽⠽⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠑⠀⠀⠀⠀⢀⣁⣾⣿⣷⠾⠛⣁⠩⢤⣲⢶⡿⣽⠟⠝⠻⣛⣿⣤⣦⣜⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠆⠉⢀⠀⠀⠀⠀⠀⡠⠜⢋⠩⢶⡾⠿⣤⠮⠀⠁⠊⠀⠛⠒⢂⣛⣭⣾⣷⣻⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠆⠀⠐⡀⠐⣀⢀⣈⠁⡶⢄⢴⠄⠀⢀⣀⡀⢀⣠⡄⠀⢢⡽⢟⣭⡾⠋⣸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣬⠔⠋⠀⠢⠾⢋⢀⠀⠰⡃⠒⠃⠈⠀⠀⠐⢏⣋⢹⣛⣥⣶⣿⢿⡵⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠡⠼⠂⠈⠁⠓⠋⠡⠃⠏⠀⣀⠒⠀⠀⠀⢂⡨⣿⣿⢛⣡⣉⣵⢞⡼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠡⠀⠀⢾⠆⠀⠀⠄⠀⠀⡈⠀⠁⠀⢴⢤⣍⣽⡿⡖⣩⣟⣳⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡖⠋⠁⠀⠀⠀⠀⢀⠀⠁⢀⠄⢀⠀⠀⡟⣻⣿⣿⡕⣫⣼⠿⠶⠒⠶⢤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⠄⠀⠀⠒⠋⢠⡀⠉⠀⣈⣡⣾⡿⣿⣟⣷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠾⣿⣦⣼⣞⣵⣶⣛⣤⣷⣿⠾⢿⡿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠉⠒⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣼⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⣠⡶⢟⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣩⠹⠗⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣶⢿⣽⣷⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣾⡀⢹⠇⠉⠍⠟⠉⠉⠉⣭⠥⣿⢸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣌⣹⣠⡠⠆⠀⠓⠀⣀⣰⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⣀⣴⣾⣿⣋⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⠃⠀⠀⣀⢴⣾⡯⣾⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣦⣤⣤⣀⣾⣿⣿⠃⡠⢔⢏⢴⡿⡫⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠟⡉⢁⢨⣚⠭⠧⠤⣲⣌⡿⢷⣧⢪⡾⢛⣵⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡫⠪⢚⣵⠶⢛⣩⣭⣶⣶⣾⣿⣿⣿⢱⣿⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣏⡞⠁⢴⠻⢲⣛⣋⡭⠽⣿⣿⠿⣋⣩⣿⠰⢿⣥⣤⣤⣤⣶⣶⣶⣾⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⡧⠂⣔⣾⣛⣭⣟⣯⣿⣟⡫⠞⣵⠯⠿⠶⢽⣿⡭⣍⣭⣍⣭⡵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⢡⣔⣺⣥⠶⠚⠛⣛⣛⡭⢻⡾⠋⡠⠐⠂⠤⠤⢈⠙⠳⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠻⣬⠻⠶⠒⣶⣶⣿⣉⣷⢶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠀⠈⠙⠶⢿⣿⣷⣾⣿⡿⢿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠂⠁⢦⡀⠈⠒⠀⠀⠲⡀⠀⠀⠀⢸⣷⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠠⠒⠁⢀⣠⠂⠀⣴⠋⠐⠒⠊⠁⣰⠇⠀⠀⠀⠈⣿⣹⢄⡀⠀⠀⠀⠀⠀⠀⠠⠊⣰⠃
⠀⡀⠀⠀⠀⠲⣄⠀⠉⢉⣀⡴⠞⠙⠲⠤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⢷⣽⣦⣤⣀⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠳⣄⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠈⠑⠒⠂⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠲⠶⠶⠚⠋
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠁⣤⣄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⢳⡇⠀⢀⡸⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡼⠧⠤⠤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⠋⠉⠁⠀⣼⢡⡾⠋⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠈⢀⣠⣴⣟⢳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢠⠔⠛⠀⠀⠀⢀⡠⣀⠀⠀⠀⠀⣀⠰⣶⡍⠛⢿⣿⢾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠉⠦⠀⡴⠈⠈⡟⠀⠀⢸⡶⡖⢊⢷⢀⡘⠳⣼⣴⡘⢻⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣤⣤⣤⣶⢶⡀⠀⠇⠀⠀⢸⠓⠙⠀⣆⢸⡟⢶⣄⠱⠃⢸⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⣸⢮⡇⢠⣳⣆⡀⠀⢀⡏⢦⠂⠰⡝⢦⠑⢦⡝⠄⣦⢸⣟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⣆⡱⣌⠃⠩⠻⡂⡼⠂⢀⠀⢠⠈⣈⠳⡅⠙⠸⣰⢞⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⣳⣍⡌⠳⡄⠀⣓⠘⢆⠈⠣⠐⠑⢿⡆⢡⢠⡄⡇⢸⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⣛⢧⡘⣷⡀⠘⢃⡈⠂⠰⡄⢌⢆⠳⠀⡸⡦⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣁⣰⣆⣙⠳⢦⡜⠆⠙⠃⠘⢃⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣷⣶⣴⣾⡷⠶⠚⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢑⣿⣥⣤⣤⣄⣤⠀⠀⡶⢰⠀⠲⡀⠰⡆⣲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⣀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣶⣿⣿⣿⢿⣿⣿⣷⣄⠀⠀⢀⣠⣶⣶⣶⣶⣴⣶⣷⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏⠀⠈⠻⣿⣿⢧⣿⣿⣿⡏⠀⠀⠘⣿⣿⣿⡆⢀⣾⣿⣿⡟⠉⠉⠻⡿⠿⠀⣾⣿⣿⣿⠁⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡿⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣄⠀⣀⣾⣿⣶⠈⢿⣿⣿⣧⣄⣀⣼⣿⣿⣿⠃⢸⣿⣿⣿⣧⠀⠀⢀⣾⣶⡆⢻⣿⣿⣿⣄⣀⣴⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠛⠿⢿⣿⣿⣿⠿⠟⠁⠀⠀⠙⢿⣿⣿⣷⣶⣿⡿⠟⠀⠀⠙⠻⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⣤⡄⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠬⣿⣧⠸⢿⣄⢰⣆⠀⠀⠀⠀⠈⠛⢷⣼⠛⠁⠀⠀⠀⠀⢰⡖⣠⡿⠇⣼⣟⠡⢶⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⢠⣾⠟⢋⣩⠖⠀⣀⣤⠿⣷⡏⢙⣷⠿⣄⣀⠀⠚⣯⡘⠻⣷⡄⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠸⣿⣿⣶⠛⠁⠈⠛⣶⣿⣿⡇⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢁⠤⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⢀⠀⣰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣔⡈⠂⠀⠀⠀⠀⠀⠀⠀⢠⡄⠰⣶⠀⠦⠀⠀⠘⢀⡿⠻⣶⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠁⠤⡄⠐⠀⠀⠀⠀⠀⠀⠀⠼⠟⠉⠋⠀⠀⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡁⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠋⠛⠀⠀⠀⠀⠀⠀⣤⣀⣠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀⣠⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⢀⠤⠁⠀⠀⢀⠀⡀⠀⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠔⠁⠀⠀⢀⠀⠀⠐⢠⣀⠒⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠔⠀⠀⠂⠁⡤⡤⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⢰⡦⠀⠀⣤⠀⢀⡀⠀⠀⠌⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⠒⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠄⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣄⠀⡰⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡠⠤⡠⠀⠈⠂⠀⠉⠱⠂⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠁⠉⢀⡀⠀⠀⠈⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠁⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠐⢢⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⣤⣤⣤⣌⡙⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⣿⣮⣍⠿⣽⣿⡿⠟⠿⠛⠿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⣿⢍⠈⢛⣱⠦⠀⠀⠀⠀⠀⠀⠈⠓⢿⣶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠇⢀⡁⠀⣉⡉⣻⣶⣤⣀⠉⠑⢶⣿⣧⣌⡱⡙⠆⠂⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⣠⣆⣸⠇⣼⣿⣧⢿⣿⠿⣿⣷⡄⠀⢿⣿⠊⠳⣵⡟⢲⠂⠀⠈⠉⠀⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣧⣾⣯⢠⡟⠛⢿⢸⠃⣀⠀⠙⣿⡆⠀⠙⢄⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠟⣸⠀⢸⠆⠈⣆⠛⠀⢀⣿⡇⠀⠀⢀⢈⡆⣀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣶⣿⣄⣀⣴⠀⠙⠿⢾⣿⠟⠁⠀⠄⠀⣞⣀⣿⣿⠁⠀⠀⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠻⢿⡿⣧⣀⠀⠀⠀⠀⣠⣶⡶⡶⣚⢿⠾⠀⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣄⠤⡀⠀⠿⠻⠆⠀⠀⠀⢰⣏⡼⣁⣽⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠆⠀⠀⠀⠀⠀⠀⢸⣿⣟⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠆⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⣠⠊⣡⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⢛⣯⠂⠙⢁⠟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⠦⣰⠎⠳⠶⠶⠶⢚⣵⣿⢻⣿⡙⠚⠁⠀⣿⣝⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢠⠟⠀⠀⠀⢀⣤⠛⣿⣯⣌⣙⣖⢠⢀⣠⣿⣿⣷⡙⢧
⠀⠀⠀⠀⠀⢀⡠⠀⠀⢀⠴⠒⠴⠋⠀⠀⠀⢠⣿⡿⠛⠁⠐⠉⠙⡋⠩⠿⠿⢿⣿⣿⠃⠘⣷⣤⣀
⠀⠀⠀⠀⠔⠁⠀⡠⠀⠀⠀⣰⠀⠀⠀⢀⣾⣦⡞⠀⠀⠀⠆⠀⠀⣰⣤⣤⣤⣤⡾⠁⠀⠀⠏⠉⠛⠿⢦⣄
⠀⠀⠂⠀⠀⠐⠁⠀⠀⠀⢠⡏⠀⢀⠴⣋⣉⣭⠀⢀⠀⠿⢦⡀⢀⣉⣉⣉⢉⡹⠁⠀⠀⣀⣰⠀⠀⠀⣸⣿
⠁⠀⠔⠀⠀⠀⠀⠀⠀⠀⠺⣠⠴⠃⠼⠿⣛⠿⠀⠋⠰⣷⣤⣈⡊⠛⠛⠛⣿⠃⠀⠐⢟⠉⠀⠀⡄⠊⠀⠈⠢⠤⢤
⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡅⠀⣰⠷⠟⠟⠀⠀⢠⣄⠀⠉⠛⠿⣿⣶⡖⡽⠀⠀⠀⠀⠢⠀⣸⣧⣠⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢠⣦⣶⣾⠃⠀⠀⠚⢿⣷⣤⡀⠀⢀⠌⠔⡗⠀⠀⠀⢠⠞⠀⢿⣿⣯⣬⣤⣀⣀⣈⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠏⠠⠛⠋⢉⣤⠠⠄⣾⣷⡀⠉⠻⢿⣷⠎⠀⣰⡇⠀⠀⣠⠇⡤⢀⡿⠛⠛⠯⠍⢁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣦⣶⣾⣿⣿⣶⡆⠘⢿⣿⣦⡀⢀⠏⠀⡼⢿⣏⠀⡼⠁⠀⠀⢸⠗⠤⡀⠉⠀⠀⠙⠂⠀⠀⣀⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⡛⠿⢿⡿⠿⠿⢿⣄⠀⠹⣿⣿⠏⠀⡀⠀⠀⣯⢰⠁⠀⠀⠀⢘⠀⠀⠈⠒⣬⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿⣶⣶⣶⣶⣿⣿⠋⢦⡀⠈⠛⠘⣼⣿⣶⣤⣼⠃⠀⠀⠀⢀⡇⠀⠀⠀⠀⠈⢳⡄⠠⡀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡌⠈⠛⠛⠛⠛⣡⣆⣀⠀⠉⠰⣅⣷⠀⠈⠙⢿⣿⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠳⡄⠹⠆⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⠸⣷⣶⣾⣿⠿⠿⠿⣿⣶⣶⠀⣿⣷⣶⣶⣿⣿⣿⣄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⡉⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠷⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠐⠁⢸⠀⠛⠛⠛⠛⠿⠿⠿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡁⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣭⣥⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣭⣀⣐⣀⣀

⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣄
⠈⠹⠇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠸⢎
⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⢷
⠰⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠤⠀⠀⠀⠴⠂⠑⠈⠐⠂⠑⢄⢁⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢀⠘⢄⠀⠀⠀⢠⣶⣎⠀⠀⠀⡙⠁⠿⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣿⣿⠄⠀⠏⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠣⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡉⢡⡀⠀⠀⠳⢀⡀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠓⠒⢄⠀⠐⠀⠑⠠⣄⣀⣀⣀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠃⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣠⠀⡄⡠⠤⢠⡄⡄⣤⠄⢠⡄⠀⠀⠀⢤
⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣀⠀⢀⠀⠀⠈⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠄⠀⣸⠛⣻⢀⡗⢇⣰⠸⣄⠇⣸⣃⢨⣇⡄⠀⠀⠹
⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠘⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤
⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⢲⠃⠀⠀⠀⠐⠃⠀⠀⠈⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠉⠒⠴⠄⠂⠀⠀⠀⠀⠀⠀⠀⢂⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⡇⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⣀⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠀⠈⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠐⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣜⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⣰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠢⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠉⠉⡏⠀⠀⡟⠈⠲⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠐⢆⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢰⠅⠀⢰⠇⠀⠀⠄⠘⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠐⠓⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⢀⣜⣀⡀⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢰⠘⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠢⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣿⣿⣿⣷⠀⢂⠀⠀⣸⠀⠀⠀⠀⠀⢸⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣶⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠘⠻⠿⠟⠃⠀⠀⠃⠀⠃⠀⠀⠀⠀⠀⠘⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠐⠃⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠐⠀⠐⠂⡀⠐⢒⠀⠸⡀⠀⠰⠀⠀⠀⠀⢡⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠐⠃⠀⠀⠠⠋⠀⠀⠄⠀⠀⠀⠀⠀⠒⠂⠀⠁⡀⠄⠀⠰⠀⠰⠀⠁⠀⠀⡌⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⣦⠀⠀⠃⠀⠀⠎⠠⠀⠈⠉⠙⠛⠓⠆⠀⠉⠀⠀⢁⠀⢡⡀⠀⠀⠀⠒⠓⠆⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠐⠐⠀⠀⣇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠄⢰⡁⠤⠤⠀⠀⠀⡆⠀⠀⣨⡀
⠰⡷⠀⠀⠈⢢⣄⡀⢠⢐⠀⠀⠄⠈⠀⢀⠀⠀⠀⠀⣤⠴⠃⠀⠰⠀⠀⠀⠙⠁⠀⠙⠮⠉⠉⠉⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⢀⠀⠀⠀⠀⠉⠳⠤⣆⡀⠀⠀⠀⠀⠉⠀⠀⠄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠐⡂⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠈⠁⠀⠁⠀⣀⠐⠒⢀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐
⢠⠰⡅⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡤⣄⣀⣀⣀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠆
⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠚⠦⠟⠻⠤⠚⠦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⡶⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⢿⡏⠉⣭⣤⣀⣀⣬⡛⠲⣀⣻⡿⣦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣯⣅⣐⣶⣄⣙⣶⣯⡽⠿⠿⢿⣿⣟⢉⣴⠖⠛⠓⠾⣍⣳⣄⣀⣀⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠋⢩⣤⣀⠘⠻⣽⣾⠋⠀⠀⠀⠀⠀⢀⣀⣉⣿⠷⠛⠛⠷⢶⣬⠉⠉⠉⣹⣿⣿⣻⠶⢦⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣋⣤⣤⣄⣀⠶⣍⠳⢄⢀⡟⠙⠲⠶⠖⣢⡾⠋⣱⡿⢶⣛⡷⠶⢤⢰⡈⢀⢀⡾⣿⣿⣽⠏⢻⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡻⢿⠿⠟⠛⠛⠛⠌⠻⡄⣼⣧⡤⠤⠤⣴⠏⠀⠀⡿⠉⠉⠉⠉⠛⠶⣝⣧⢸⣾⢀⢛⣛⣽⡒⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢠⡴⠶⠶⠶⠶⠀⣠⣾⠋⠀⠀⠀⣠⡟⠀⠀⠀⣷⠲⠶⣤⡀⢀⣠⣈⣿⠟⣿⣿⣿⡿⣯⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣬⣄⣀⣠⣤⡴⠿⠋⠁⠠⢀⣤⡾⢿⡇⠀⠀⠀⣿⢦⣄⠀⡍⣾⢷⣿⢿⢊⡱⡎⠳⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣭⣛⠻⠷⠒⠂⣠⡞⢠⣴⣾⠟⠋⠀⣼⠁⠀⠀⣰⠿⢦⡙⣷⣧⡿⣿⠣⣜⠿⠙⢀⣤⣄⢸⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⢿⣿⣻⡴⠚⠋⠀⣰⠟⠁⠀⠀⠀⣿⠀⢀⣴⠋⠀⣤⣿⣿⡟⣷⢧⡙⠎⠁⠀⠉⠀⠙⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣬⠉⠉⢁⡴⠁⠦⣄⣇⡀⠀⠀⠀⢀⣧⡴⠚⠁⠙⣦⣷⣿⡿⣋⡻⠟⠀⠀⠀⢰⣖⡶⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⠙⣷⡀⡾⠁⠀⠀⠈⠉⠛⠛⠛⣰⠏⠀⢤⡘⢶⡀⢸⡿⢻⠛⠿⠋⠀⣀⠀⠀⠀⠌⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡞⣧⡈⠻⢷⣤⣄⠀⠀⠀⢀⡔⠚⠁⢦⡀⠀⠻⠀⠁⣼⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡀⢳⡹⣎⢷⣀⠀⠈⠉⠛⠳⠶⢴⡇⠀⠀⠀⠻⡀⠀⠀⠠⠉⠀⠀⠀⠀⢠⡆⡆⡆⡄⠈⢴⡄⢠⠀⠀⠀⢝
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⢻⡝⢷⣝⠓⠲⠄⠀⠀⢠⡞⠀⠘⠛⢛⣛⣻⠗⠀⠀⠀⡀⢧⢷⠦⠀⠐⠃⡟⡇⢦⢀⠀⠘⠦⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⢧⣹⣦⡈⠛⠲⠄⠀⠀⢸⠀⢀⣀⣈⣩⡭⠂⠀⠀⢄⠀⠙⡌⠊⠁⠀⠀⠀⠁⠃⠸⠸⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢿⣿⣝⠶⣤⣀⡀⠀⢸⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⢾⣦⢀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠻⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠻⢿⣖⠂⠀⢀⡟⠛⠛⠋⡀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣦⠰⡄⠀⠀⠐⠇⠋⠸⠀⠢⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣈⡓⣄⡼⠿⣯⣾⠞⡠⠂⠀⠀⠀⠀⠀⠀⠀⠹⣿⢷⣙⠜⢦⡲⣤⣄⣀⣀⡀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⣫⠵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⠉⠉⡩⠒⠒⠒⠂⠋⠻⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡤⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡝⠂⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠀⡇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡘⢠⠃⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⠤⠤⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠀⠀⠀⠀⡼⡹⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡞⢸⠀⠀⢀⡞⢠⠁⠀⠀⢀⡤⢚⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⣄⣀⣀⡀⠀⠀⢮⢹⡀⠀⡇⠸⡀⠀⡜⠀⡞⠀⢀⡴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⣀⡀⠤⠤⠀⠀⠀⠈⠉⠑⠢⢼⣀⢳⡀⡇⡀⡇⢰⠁⢰⢁⡴⣫⠞⠁⣀⣠⠤⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠈⠳⣧⢻⠁⢳⢸⠀⡿⣫⣾⠵⢚⠉⢀⡤⠊
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠔⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⠬⢿⣇⣸⠞⠛⠛⠛⠲⠮⣤⡚⠁
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⡠⠐⠈⠀⢀⡠⢴⡲⠭⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⢿⠃⠀⢀⡤⠖⢤⣀⣀⠉⠛⠯⡀
⠀⠀⠀⠀⡴⢁⠎⠀⠀⠀⡴⠋⠀⢀⡤⠚⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠃⠸⡄⠀⣸⠀⠀⠀⠀⠈⠓⢢⣄⠈⠳⢄⡀
⠀⠀⠀⢰⠁⡌⠀⠀⠠⠊⠀⣠⢖⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⢠⠃⠀⠀⢣⠀⠈⣇⠂⠀⠀⠀⠀⠀⠈⠲⢄⠀⠙⢆
⠀⠀⠀⡇⠰⠀⠀⠀⠀⡠⢊⠕⠁⠀⠀⢀⠤⠒⠁⠀⠀⢀⣉⣀⣀⣀⣀⣀⡎⠠⠀⠀⠈⢧⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⡈⢡⡀⠈⢇
⠀⠀⠀⡇⠀⠀⠀⢀⠌⡔⠁⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⢴⡁⠀⠱⣄⠀⠱⢤⡀⠀⠀⠀⠀⠡⠈⡇⠀⢸
⠀⠀⠀⢱⠀⠀⡰⠁⠊⠀⠀⠠⠤⠒⠉⢀⠔⠋⠀⠀⢀⡤⠖⠒⠒⠞⠄⢀⠀⠀⠀⠀⠙⣆⠀⠀⠙⠢⣄⡉⠓⠒⠦⠤⠤⠶⠁⠀⢸
⠀⠀⠀⡸⢀⠜⠀⠀⠀⠀⠀⠀⠤⢔⡾⠁⠀⠀⣠⠔⢋⠀⠂⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢸⢷⣄⣀⣀⡀⠉⠑⠒⠤⠤⠤⠤⠤⣴⠋
⠀⠀⠀⠳⠤⠤⣄⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣼⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡾⠀⠀⠀⠉⢦⠄⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣀⡟⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠙⠒⠤⣼⠁⠀⠀⠀⠀⠈⡧⠒⠁⣠⣴⣥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣇⣠⣤⣤⣤⠄⣼⣥⣶⠿⡯⠔⠒⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⠠⣳⣄⠀⠀⠀⠀⢁⣾⣿⣿⢧⠀⠀⠀⠀⠀⠀⣗⣛⣉⣉⣉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⠑⠢⠤⣀⣠⠤⠴⠒⠋⠁⣀⠝⠒⠒⠚⠉⢹⠟⣿⢂⠳⣄⠀⠀⠀⢠⠧⠶⣦⣤⣬⣭⠭⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠧⣀⠀⠀⠀⢀⠜⢠⠇⠈⠀⠈⠱⣶⡒⠫⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢽⡒⠦⠤⠤⠶⠒⠚⠉⢁⡀⠀⢀⡹⢍⣉⣁⣴⠋⠀⠀⠀⣀⣠⠧⠹⡗⢬⡒⠌⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠶⠖⠒⠒⠚⠉⠁⠀⠀⠀⠀⢻⢱⡖⠲⡻⠸⡌⢣⡱⠘⢆⠈⠓⠲⠦⢍⣦⡀
⠀⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠃⠀⠳⠀⡇⠀⠙⢄⡈⣆⠀⠀⠀⠀⠀⠁
⡼⠀⠀⠊⠀⡀⢀⡀⠀⡀⢀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠳⣵⠀⠀⠀⠙⠺⣆
⣇⠀⠀⠸⣄⠕⢇⡀⢦⡉⠸⠈⢇⠶⠰⡄⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⣬⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⢁⡩⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠈⠃⠴⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⣀⠂⠀⠀⠀⢰⠟
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠈⠁⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⢘⡆
⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡌⠁⢀⠀⠀⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⠷⠀⠀⠀⠀⢰⡀⠄⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠐⡞⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠢⠄⠀⣀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠁⠐⠒

⣿⣿⡿⠿⢿⠿⠿⠿⠿⡿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣶⣷⣷⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⢶⢿⣇⡀
⠀⠀⠀⠀⠀⣰⣿⣳⠔⠊⢉⡙⠛⠣⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⡽⣿⢗⣾⢺⢻⢷⡄
⠀⠀⠀⠀⠀⣿⣯⣤⠆⠛⠡⠉⡀⠀⠜⣿⡤⠀⠀⠀⠀⠀⠀⠀⡠⠀⡁⠀⠈⠙⠻⣟⣴⡟⣆⡸⣰⢰⣻⡷
⠀⠀⠀⠀⠀⢹⣽⣦⣴⣔⣛⣒⠖⠂⢶⠟⠃⠀⠀⢠⣀⣀⣀⣼⡃⠈⠀⠀⠀⠀⠀⢸⡟⣰⠋⣰⢟⣜⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣮⣷⣺⡿⠋⠀⠀⠀⠀⠘⣷⣿⣿⣿⣇⠠⡀⠀⠀⠀⠀⢸⣷⡿⢋⣡⣾⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢷⣌⣐⣀⣀⣐⡿⣭⣴⣷⣷⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠛⠉⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢒⣲⠶⡒⠉⠑⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⠔⠋⢀⡴⠓⡄⠑⠄⠈⠲⡄
⠀⠀⠀⠀⢀⡴⠁⠀⢀⠔⠁⠀⣰⠏⠀⠀⢸⠀⠘⡄⠀⠈⢦
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢣
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⢀⢂⡏⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠
⠃⢸⠁⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⢃⠀⠀⠀⠀⠀⡀⠀⠄⠐⠁⠀⡀⠀⠠⠀⠀⠒⠂⠀⠄
⠀⢸⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠀⠁⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠕⡆
⠀⢻⠀⢠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠔⠁⢻
⠁⠸⡆⢸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢐⠎⠴⠊⠀⠁⠀⠈
⠀⠀⢳⡸⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⠔⠁⢀⡠⢃⠊
⠀⠀⠀⠱⣷⡀⠀⠀⢸⠀⢀⠀⠀⠀⡌⠀⢧⠂⠀⠀⠁⠀⠀⠀⠔⠈⠀⢀⠄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⠛⠦⣄⣘⣄⡜⠀⢀⡔⢀⡴⢛⡦⢀⠀⠀⠀⠀⡀⠠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠁⠈⢦⠈⠈⠈⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⣀⠄⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣀⡠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠒⠤⠄⣀⣐⣊⣵⣶⡶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⠾⠿⣛⠛⠛⢿⣿⣿⣟⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⣯⡡⠥⠀⠀⠀⠈⠉⢀⣀⣈⣩⠭⠭⠭⠭⣉⣿⡿⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠋⠁⠀⣠⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⢈⡐⠒⠒⣿⣿⣇⣨⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣯⠿⠋⠁⠀⠀⠀⠈⠀⠀⠀⠀⡀⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⢓⣿⢷⡮⠿⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣲⣿⢫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⢾⣿⣷⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣀⠠⣰⢏⠕⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠚⠁⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠙⡿⣷⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⠉⢵⠟⣥⠋⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠎⣿⢃⢏⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⢏⡾⠁⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠠⠄⢰⡟⡟⠘⣽⡏⡉⣿⢿⡇
⠀⠀⠀⠀⢀⣾⡟⠁⠌⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡟⡜⣴⠃⢻⠃⡁⣽⣾⣿
⠀⠀⠀⠀⢰⢿⡧⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣹⡏⡌⡾⣸⣧⣿⣿⣿
⠀⠀⠀⢐⣿⢸⣃⡀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⠟⡰⡿⢠⣿⢇⡟⢿⣻⣿⣿⡆
⠀⠀⠀⢸⣷⢸⢹⠁⠀⠀⠠⠁⠀⠀⠀⡀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣮⣾⡃⣰⣿⣿⢏⡟⣼⢠⣾⠻⣼⣿⠇
⠀⠀⠀⢸⡧⣾⢸⠀⠐⠀⠀⠀⡠⠅⡰⢁⡾⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠘⠀⠀⢀⠰⠋⠐⠉⠀⣸⢟⡿⣿⣾⠁⡣⢋⡞⣷⠇⣼⣧⡿⢹⣿
⠀⠀⠀⢸⢠⡿⢺⠀⠀⢀⠀⠀⠃⠘⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠊⠀⠓⣀⠔⡹⣫⢞⠟⠛⢹⣿⢯⡞⣹⡟⣼⣻⣿⠃⣿⡇
⠀⠀⠀⢸⣦⡇⢹⠀⡄⢸⠀⡌⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡠⠀⠀⢐⡠⠂⡡⣪⠞⣡⣫⠆⣠⣿⢫⠞⣱⣿⡿⢡⡟⢩⣾⣿⠁
⠀⠀⠀⢀⣿⣧⠸⡆⠧⢼⠀⢃⡞⢀⠄⠀⠀⠀⢀⠔⠀⢄⠔⠀⣠⡮⠊⠀⠀⠀⠈⣠⢞⢐⡷⢫⡟⡡⣪⠟⣡⢋⣴⡟⣱⣧⡿⣀⣮⡿⠁
⠀⠀⠀⠄⢹⣿⡶⡇⠆⢸⢠⢿⡄⡈⠀⠜⠀⢀⡠⠂⠀⠀⠀⣴⠏⠀⠂⠀⣀⡴⠃⢐⡷⢃⣶⡿⠳⣾⢣⠞⣱⠟⣉⣴⢣⣿⢓⣼⡿⢁
⠀⠀⠀⠀⠘⣿⡇⢷⡅⢸⣼⢸⡇⢀⠌⡀⠀⢁⠔⠁⣀⣴⠟⠁⠊⢀⠄⠨⢋⣠⠞⢉⣤⠜⢋⣠⠞⣉⡽⠟⣋⣴⠻⣫⣿⠱⣡⡟⠁
⠀⠀⠀⠀⠀⢻⣧⢸⣇⣨⡏⣼⠃⡮⢂⠈⠀⢀⠔⣪⠞⠁⢀⡠⠞⠉⢀⡾⠋⢀⠀⠉⠴⣺⢟⣡⠾⠯⠒⣊⡼⡣⣨⣟⡵⡿⠛
⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣈⠕⣩⠀⢒⡵⢚⢡⠤⠚⢉⣠⡤⣖⠫⠖⠊⠡⠀⠂⠌⠒⠋⣁⢠⡶⠚⠩⣪⠞⣽⣫⠞⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⢕⣩⡶⠿⠿⠦⢴⣶⠶⠿⣛⡶⠿⠃⠉⢑⣈⣁⡔⠀⢀⣤⢒⡥⣊⣴⠶⣻⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⣿⣭⣾⣿⣿⠿⢿⣛⠉⢥⣤⡤⠶⠒⣋⣉⠭⠙⣁⡤⢌⣚⣭⠾⣻⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣻⣿⣿⣾⡧⠴⠶⠷⠶⠆⣲⣾⡿⢯⣽⠶⠿⠻⢓⣩⣽⡫⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⣩⠝⠛⠛⠻⠶⣶⠼⠏⣵⡤⠿⢯⠤⠶⠓⢚⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠐⠀⠀⠀⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣤⣀⠀⣠⣤⠒⠘⠚⠋⠛⠻⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⠁⢀⣀⣀⠈⠙⢿⣿⣒⣩⣶⣟⠉⠁⠉⠉⠻⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⢷⡀⠀⠀⠀⠁⠤⣀⠉⢻⣿⣿⣿⣦⠀⠀⠀⢨⣷
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠆⠳⢤⡐⢄⣀⡄⠜⣷⠀⠹⣿⣿⣿⣦⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⢀⣤⣽⣮⣙⢻⣿⡼⣦⠀⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢻⠄⢀⡠⣾⣿⣿⣿⣿⣧⣉⡉⠉⣠⣟⣩⣵⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⠿⠉⡁⠤⠀⢒⡠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣿⣿⣿⣿⣿⡿⣔⠎⠻⣿⢥⡲⣄⡤⣴⣀⠀⢐⣒⠑⢀⡠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠳⣄⢬⡓⢍⠳⣕⠢⣍⠛⠙⠫⢶⣒⠋⠭⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠢⠙⠦⡑⠬⡑⠦⢍⠒⠮⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣿⡏⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⡶⢦⣄⡀⢀⣴⣶⡛⠉⠉⠛⠉⠈⣛⡛⣛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠁⠀⠀⡀⠀⠈⠙⠻⣿⣿⠥⢊⣩⣶⡞⠋⠉⠁⠉⠉⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠸⣇⠀⠀⠉⠉⠉⠒⢀⡀⠈⠛⢾⣿⣿⣿⣿⡆⡀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣥⠹⣇⠀⠀⡀⠀⠀⠈⠉⢧⣄⠀⠿⣿⣿⣿⣿⣎⠀⠀⢀⣤⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠘⠁⠉⠛⢦⡙⢷⣤⡴⠨⢅⣿⡆⠀⢹⣿⣿⣿⣿⣷⣷⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⣤⣽⣦⣈⠛⣿⣯⡰⣶⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⢀⣼⣯⣾⣿⣿⣿⣷⡉⠛⠓⠛⠁⢰⡿⢛⣩⣭⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢾⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⠿⠟⠛⣛⣛⣛⠿⠟⣁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣷⣾⡿⣿⠟⠋⠉⠀⠒⠊⠉⠉⠉⠒⠤⠤⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣬⡳⠈⠻⣝⠶⣜⠳⣤⠴⣶⣇⡀⣐⢒⣛⡂⠉⡩⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⠉⠀⠤⠄⠈⠳⣄⠠⣌⠳⢬⡛⢦⣑⠢⣍⠓⠮⠑⠮⢵⣲⠾⠭⢭⣭⣉⣉⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⠓⢦⡙⢦⣍⠳⣌⠻⢦⣀⡒⠦⣬⡙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠳⠄⠙⠢⠈⠙⠒⠀⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣲⣯⣍⣭⣭⣍⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡯⠈⣀⠙⠿⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠾⠛⠀⠀⠀⠀⠀⠀⡙⣄
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡐⠘⣆⠀⣀⡀⠠⠤⠤⣀⣀⡀
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠀⢣⠰⢁⡴⠋⠕⠀⢀⣈⡁⡈⣁⣀⠺⢵⣦⡀
⠀⠀⠀⠀⢸⡇⣰⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠄⢠⡫⠁⠀⡴⠊⠁⠀⠀⠀⠀⠀⠙⢄⡙⣷⡀
⠀⠀⠀⠀⢸⣿⣿⠀⢠⠀⠀⡇⠀⡄⢰⢀⢰⢠⣿⠁⠀⡜⠀⠀⠀⠀⠀⠀⢀⡠⠄⡐⠃⣸⣷
⠀⠀⠀⠀⠈⢿⣿⡄⠜⡆⠂⡇⡆⣷⣼⣼⡇⠈⣿⠀⠀⣇⠀⠀⠀⠀⠀⡜⣵⣶⠿⠿⠛⠻⢿⠃
⠀⠀⠀⠀⠀⠘⢿⣷⣀⣻⣦⢱⣿⡟⢿⣿⡇⣾⢻⡆⠀⠘⡀⠀⢀⠀⡠⠀⣿⠁⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣦⡀⠈⣉⣉⣉⣤⡾⠃⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠟⠛⠋⠉⠀⠘⢿⣝⢟⡻⢿⠏⠉⠳⠀⠀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣓⣬⣀⣀⠀⣀⣄⡼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋⠉⠉⠩⠟⠛⠻⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠂⢠⠂⠀⢀⡀⠀⠀⠀⣀⣈⣏⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⢰⣿⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢅⠷⠀⠀⠀⠀⣀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠁⠀⠀⠀⠀⢽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣞⣲⣲⣾⣿⣿⣿⣿⠲⠶⠦⠤⠤⠤⠖⠒⠒⠊⠉⣳⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠾⣥⣔⡀⠀⠀⠀⠀⠀⠀⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠰⠶⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠶⠶⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⢀⡠⠤⠴⠦⢤⡈⠙⢻⣝⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠉⠁⢩⢾⠿⣧
⠀⠀⠀⠀⠀⠀⢀⡔⠁⣠⠖⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⡆⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣁⣱⠊⠀⠹⣇
⠀⠀⠀⠀⠀⣰⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⠀⠀⢼⡆⣠⣤⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠦⣤⣼⡟⠛⠶⠾⣴⣿⡆
⠀⠀⠀⠀⣴⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢸⡇⠀⢲⣿⣿⣿⣤⣶⣟⣛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡿⢧
⠀⠀⠀⢰⡷⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⠀⣬⣽⣿⠀⠓⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣯⣦⠀⠸⡇
⠀⠀⠀⣼⡇⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠋⢀⣾⠃⠀⣸⣿⡏⢀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⣿⣿⣄⠀⡇
⠀⠀⠀⢿⣇⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠞⠁⢠⡾⠃⠀⠀⡸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⡿⢸⢀⡇
⠀⠀⠐⣿⠻⣦⡀⠹⢦⣄⣀⣀⣀⣦⡄⠈⢁⣤⠾⠋⠀⠀⢀⡀⢻⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡼⢸⠃
⠀⠀⠀⠈⢣⠀⡙⠷⣦⣄⣈⣀⣠⣤⣴⠾⠛⠁⢀⠀⢠⣶⣾⣿⣿⡿⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⢇⡟
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠉⠁⠀⢀⠀⣶⠚⠚⠚⠉⠉⠻⢿⡟⠁⠘⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡜⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡙⣲⣶⣤⣶⣤⣿⣧⡀⠑⢀⠄⠀⠀⠉⠒⠢⠾⢬⣌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⣿⣿⣿⣿⣆⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠉⢳⣆⣐⣀⣐⣒⣦⣾⣭⣥⣶⡾⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂⠈⠉⠉⠉⠉⠁⠀⠉⡻⣝⠙⠳⢦⠄⠀⣀⣠⣤⣤⣴⣶⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⢠⠏⠙⠒⠂⠀⠄⠀⠠⠒⠒⠒⢊⣠⣼⣿⠆⠀⠀⠀⠀⠒⣺⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣷⣦⣀⠀⢀⣀⣀⣀⡤⠞⣛⣽⣿⠟⠉⠑⠓⠾⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠧⢄⠀⠀⠠⠤⠞⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣄⣢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢬⣙⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⣹⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡈⢹⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡚⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡴⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠖⠒⠛⠛⠋⠉⠉⠉⠉⠉⠙⢿⠁⠹⣶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠈⠉⢛⠗⠈⠳⡄⠈⠆⠠⠛⢛⠳⣄⠀⠀⠀⠀⢀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⣠⠤⠄⠀⠀⠀⠉⠀⠀⣀⠤⠶⠒⠒⠒⠒⡇⠀⠀⠐⢩⠀⠘⠳⣄⠶⠠⠘⠓⠚⠛⠉⠉⠉⠉⠉⠉⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣇⠀⠀⠘⣧⡀⠀⠀⠀⢁⡀⠤⠀⢲⠒⠒⠒⠒⠒⠲⠤⠼
⠀⠀⠀⠀⠀⣿⠈⠉⠒⠢⢤⣔⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡨⠓⡆⠀⠀⠙⠒⠖⠒⠋⠁⠀⠀⣸⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠒⢦⣤⣀⣟⣷⠯⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠘⢤⣀⠀⠀⢀⡄⣀⣀⣠⠴⡃⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⣹⠛⠎⢱⣦⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠋⠹⡇⠉⡅⠀⢢⠙⢦⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠘⡏⠀⢳⡿⠶⠶⠶⠶⠶⠀⢀⣀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢹⠀⠈⠇⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⠤⠤⣴⡻⣦⠈⢻⡥⠭⣭⣄⣀⡳⣄⠈⢟⠲⢄⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣠⢾⠃⠀⡇⠀⠀⠀⠀⠈⢧⠈⢷⠀⠀⠀⠀⠹⣌⢢⡀⢦⡀⠈⠓⢦⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⣀⡴⠚⠁⢸⣀⠀⠉⠢⣄⠀⠀⠀⠈⢧⠈⢧⠀⠀⠀⠀⣨⠞⠁⢈⠧⡀⠀⠀⠈⢳⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⡇
⢀⡠⠴⠚⠱⢂⣠⠖⠋⠈⠓⠦⣄⡈⠙⠂⠠⠤⠬⢧⡬⠧⠠⠒⠋⢁⡤⠖⠁⠀⠀⠉⠲⢤⡀⠙⠉⢦⡀⠀⣸⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾
⡁⢀⢠⠴⠖⠉⠀⠀⠀⡀⠀⠀⣠⠟⠙⠙⠓⠒⠒⠒⠂⠒⠒⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡈⢿⠰⠋⢰⠇⠘⠀⠀⠀⠀⠀⠀⢠⠇
⢻⡀⠀⠀⠀⠛⠀⠀⠈⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠺⣧⢰⡎⠀⠀⠀⠀⠀⡀⠀⢀⡞
⡀⢧⠀⠀⠀⢀⡤⠀⢀⡴⠃⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄⠀⠀⠀⢸⢰⡇⠴⠁⠀⠀⠠⠃⠀⡞
⠁⠈⢧⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢨⡇⠀⠀⠀⠀⠀⢀⠌
⢸⠀⢸⠧⢤⡖⠉⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⢻⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⡠⠊⠀⡠⠊
⠈⡄⠘⡇⠀⠉⠱⡦⢤⣀⡀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡴⠁⠀⠀⢸⠵⠊⠀⠠⠊
⠀⢡⠀⠇⠀⠀⠀⢷⠀⠈⠉⠙⠒⠲⢅⣀⣀⠀⠀⠃⠀⠀⠀⢀⣸⣀⠀⠀⠀⠀⠀⠀⢀⡀⠔⢻⠁⠀⠀⢀⡟
⠀⠈⢆⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠁⠈⠁⠀⠀⠉⢹⠟⠛⠛⠛⠋⠉⠀⢀⠎⠀⡄⠀⡼⠁
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡼⠃
⠀⠀⠀⠘⢿⡆⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡜⠁
⠀⠀⠀⠀⠈⠳⡄⠀⠀⠁⠀⠀⠀⠀⣦⠀⠀⠰⡆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠊
⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠄⠀⢀⡄⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⣷⣄⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡴⠋⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠳⠆⠁⠦⣄⠀⢀⣀⢀⡤⠀⠀⠈
⣾⣾⣶⡾⣿⣶⣾⣿⣿⣿⣿⣿⣶⣾⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⣶⣾⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣷⣾⣷⣾⣶⣶
⣿⣿⣿⣀⣀⣠⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠛⣉⣡⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⢛⣉⣥⣴⡾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⣛⣭⣶⣶⣶⣿⣿⣿⣿⣿⡷⣶⣄⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⠿⣛⣭⣶⢿⣿⠿⠛⣩⣿⠿⠿⠿⣿⣿⣷⠟⠛⠉⠉⠉⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⢋⣩⣴⡶⢿⣿⡿⠿⠻⣿⣀⣰⣿⠁⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⣀⣼⠟⠿⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣀⣤⡶⠟⠋⣡⣾⠟⠉⠀⠀⠀⠈⠙⠛⢿⣤⣀⣀⣀⣠⣴⠿⠷⣶⣶⠶⠿⠛⠁⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣴⡿⢋⣴⡿⠋⠁⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⢸⡟⣰⡟⠁⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⢠⣿⠁⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠙⢧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢀⣴⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡅⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠈⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣠⣤⣤⠴⠖⠛⠁⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣤⣤⣤⣶⠾⠿⠿⠿⠷⠶⠶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠠⢄⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠓⠺⣉⠙⣒⠻⢄⠀⠀⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠋⠉⠉⠉⣲⣦⣬⣥⣄⣑⠢⢵⣦⡀⡼⢀⡠⠤⠤⠤⣤⡤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⠀⠀⠀⠀⠙⠓⢮⢯⡣⣨⠌⣠⡷⠚⠂⠀⠀⠀⠀⠉⠲⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣀⠤⠤⠒⢾⣟⠟⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⡀⡠⠖⠋⣠⡴⡾⠿⠋⠙⠗⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠻⠿⢶⣿⠋⠈⠀⠀⠀⠀⠀⢰⣴⣷⡀⠀⠐⢤⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⣷⡀⠠⠠⢉⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢞⠀⠙⢦⠴⣶⣬⣵⡶⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⠀⢀⡼⢇⠀⠀⠀⠀⠀⠀⠀⢘⡄⠈⠀⠀⠘⡄⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⢤⡀⠀⠀⣠⡾⣠⡾⠃⢀⠀⠀⠀⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠛⠋⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣤⡤⠶⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠁⣴⣾⣿⠗⠀⠰⣿⣯⣀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠉⠉⠀⠀⣤⡀⡄⢁⡁⠀⠘⠏⣶⢄
⠀⠀⠀⠀⠀⠀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠇⠘⠀⢀⢨⢘⠆
⠀⠀⠀⠀⢀⣼⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈
⠀⠀⠀⣰⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⢰⠏⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠃⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵
⠀⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⢀⣰⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠁⠸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⣤⠄⠠⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡀
⡄⠀⡜⡀⠀⠀⢠⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡏⠀⠀⠀⢀⣀⠈⠆⠀⠂⡉⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠂
⡉⢤⠀⠀⣀⠆⠠⠀⡁⠀⢈⠘⠐⠀⠀⠀⢀⠀⠀⠰⢸⡋⠀⢀⡤⠐⢋⠠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀
⠇⣾⢐⡀⠟⠆⡀⠀⢠⠀⢘⠀⠀⠀⠀⠆⠘⠀⠀⡀⡘⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⠶⠿⢤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⢠⡠⢸⢹⣧⠀⡁⣀⡀⠳⠊⠀⠀⠀⠀⠀⠄⠀⠀⢀⠄⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⡛⠃⠐⠀⠁⠁⠉⣀⡆⡁⢦⣠⡤⠦⠀⠀⠀⠀⡷
⠘⢻⣿⡸⣾⡤⢻⣯⠙⣷⢠⡄⠀⡀⠀⠀⢀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡷⣡⢚⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠇⠀⠀⠀⠀⡾⠰⣿
⠀⠸⣛⣧⣿⣿⣹⣿⣻⣿⢸⣿⡆⣇⠘⢢⣯⢘⡟⢤⠁⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⢜⡱⣁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡼⠀⣼⡏
⠀⠀⢡⣼⢿⡫⡁⡁⢙⢻⣿⢼⠀⣧⠸⣸⡫⣟⡗⠶⠀⠀⠀⠀⣠⠴⠿⣛⢹⣽⢃⡾⠃⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠈⢀⣜⣿⣿
⠀⠀⠀⠙⢄⢳⣿⣿⢸⢋⣧⡎⢰⣿⠉⣾⡔⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⡠⣺⣫⠼⠉
⠀⠀⠀⠀⠈⠙⢿⡻⢯⡳⣿⣥⣼⣿⢸⣾⣣⡎⠼⣷⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⣴⢺⢐⡿⣏⡜
⠀⠀⠀⠀⠀⠀⠀⠉⠂⢽⣎⣣⣽⡿⡃⠛⠛⡕⣃⠻⣧⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⠀⠀⠀⣀⡀⢄⢰⠄⠀⣭⡀⠸⣵⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠋⠱⣍⠛⢛⣏⣲⡖⢦⠀⣁⠀⣄⠀⣤⢀⡐⣂⡀⠆⡌⡀⣌⣚⡴⡶⣻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣻⠈⣩⢳⣯⣿⣷⡌⢿⢿⡘⠡⢸⠃⢐⣣⢺⣼⣿⣵⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢟⣷⣿⣿⣯⣿⣿⣕⢿⡶⠿⡜⣙⣳⣟⠫⠟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠒⠛⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢗⡂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⣙⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣌⡙⡶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣎⣹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠨⠱⣎⡹⢦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠉⢀⠀⠀⠀⠀⠠⠤⢤⡌⠳⡀⠹⡉⢹⢦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⣀⡄⠀⠀⠀⠊⠉⢀⣠⠤⠤⠤⠤⡎⠀⠀⢜⡀⠰⢤⡠⡀⠹⠦⠐⠒⠒⠒⠒⠒⢒⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⣠⠤⢇⠀⠀⢳⡀⠀⠀⠁⡀⠠⠀⡖⠒⠒⠒⠒⠦⠼⠧
⠀⠀⠀⠀⠸⣀⣈⠑⠢⢾⣀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⡂⠀⠈⠑⠒⠋⠀⠀⢀⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠉⢙⠒⠲⢯⣟⠷⡀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠙⠢⣤⡠⢴⠢⡤⠒⠛⢄⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⣴⠛⢄⣞⣀⣀⣀⣀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⢹⠀⠹⡈⠃⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⠡⡤⣼⣆⠘⣶⣂⣀⣀⣐⢤⡉⢷⠦⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢀⡴⡏⠀⣏⠀⠀⠀⠈⢧⠘⣆⠀⠀⠈⠳⡱⡄⢳⡀⢙⠢⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇
⠀⠀⢀⡠⠖⠉⢀⠧⣀⠈⠲⢄⡀⠀⠈⢧⠘⡄⠀⢀⡠⠞⠁⡠⠃⢀⡀⠀⠹⣦⡀⠀⠀⢠⠀⠀⠀⠀⠀⠸⠀⠀⢸
⠔⠚⠉⣀⠥⠚⠁⠀⠀⠙⢲⡤⠁⣀⣀⣚⣓⣛⣀⣉⡤⠖⠉⠀⠀⠀⠈⠑⠦⣀⠈⢦⠀⡜⢠⠀⠟⠀⠀⠀⠀⠀⡟
⣦⠀⠉⠁⠤⠀⠀⠂⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠑⢾⣆⢠⠋⠀⠀⠀⠀⠀⠀⣸⠁
⠘⡆⠀⠀⢀⡄⠀⣠⠎⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⢀⠀⠀⡀⠀⠀⢹⢈⠀⠆⠀⠀⠰⠀⢠⠃
⠀⠘⡄⠀⠀⣠⠞⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠈⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸⠀⠀⢀⠀⠀⡠⠃
⠐⠀⣏⠲⢎⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⢀⠀⠀⣠⠋⠀⢸⢀⡴⠋⢀⠄
⠈⡄⢹⠀⠀⠘⡙⠒⠦⠤⣀⣰⠁⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⠀⡜⠉
⠀⢱⠀⠀⠀⠀⢣⠀⠀⠀⠀⠉⠐⢒⠖⠶⠶⠖⠂⠀⠓⠒⡶⠠⠤⠀⠒⠊⠀⠎⢀⠀⢰⠃
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠈⠀⡎⢠⠃
⠀⠀⠀⠻⡆⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡱⠃
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠸⡄⠀⠘⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣨⠞⠁
⠀⠀⠀⠀⠀⠀⠑⠦⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀⡔⠁⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠄⠲⣄⠢⣀⡀⠀⠀⢀⡀⠀⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⠉⠉⠉⠉⠓⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣠⠶⠛⠛⠛⠳⠦⣤⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⢠⣟⣷⡄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠘⣷⣀⠀⠀⠀⠀⠀⠄⠘⣹⣿⡄⠀⢧
⠀⠀⣀⣴⣾⠽⠗⠒⠒⠒⠒⠢⠭⢝⡒⢤⣀⠀⠀⠀⠀⣿⡏⡷⣄⠈⠙⠷⣄⡀⠀⠀⠀⠐⣴⣿⠇⠀⠈
⢀⣾⣿⠵⠒⠒⠂⠀⠀⠀⠉⠁⠒⠢⠬⣑⡺⢷⣄⠀⠀⢹⣧⣇⢸⢳⣄⠀⠈⠛⠶⠤⠶⠶⠟⠁⠀⠀⣸
⣾⣯⣀⣈⠉⢉⣉⣉⣉⠉⠒⠒⠦⠭⣐⠢⠬⣑⢾⣷⡄⠀⢿⣿⣌⢸⢹⠓⡦⣤⣀⣀⢀⣀⣠⣴⣶⡿⠃
⣿⡟⢦⡉⠙⠒⠤⣀⠀⠉⠉⠒⠒⠤⣀⣉⠒⢤⣑⢾⣿⡄⠀⠻⣾⣸⡤⢊⠔⢡⣚⠽⢻⣻⣿⡿⠋
⠹⣿⡶⣝⠦⣄⠢⢄⡉⠒⠒⠤⠤⠤⢄⣈⣉⣒⠮⣷⣿⣿⡀⠀⠀⠙⠻⠿⣾⣿⣷⡿⠿⠛⠉
⠀⠙⢿⣶⣅⡢⢝⣦⣀⡭⠉⣑⣒⡒⢒⣒⣒⣒⣲⣮⣿⣿⠃
⠀⠀⠀⠙⢿⣯⣑⡻⣗⡯⣷⣖⣒⣚⣛⣯⣭⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣭⣿⣛⣿⣿⣶⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⢒⣒⠒⠚⠉⠲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⢀⡴⠛⠉⢈⣷⡀⠠⢄⠉⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠞⠁⠀⢀⣴⠟⠁⠘⡄⠀⢱⡀⠀⠈⠳⡀
⠀⠀⠀⠀⢀⠀⣤⠞⠁⠀⠀⢀⠔⠁⠀⠀⣴⡗⠁⠀⠀⠀⠃⠀⠀⢳⠀⠀⠄⠙⣄⠄
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠠⠊⠀⠀⢀⢎⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈⠀⠘⣆
⠀⠀⠀⢐⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⣼⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⢀⡔⢹⠇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⣇⣠
⡾⠀⣿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⠆⠀⠀⠀⢠⠀⠀⠀⡀⠀⢀⢀⡠⡒⠀⠀⠉⠐⠠⣄⠠⡤⠤⠄⠤⢄⡀
⠀⠀⡇⡀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⢀⠀⠀⠀⢇⡠⠤⠂⠊⠀⢀⡴⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢔⡢⢄
⠀⠀⡷⠁⠀⠆⠀⠀⠀⠙⠢⡀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠔⢸⡀⠀⠀⠁⠀⠀⢀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⢉⡆⣇
⢠⠚⡇⠀⢰⡀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⡼⡁⠁⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣠⣀⠴⢊⠔⢹
⠉⠀⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡐⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠁⢤⡖⢃⡤⠖⠀⠚⠁⠀⠘⡆
⠀⠀⠸⡆⢸⣅⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡄⠀⠀⠀⠠⢰⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠞⡠⠋⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠹⡄⣟⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠁⢰⢸⠀⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⢀⡴⢃⠔⠁⠀⠘⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠙⣾⣷⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⡌⠀⠸⡜⡃⠀⠀⠀⠡⡀⠀⢀⡀⠤⠊⠁⠀⠀⠀⠔⠡⠔⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠈⠛⢷⣀⠀⠀⢸⡀⢠⡂⠀⠀⠀⡼⠀⢀⣴⢿⢔⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⡊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠧⣾⣅⣀⣤⣞⣠⣴⣿⠥⠞⢧⡑⠬⢔⣀⡤⢄⣐⡒⠭⠅⠂⠻⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠢⣥⠔⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢕⢄⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠸⡀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠤⣉⣒⢤⣤⣀⣠⣤⠾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣭⣭⣷⣶⣶⣶⣾⣽⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⣸⣿⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⣿⣿⡆⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢿⣿⡿⣄⣿⣿⣇⣾⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢿⣷⣌⣿⣿⣼⣿⣿⣿⡟⢉⣭⣭⣍⡉⠓⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⣁⡂⣀⡙⢿⣿⣿⣿⣿⣿⣿⡇⢸⡟⠁⠀⠀⠀⠀⠠⡈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣈⣀⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⡄⠻⠇⠀⠀⠀⠀⠀⠈⠶⣄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣼⣦⡀⠀⠀⢀⠀⢠⣀⠠⣻⣦⠈⢧
⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠙⢙⣿⣻⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣷⣦⣤⡈⠙⠻⠿⠿⠿⠃⢸⡆
⠀⠀⠀⠀⠀⠀⢸⣦⣬⣖⣂⣀⠠⠤⠞⠛⠿⢛⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣭⣭⣠⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣟⡘⢿⣿⣿⣿⣿⣿⣽⣿⣿⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣟⠛⠙⠀⢀⣹⡟⣿⣟⠙⠮⡻⠿⠿⠟⠛⢻⣿⠟⠋⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣅⡀⠁⣴⠶⣏⣾⠇⠈⠻⣷⣄⣼⣷⣶⡀⠀⠚⠁⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⡶⠟⠁⠀⠀⠀⠈⠛⠿⠿⣿⣶⣴⣶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣠⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠛⠛⠋⠁⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣾⡿⠟⠋⠀⠈⠉⠀⠀⠀⠀⢀⡀⠀⠀⠙⣦
⠀⠀⠀⠀⢀⡾⠋⠙⠛⠛⠉⠛⠿⠿⠟⠋⠉⠛⠿⠿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⢳⡄
⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠹⡄
⠀⠀⣴⠏⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢻
⠀⣰⠏⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢸
⢠⡏⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢰
⣼⠁⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣸
⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⢿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢸⡷⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⢸⡄⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣼⣁⣀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⢷⡀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⣰⠏⠈⠉⠙⠓⠲⠶⠶⠖⠋
⠀⠈⢳⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⠏
⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣳⣶⣶⣶⣚⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠈⠉⠑⣲⣖⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠛⠁⣠⣶⠆⠀⠁⠀⠀⠀⠌⠳⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⢀⠐⡌⢧
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠱⡘⡈⣷⡄⣀⣤⣤⠤⠴⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸⡄⢆⠁⣠⢞⠭⠕⠀⠀⣀⣉⣀⣈⣀⡐⠒⢮⣕⢤⡀
⠀⠀⠀⠀⠀⢸⡏⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠇⠡⢠⢞⠕⠁⠀⣠⠴⠋⠉⠀⠀⠀⠀⠉⠙⢦⡈⠳⣿⡄
⠀⠀⠀⠀⠀⢸⣇⢼⣿⠀⠘⠀⢠⢰⡇⠄⠀⠀⡀⠀⢀⠘⢠⣏⠆⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⢹⣿⡄
⠀⠀⠀⠀⠀⢈⣿⣼⣷⠀⠐⡆⢠⠀⡇⡀⡆⠇⣷⢰⡌⠂⡿⣞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢊⣡⣬⣤⣼⣿⣧
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⡅⣧⡀⡄⡇⣇⣷⣦⣿⢸⡇⡄⢰⣟⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡎⣴⣿⡟⠟⡟⠋⠟⠿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡐⣸⣷⡀⢧⣹⠙⢿⢸⣼⡇⣷⡿⣿⡄⠀⠈⢇⠀⠀⠀⠀⠀⡼⠀⣿⡇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣷⣸⣿⣷⣿⣾⣿⣷⣿⣷⣿⣷⣄⠀⠀⠑⠒⠛⠛⠋⢁⣴⠏⠁⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢹⣿⢷⣦⣶⣶⣿⣿⡿⡿⡏⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⢽⣷⣝⠢⣝⠙⡟⠄⠀⠀⠀⠀⣠⣇⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⣦⣄⣀⣀⣀⣠⣤⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠉




⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠄⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠐⠛⠚⠸⠓⠛⠟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⠤⠒⠛⢩⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢶⠎⠉⠀⡠⠁⣠⡾⠏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠈⣠⣾⢿⣹⡶⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⡦⢄⠜⢧⢘⠷⡆⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⡀⣷⣿⠮⡳⢸⡎⣧⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠀⠀⡀⠀⠀⠀⣀⢴⠻⡅⠉⢧⠹⡞⢿⣆⠁⠈⠧⣄⢻⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⣦⢶⠤⠀⠁⠀⢀⠔⢾⣥⢀⠃⠃⡜⣆⠀⠑⠀⡈⡣⡀⠀⢻⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠈⠀⠀⣀⡤⢶⡿⣤⠀⢢⣄⠱⣆⢤⠈⠈⠀⢰⠀⢻⡀⠹⠀⢠⢁⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡶⣶⣿⣿⣟⢀⢳⣜⠄⣼⡝⢟⠼⡌⠃⠘⢦⡈⠄⠀⠁⢰⡇⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣌⣿⢿⡧⠙⢿⣆⠺⡎⢿⡠⣿⡄⣿⣷⢀⠠⠸⡄⢸⠇⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡙⠷⢤⡐⢤⡱⣜⠃⠢⡱⡌⠻⡄⢧⢇⠻⠈⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣷⣻⣦⣽⣮⠤⣀⠳⢬⡀⣜⠘⠈⢸⣶⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣷⣬⣵⣮⣳⣮⣥⣠⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡴⣏⣠⠞⠉⠀⠀⠀⠀⣰⢤⣄⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢴⠶⢾⣏⣴⠟⠁⠀⠀⠀⢀⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢶
⣿⡿⢿⣤⣤⡶⠒⠀⣾⡙⡙⣿⣻⡷⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⣿⣿⣟⠿⣷⣤⣤⠶⠂⢠⣞⣉⠗⣟⣿⡧⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢼⠃⣸⣿
⠃⠀⠀⠈⠂⠀⠀⠀⢿⣿⠆⠣⡟⠀⠀⠀⠀⣧⣠⣤⠀⠀⠀⠀⠀⠈⠾⣿⣯⣿⠁⠀⠀⠉⠄⠀⠀⠀⣿⣞⠌⢻⡏⠀⠀⠀⢈⣦⣤⡄⠀⠀⠀⠀⠀⠘⢾⣾⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡷⣄⣀⣀⣼⣿⠿⠁⠀⠀⠀⠀⠀⠀⠐⠀⠁⠸⣄⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣬⠷⣀⣀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⡀⠉⠙⠳⣤⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣰⠟⠊⣻⣷⣄⠀⠀⠀⠈⠀⠀⣀⠀⢀⡀⠉⠛⢲⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⠛⠉⣻⣶⡀⠀⠀⠀⠁⠀⢀⡀
⡥⠈⠀⡀⢽⡇⠀⠀⠀⠀⣀⡀⠒⠀⠀⣿⠀⢀⡀⠹⣿⠀⠀⠀⠀⢠⠂⠉⡟⢿⡅⠁⢀⡄⢿⡆⠀⠀⠀⠀⣀⡀⠂⠀⠀⡧⡀⢀⠈⠻⣿⠀⠀⠂⠀⡱⠀⢹⡟
⣟⣆⣤⢾⣿⠟⠀⣠⡞⠩⠛⠉⢳⡄⠀⠘⠻⢄⣦⣽⠏⠀⢠⡀⠀⡌⠀⢀⡇⢺⣻⣠⡴⢿⣿⠇⠀⣴⡎⠝⠋⠙⢦⡀⠀⠙⠯⣀⣤⡿⠃⠀⢠⠀⠀⠁⠀⢸⠃
⣻⣿⣿⣿⣥⡀⠀⢻⣆⣀⣀⠀⢠⠗⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠈⠃⣀⣼⣷⣾⣿⣿⣿⣿⣅⠀⠀⢿⣂⣀⣀⠄⣨⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠘⠀⣠⣾⣶
⠉⠀⠈⠉⠈⠁⠀⠈⠛⠿⠶⠷⠋⠀⠀⠀⣼⠁⢀⡤⠞⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠉⠈⠁⠀⠈⠻⠷⠾⠖⠃⠀⠀⢀⡾⠀⣀⡴⠊⠁⠀⠀⠀⠀⠉⠉⠉
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⣺⣟⣾⣧⣾⠋⠀⠀⠀⠀⢀⣾⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢀⣻⣓⣻⣤⡾⠃⠀⠀⠀⠀⣠⣶⣶⣤⣄
⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠘⡇⣸⣿⣿⡯⠟⠻⢶⠶⠛⠉⠀⣿⣠⢁⡿⣿⠗⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⢇⣼⣿⣿⠯⠛⠷⡶⠶⠛⠁⠰⣯⣘⢹⢿⡿⠃
⠀⣀⣿⣴⡶⠀⠀⠀⠀⠀⠀⠙⠿⠷⢿⠀⠀⠀⠀⠂⠀⠀⠀⢿⣮⡃⢱⡇⠀⠀⠀⢀⣷⣶⡆⠀⠀⠀⠀⠀⠈⠛⠿⠿⣟⠀⠀⠀⠈⡆⠀⠀⠀⣿⣏⠊⢺⡇
⣴⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠦⣀⣀⡀⠀⠀⠀⠀⠈⠙⠿⠶⠟⢦⣤⡴⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢦⣀⣀⡀⠀⠀⠀⠀⠈⠻⠷⠾⠳⢤
⠀⣀⢀⣀⡀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂
⣸⡏⠁⠌⣿⣦⠀⠀⠀⠀⢀⠀⢤⣀⣠⡄⠀⠈⠹⣶⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡾⠉⠀⠽⣿⣆⠀⠀⠀⠀⠀⠀⣄⣀⣠⠌⡀⠉⠻⣦⠀⠀⠀⠀⠀⢄
⢿⣧⠀⡄⢈⣿⠇⠀⠈⠀⢰⠁⠀⣯⠻⣖⠀⠠⢆⣿⣇⠀⠀⢀⣀⣠⣄⠉⠀⠀⣯⣄⠢⠀⣙⣿⠀⠠⠁⠀⡼⠀⠈⡏⣳⡆⠀⠠⣀⣻⣂⠀⠀⢀⣀⣤⣀⠁
⠀⠙⠢⠵⠾⠃⠀⠘⣄⠀⡀⠀⢀⡏⢘⣽⣴⣾⣻⡽⠋⠀⣴⠏⠂⠁⠈⢱⡄⠀⠈⠑⠤⠷⠾⠁⠀⠰⣄⢀⡇⠀⢰⠃⣹⣿⣴⣞⣿⡿⠁⢠⣾⠃⠂⠁⠈⢷⡀
⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠁⢤⣾⣿⣿⡽⠿⢿⣿⣦⡀⠀⢻⣥⣤⡤⠂⡰⠋⠀⠀⢀⡄⠀⠀⢀⡀⠀⠀⠀⠀⣤⣿⣿⣿⡿⠽⣿⡿⣦⠀⠀⢿⣥⡤⢤⢀⡞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡒⠂⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠃⠈⠀⠀⠀⠈⠉⣀⡀⢠⡀⡀
⠀⠀⠀⠀⠀⣾⡫⠂⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠁⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠠⡆⡗⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⢀⡆⠡⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣰⢠⣿⡿⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠈⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣨⡿⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇
⠀⠀⠀⠀⢹⣿⣯⠎⣡⡄⣤⣤⣾⢤⣄⣭⣤⡾⠛⠀⠀⠀⢹⣦⣄⣀⣀⣀⣀⡀⣀⣀⡤⢴⣾⣷⣿⠟
⠀⠀⠀⠀⠘⠻⣿⣯⣿⣷⣿⣿⣿⠵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣍⣡⣠⣴⣾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢤⠤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⡔⢂⣧⢔⣂⡀⢐⡒⠀⠴⣮⣭⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠐⠀⡀⢀⣤⢂⣀⢭⣭⣕⡶⢒⣒⠲⠶⢬⣍⣍⣻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠼⣥⣀⠀⠀⠂⠋⢍⣫⣥⣶⣿⠿⠿⢿⣒⣲⣿⣟⣷⣿⣟⠻⡝⡄
⠀⠀⠀⠀⠀⠀⣤⠐⠃⠈⠀⠀⠀⠀⡺⠿⣛⣫⣵⣒⡌⠿⠻⠛⢯⡉⢭⣷⣻⣾⣿⣾
⠀⠀⠀⠀⠀⠀⢰⠐⠈⠈⠀⡠⠔⡉⣰⢪⣬⣭⡥⠉⠀⣀⡀⢀⡀⠐⣹⡿⣻⣿⢏⡏
⠀⠀⠀⠀⠀⠀⢸⠀⣤⠕⣋⢐⠾⣛⣁⡍⠾⠐⠓⠙⠉⠀⢞⣛⣿⣛⣵⣾⢿⡷⢿⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠁⠞⠁⡈⠘⠉⠙⠛⠁⣠⡔⠀⠀⢐⣄⣿⢟⣿⣬⣷⣯⡷
⠀⠀⠀⠀⠀⠀⠀⠻⣌⣢⣤⡏⠀⠐⠒⠀⠠⠀⠀⠀⠛⢷⣾⣿⣧⢿⣿⣿⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣶⣀⠠⠀⣠⠞⡀⠰⠂⠰⢀⣼⣾⣿⣿⡷⠛⠉⠁⠀⠉⠙⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣦⣶⣤⣶⣿⣤⢶⣹⣿⣯⡿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⢰⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⢷⣄⣀⡀⠀⠀⠀⠀⠀⣀⣤⣶⣯⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣖⠸⡿⢛⡛⠟⠛⠋⣽⣩⣧⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⣽⣤⣤⢂⣘⣂⣠⡼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡿⠀⠀⠀⢀⠄⠀⠀⠄⠐⠀⠂⠀⠈⠂⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⢀⠃⡠⠀⠠⢀⠂⠇⠠⠂⠀⠀⠏⠁⠀⠀⠀⠀⠸⠀⠀⠀⠡⠀⠀⠂⠐⡀
⠀⠀⠀⠀⠀⠠⢃⡴⠙⠀⠀⠀⢀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠓
⠀⠀⠀⠀⠀⠀⣰⠡⠀⠀⠁⠄⠀⢠⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⡄⠠⣠⡐⣆⠂
⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⢈⠄⢠⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢐⠀⠁⠀⠁⢲⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠈⢀⠘⠀⢐⠀⠀⠀⠀⠀⠀⡀⠀⠁⡀⠀⠀⠈⢀⠏⢁⡁⠛⠀⠰
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠸⠚⡔⠐⠉⠁⢀⠀⠀⠀⡀⠁⠀⠀⠉⠀⠃⠺⡘⠀⠘⠁⠠⠀⠀⡀
⠀⠀⠀⠀⢰⢬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⠀⡹⠀⡄⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⢰⡇
⠀⠀⠀⠀⠸⡔⡇⠓⡤⢤⡄⡈⡄⢀⡴⠂⡆⢸⢸⠢⠹⢄⡇⠙⠀⢠⠀⠀⠀⡀⡀⢐⡆⡤⣿⠇
⠀⠀⠀⠀⠈⠁⢳⣤⠋⢸⡗⡇⣿⢆⢡⢠⣧⠲⢀⠐⢀⡀⡒⠸⠀⡜⠈⠐⠠⠃⠑⢻⠡⣷⣹
⠀⠀⠀⠀⠀⠀⢳⡻⡆⣟⠏⣇⡃⢘⣈⡄⣿⡄⡈⡄⢘⡤⠉⠀⢀⠁⠈⡁⠀⠠⣶⢫⡴⡘⠁
⠀⠀⠀⠀⠀⠀⠘⢱⠀⢻⡹⢨⡇⠺⣿⠃⡷⠃⠀⡄⠈⣞⢀⠀⡿⠃⢠⡧⢆⠘⠻⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⡧⡴⣾⡠⣷⢄⣆⣾⢰⣸⡘⣼⣷⡗⢠⣰⣿⣷⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣕⠟⢿⣿⣞⣿⣽⡿⡼⣽⢶⢿⣿⣷⡿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣮⣗⣿⡃⣳⣇⣽⣯⣤⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣠⠶⠒⢻⣟⣻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⢶⣻⣧⡄
⠀⠀⠀⠀⢠⣿⡯⠑⣂⡠⣌⠉⠃⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣰⣿⡾⣻⣟⢼⢹⠹⣻⡆
⠀⠀⠀⠀⠸⣿⡖⢃⠁⣈⣂⠀⠀⢨⣽⠂⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈⠻⣵⡟⣽⠜⣸⢸⣿⡇
⠀⠀⠀⠀⠀⠳⣿⣷⣷⣒⣞⣉⣤⡽⠁⠀⠀⠀⣷⢮⢤⣾⡇⠀⠀⠀⠀⠀⠀⣿⢰⣧⠴⢫⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠞⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠂⡀⠀⠀⣠⣿⠟⡡⣶⣿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣷⣶⣶⡶⠞⠙⠛⠻⠟⠋⠁

⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤⣤⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡻⠟⠛⠟⢻⡦⡀⠐⢘⠀⠀⠀⢀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⡿⣷⣶⣤⡻⢤⡄⠀⠀⠜⠷⠧⠛⠛⠛⢿⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣾⣿⢹⣽⠿⣿⡭⠟⠋⠁⢀⡄⠘⣄⣀⣄⣤⣤⣀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠼⠟⠃⠀⢀⡴⠋⠀⠀⠀⡀⢊⣽⠀⣿⣆⠈⠻⢟⠏⣵⣦⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠙⠘⡘⠢⣿⣿⣆⠐⠈⠰⣸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⡈⢡⣷⠀⢙⣿⣿⠀⠀⠀⠘⠋⠛⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⡤⠀⠐⣿⠀⠘⢿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠇⠀⢠⣤⣤⣤⢤⣄⢁⣤⣤⠛⢤⡤⢿⣿⠀⠠⢤⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠸⠀⠀⠒⠛⠛⢁⠲⠈⠁⠑⠲⠿⠿⠇⠸⣿⠀⠀⠀⠈⠉⠉⠉⠙⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠁⠁⠀⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠠⠤
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⢁⡈⠢⠰⠦⠠⠀⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⣤⠤⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠉⠉⠉⠐⠛⠂⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠴⣶⣶⣀⡈⠙⠛⠊⠀⠀⠐⠚⠲⠶⠶⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⣀⣤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠤⠈⠷⠀⠠⠄
⠀⠀⠀⠀⠈⠸⠛⠶⠒⠋⠛⠁⠈⠉

⠀⠀⠀⢀⠄⠀⠀⠨⣍⡉⠉⠑⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠂⠂⠀⠀⠒⠤⡀
⠀⠀⡐⠁⠀⠀⠐⠢⠀⠨⡀⠐⠨⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠈⠀⠀⠈⢀⠀⠈⠁⢄
⢀⠌⠀⠀⡀⠑⠂⠄⠀⠤⣈⠠⡀⠀⢅⠈⠊⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⢀⡀⠀⠀⢀⠠⠀⠀⢀⠠⢀⠀⠀⢀
⢈⢀⠐⢄⠀⠁⠂⠄⡀⠠⡈⡀⠀⠀⠠⠁⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠄⠈⠀⠀⠀⠀⠀⠴⠊⠀⠐⠀⠀⠀⠸
⠸⡌⢣⡀⠀⠠⠀⠀⠀⠀⠈⠢⢙⠦⡀⠀⡀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠈⢀⡈⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠙⡌⢷⡄⠑⢄⡀⠀⠀⠀⢀⠀⠰⡘⢎⡈⢀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠗⢀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠲
⠀⠀⠘⢬⡙⠦⢄⣁⠀⠀⠠⠀⠀⠀⠃⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⡄⠁⢠⠀⠐⠂⠀⠀⠀⠠⣠⡅⠀⠄⠄⡠
⠀⠀⠀⠀⠑⠰⢤⡀⡉⠁⠐⠂⠂⠈⣂⡌⠭⠃⠀⠀⠀⠀⠀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠈⠀⠠⢀⡀⠀⠀⠀⣠⡤⣑⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠉⠉⠉⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠢⠀⠉⠒⠤⡀⠀⠀⠀⠀⠉⠁⠂⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡣⠖⢑⠈⠄⠀⣀⠈⢉⠂⠒⠂⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠡⠒⠩⠔⣀⡀⠠⠔⠒⠂⠀⠈⠉⠁⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠠⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⣇⡀⠀⠘⠉⠉⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀⠄⠀⠐⠂⠁⠀⠀⠉⡁⠀⠀⣀⡐⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄⣀⠀⠀⠀⠀⠥⠤⠐⠀⠁⠖⠁
⠀⠀⠀⣀⠀⠀⣠⠴⡊⠐⠂⠛⡉⠁⠢⢤⡆⡀⠀⠀⠉⠉⠋⠠⠈⠙⠋⠁⠀⠀⠀⠀⠀⡠⠒⠂⠉⠈⠉⠁⠐⠂⠤⡀
⠀⠀⠐⢡⠖⢁⠀⠀⠀⠀⡠⢊⠐⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠘⠛⠁⠀⠀⠀⠉⠐⠄⠲⠄⠀⠈⠳⡀
⠀⠀⡖⠁⠀⠁⢈⡔⠁⡐⡠⢣⢢⠄⠀⠀⠄⠈⢳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠐⠠⣑⠂⠄⡀⢤⠀⠀⠀⠙⢆
⠀⠸⠁⢀⠀⠠⠊⠀⡰⠐⠐⡠⠀⠀⠀⡠⠀⠠⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠈⠀⠁⠀⢤⡀⠀⠄⠀⠀⠈⠢⡀⠀⠀⠀⠸
⠀⡟⢀⠀⠀⠁⠀⠐⠀⠀⠈⠀⢀⠵⠋⠀⣠⠔⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠀⠀⢄⠀⠐⢄⠐⣄⠈⠀⠀⠐
⠀⣅⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⢀⠴⠀⠨⡱⢊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠐⠈⠂⠄⠀⠐⢕⠌⢢⠀⠈
⠀⠘⡀⠀⠀⠀⠀⠂⠁⠀⢂⡀⠀⠀⠀⠈⢴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠂⠀⠀⠈⠢⠀⠀⠀⠀⠓⢄⠣⠀⣰
⠀⠀⠘⡄⠀⠀⠀⠀⠈⢋⠁⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠑⠤⠀⠀⠀⠀⠀⠀⠈⠀⢀⡴⠃
⠀⠀⠀⠘⠊⠓⠦⠄⠇⢀⣀⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠄⠀⠈⠡⠌⠒⠊⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣵⣿⣿⣿⣿⣿⣿⡿⢽⣿⡛⢿⡷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣷⣿⣿⣿⣿⠿⠿⢿⣷⣶⣤⡄⣀⣀⣻⣿⣿⣷⡒⢄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣟⣙⡻⢿⣿⠿⠶⠤⡤⠤⠀⠈⠉⠙⠋⠽⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣀⣴⠋⠠⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠶⢤⢤⣀⣀⠀⠁⠂⠌⠙⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⡀⠀⠤⠀⠀⠒⠒⠲⠦⣄⣀⠀⠀⠀⠀⠀⠲⠤⣤⣰⣶⣕⣾⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⢨⡻⣿⣿⣿⣿⣦⡀⠀⠒⢒⣂⣠⡀⠀⣀⡀⢀⣀⡀⠀⠈⠽⣷⣮⣽⣻⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣞⣿⣿⣿⣿⣷⣦⣄⣤⣀⡀⠙⠻⠶⠶⢤⣍⣙⡛⠫⣤⣴⣿⣿⣿⣿⣿⣿⡿⢟⣿⣭⣴⣶⣶⣾⣴⣉⢛⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣏⡭⣟⣻⠎⠭⢀⣀⠤⠤⣤⣄⣠⣤⣦⣠⣭⣹⣿⣿⡿⣀⡜⣋⣁⣠⣤⣀⣀⠀⠀⠙⠻⣶⣀⠙⢷⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡶⠺⠭⣗⣶⣦⣬⣽⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠁⠰⠛⠉⠉⠉⠀⠀⠉⠙⣄⠀⠀⠈⣻⣖⠀⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⣭⣻⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣷⣦⣠⢿⣿⠟⣑⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠤⠂⠰⠀⠤⣉⣬⣻⣿⣿⣹⡿⠊⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⣽⣯⣗⡯⠝⠿⣿⣿⣿⣿⣿⡿⠿⢿⣯⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢸⣽⣿⣿⣿⣿⡇⣀⣹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣤⣾⣿⡷⣶⡶⠖⠛⠿⣿⣈⡀⠸⢆⠀⠠⠀⠀⢠⠡⠛⠈⠈⣷⣿⡏⣸⡟⠀⣙⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠁⠀⠀⠸⣿⢷⣄⠈⠷⣄⠀⠀⠀⠀⠀⠀⣰⣟⣻⣴⡿⡄⢺⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⢷⣦⣤⣄⣀⣤⣤⣶⣯⣿⣿⠟⠁⣠⣴⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣧⣈⠙⠛⠿⠿⠛⠉⠉⠉⣅⣠⣷⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⣤⣶⣶⣶⣾⣿⣿⣶⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠛⣿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣵⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢱⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠉⠉⠀⠠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠄⠈⠉⠙⠛⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠤⢤⣤⣤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⣤⠤⠴⠶⠖⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣛⠛⠿⣿⣿⣿⣿⢛⣩⣭⣭⣹⣿⣿⠿⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠾⠿⠿⠿⠿⠟⠛⠛⠉⠁


⣿⢿⠿⠿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢈⣴⣧⡖⣰⣶⣴⣶⣶⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⢫⣿⣿⣿⣧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠳⣤⣤⠲⠋⠁⠀⡱⠀⠀⣴⣿⠛⣷⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠙⠂⠀⠀⠠⠊⠀⣠⣾⢿⣈⡀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠿⢦⡿⠙⣿⠿⢹⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣻⡴⣄⠄⠻⡄⢘⠿⣾⢀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⣁⢲⣼⣷⣌⠳⡀⣿⡘⡇⣾⣼⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⠻⣿⡖⢧⣞⣿⣷⠉⢣⠠⢹⡄⠙⢻⢻⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠈⠀⠀⠀⡠⠀⠀⠀⠀⢀⡤⠞⢯⢹⢮⠀⡈⢷⠈⣷⠈⠻⢷⡀⠆⠀⠃⣶⣰⢸⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⣾⡴⢯⠴⠂⠁⠀⠀⢀⡤⠚⢿⡰⡀⡌⢇⠂⢣⠹⣄⠀⠠⠁⢰⡈⠝⢌⡀⠀⠸⣿⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠈⠁⠀⠀⠀⢀⣠⣴⢮⣡⡀⠐⣌⡁⠘⢾⡄⣀⠈⠃⠈⠂⢠⠃⠀⢷⡈⠘⠧⠀⢀⡹⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣀⣤⣴⣾⣿⡄⠈⣧⠹⡇⠄⢬⡻⣖⢎⢿⠈⢧⠀⢠⡀⠀⢧⠀⠈⢣⠀⣴⡀⢸⣇⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⢻⡝⢿⣽⣿⣎⠲⣝⣷⠍⠀⣻⡧⣘⣎⠙⣷⠈⢢⣀⢃⠧⠈⠀⢠⠀⡀⢸⡇⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣷⣄⣿⠳⣝⠧⠉⠙⡷⡄⠹⣧⠘⣷⠰⢽⣇⠹⣷⣯⡂⣄⢠⠘⣇⢰⣿⠁⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡛⢿⣷⣌⢳⢷⣤⡀⠢⣀⠈⣆⠻⠌⢂⡙⢆⠈⠻⣇⠸⡌⢇⠻⠌⠙⢰⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣾⢷⣥⣢⣽⣧⡈⠳⣌⢳⠀⠠⣰⣌⠃⢀⠙⠆⠿⣸⢰⣃⣤⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣮⣭⣻⣿⣯⡙⠲⣄⡙⢿⡢⠑⢦⡀⠀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿⣶⣶⣿⣶⣭⣷⣦⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⢁⡉⠀⠉⠉⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢈⡤⢄⠴⡠⠤⣴⢠⠀⡴⣠⢠⠎⡤⠄⠀⠀⠀⠀⠀⣠⡾⠏⠁⠀⠠⠐⠻⡈⠉⠙⠲⡄⠀⠘⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠔⠊⠘⠂⠲⠐⠃⠐⠋⠘⠚⠉⠃⠃⠰⠃⠀⠀⠀⠀⢠⣾⠟⠃⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⢸⣄⠀⠀⣿⣿⣧
⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠠⢘⠂⠀⣿⣿⣿⠇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⢶⠋⠀⢠⣿⣿⣿⡇
⠀⢻⡄⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣠⠃⠀⢀⣼⣿⢿⣿⡇
⠀⠈⢷⡀⠀⠀⠈⠀⠀⢀⡀⡄⠈⠎⠁⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠐⢤⣀⣀⡀⣐⣀⣀⡠⠜⠁⢀⣴⣿⣿⣿⣿⡟
⠀⠀⠈⢷⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣄⡀⠀⠀⠈⠉⠉⠁⠀⢀⣤⣾⣿⣯⣛⣿⣿⠇
⠀⠀⠀⠀⠙⢷⣀⠀⠀⠀⠀⠀⠀⣤⣾⡯⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣶⣶⣶⣶⣷⡾⢿⢻⣷⣮⣯⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠙⠛⠿⠷⠶⠟⠛⠉⠁⠀⠀⠄⠀⠐⠀⢀⡠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣬⣷⣼⣿⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠱⡂⠀⠀⢀⣀⣀⣀⣩⣭⣉⡉⠉
⠀⠀⠀⠀⠀⣠⡶⠿⠋⠉⠋⠉⢛⠳⢤⣀⠀⠀⠀⠙⠠⣀⣄⠀⠀⠀⢀⣠⠴⠊⠁⢄⠸⣟⠓⠽⣤⣍⠻⠻⣯⣽⣷⣶⣶⡄
⠀⠀⠀⢀⣾⡿⠄⢀⣴⠒⠉⠉⠉⠲⠄⠉⠛⠦⢤⣀⡀⠀⠈⠉⠁⠀⠉⠀⢀⡾⠓⢿⣛⡒⠆⠀⠂⠈⢀⠑⠛⢿⣯⣝⣇⢻⣣⡀
⠀⠀⠀⢉⠹⢧⣀⢸⣆⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠼⠍⠒⠏⠚⠳⣦⡄⠀⠄⠀⠀⠈⠀⡿⣿⣍⢳⠻⡱⣆
⠀⠀⠀⢀⠅⠀⠳⢑⡌⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠄⠀⠈⢀⠀⢅⠠⠈⠹⣷⡀⠩⣄⠀⠄⠶⠘⢿⣿⣦⢳⣿⢗
⠀⠀⠀⠋⠀⠀⢠⠀⢹⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢷⡀⠀⠸⡆⠀⠀⠀⠀⠈⡗⣆⣑⠌⢹⣆⠈⠑⢄⠀⣓⠸⣿⣯⡎⣿⣸⣧
⠀⠀⠀⠀⠀⡆⠀⠆⠊⠟⠰⣦⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣧⠀⢠⠀⠠⠀⠀⠀⠸⣷⣬⡉⠗⠀⠈⢷⣲⣤⠡⣸⠹⣆⣹⣵⢸⣿⣿
⠀⠈⡠⢀⠀⠔⠀⠀⠜⢡⠧⣦⣿⣯⢿⣿⣶⣦⣤⣄⠀⠀⠀⣰⡟⠀⠐⡆⡀⠀⠀⠀⢄⣈⠲⢯⠲⣄⢾⣦⣽⣿⣷⠎⢳⡈⣿⣿⣾⡿⠗
⠀⠀⠘⣺⣾⣄⣰⣀⢀⠜⣿⣿⣵⣿⣿⣯⣿⣿⡿⢿⣧⣤⣴⡟⠀⠀⠀⠰⠓⠐⢄⡀⠀⠈⠙⠢⣙⣾⣿⣻⣍⣿⣿⣶⢳⣝⣹⢿⣿⣷⡆
⠀⠀⠀⢸⣿⡟⢹⣿⣼⣾⣿⣷⣿⣿⣿⣿⣿⠏⢈⡽⢛⣻⠏⠀⠀⠀⠀⠀⠓⠤⠞⠋⣗⣤⣶⣤⣄⡙⣿⣿⡿⣿⣿⣿⣯⣿⣥⣿⣿⡿
⠀⠀⠀⠈⠙⢥⣿⣿⣿⣿⣿⣿⡟⣿⣷⣾⣷⣿⣼⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡌⢁⠉⠃⠼⣿⣿⣿⣷⣾⣻⣿⣹⣻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠙⠻⠿⣟⠾⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠗⠛⠀⣉⡙⠛⠛⠩⣿⠟⡫⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⣤⣴⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠏⠈⢀⡀⠀⠐⢛⠙⠉⠛⠙⠛⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠂⢠⣞⠧⠀⢁⣀⠈⠀⠀⠀⠈⣙⣻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣀⠁⢠⣶⠁⠀⠀⠉⠀⠀⠀⠀⢧⣭⣿⡿⠿⠟⠛⠛⠛⠁⠀⠀⠀⠐⠒⠂⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⢠⣞⡛⠀⠀⠀⠀⢀⢠⣤⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣺⠶⡙⢡⠀⠀⠀⠀⢶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣷⢬⣠⠠⡀⠀⠀⢸⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣛⣶⢿⣾⣿⣿⣿⣿⣿⣶⢶⡶⠤⠤⠤⠤⠤⠤⠤⠶⠒⠚⢻⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣽⣿⢆⡱⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠙⠻⠷⣷⡠⣀⡀⢀⣀⣀⣠⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠖⠂⠀⠀⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠠⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠤⠄⢉⣉⡐⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⣐⣂⣳⡘⢦⣤⣤⣰⠆⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠈⠛⠻⠛⠿⠷⠐⠛⠉⠁⠀⠀⠠⠈⠙⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⡀⠀⠀⢀⣀⣠⣴⣾⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⣒⡲⠖⠚⠉⢲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⣠⠖⠋⠉⢙⣆⠀⠀⣄⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⢀⡠⠚⠁⠀⢠⣶⠟⠉⠱⡀⠀⢳⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠊⠀⠀⢀⣔⠝⠁⠀⠀⠀⡇⠀⠀⢳⠀⠀⢄⠘⢆
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢀⠜⠁⠀⠀⠠⠪⠋⠀⠀⠀⠀⠀⠃⠀⠀⠈⣇⠀⠈⠄⠈⢷⠁
⠀⠀⠀⢀⢠⡞⠁⠀⠀⠀⠀⠈⠀⠀⠀⠰⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⢀⠄⡾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⢠⠋⢰⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡈⠧⠏⢄⡀
⠛⠀⣾⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠤⠠⡪⠀⠀⠀⠀⠈⠉⠲⠂⠢⠀⠀⠀⠀⠂⠤⡀⢀
⠀⠀⣿⠐⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⢸⠀⠀⡀⢚⠄⠒⠊⠉⠁⢀⡠⠞⠑⠢⠀⠠⠤⠀⠀⠀⠀⠀⢀⡀⠀⠐⠪⢕⡢⣄
⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠒⢸⡦⠊⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⡇⣸⡀
⢠⠊⣿⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠁⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣠⡠⠤⡠⠔⢋⠔⠙⡇
⠉⠀⢹⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡔⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠋⠠⣴⠒⢡⠤⠖⠀⠊⠁⠀⠀⠷
⠀⠀⠘⣇⠀⣇⡄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⢰⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣠⠃⡴⠉⡆⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠹⣆⢹⣃⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⢸⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⣠⠞⢡⠞⠀⠀⠸⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠙⣮⣿⡀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⢀⠇⠀⢸⡰⡂⠀⠀⠀⠹⡀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⡠⠚⡡⠚⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⢸⠀⠀⡞⠀⠀⠀⢀⡞⠀⠀⣸⡧⡡⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡠⠔⡉⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣈⣇⣸⡇⠀⠀⣠⠞⢀⣠⠾⣋⣹⣜⠮⣀⠄⢀⢀⣀⣀⡠⠤⢒⡊⠅⢶⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠇⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠘⢦⡀⠉⠁⠒⠒⠒⠈⠉⠁⠀⠀⠀⠣⡀⠀⠀⠀⠀⢀⠈⡄⡀⠀⠀⠀⣼⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠏⠀⠀⢀⣼⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠋⠢⢄⡀⠀⠀⠀⠀⠀⡀⠐⠤⣀⠀⠀⠀⠀⠀⠘⣤⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠗⠢⢤⣀⣀⡀⠑⠒⠤⠭⣷⣶⣶⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⣀⣤⠶⠒⠛⠾⠛⠓⠿⠿⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠉⠁⠉⠉⠉⠛⠶⣾⣿⣿⣂⠤⢒⣀⣴⠶⠖⠂⠲⠒⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣾⠀⠀⠠⠖⠢⠦⣄⠀⠈⠛⣿⣵⣶⣿⣿⣧⡄⠀⡀⠀⠀⠀⢨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢤⡸⣧⠀⠅⠀⠀⠀⠀⠚⠂⠀⠀⠙⠙⣿⢛⣿⠋⠞⠀⠀⠀⠀⠐⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠘⡧⠙⠦⣄⡐⣤⡀⠀⢀⠀⠈⣤⠀⠀⢿⣳⣿⣆⣷⠀⠀⠀⣿⣜⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡈⢻⣄⠐⠇⢠⡄⠀⠀⠀⠀⢸⠛⣿⣽⣿⣟⣿⣶⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣰⢟⣿⣷⣷⣦⣄⢧⣴⣂⣴⠄⢀⣴⣿⠿⠿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢀⡴⢾⣿⣿⣿⣿⣿⣿⣿⣦⣄⣈⠀⣀⣼⣏⣤⣶⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠸⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣭⣥⣤⣴⡭⠛⢉⣐⣖⠤⠤⢖⣂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⣝⢿⣿⣟⡯⢉⣀⠀⠀⢉⣀⡀⠀⢀⣉⣒⣚⡫⠭⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠘⠛⠿⠿⠿⡿⡿⠿⠟⡛⠛⢷⣍⠀⠈⠻⣝⠳⣍⡳⣟⠛⠶⣴⡢⣥⠦⢦⣖⡲⢒⣛⣉⣙⣛⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠙⢧⣘⠶⣌⠳⣌⡛⢦⡙⠲⣄⡉⠂⠉⠒⠿⣭⣛⡒⠲⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠌⠳⢌⠙⢦⡈⠳⣌⡛⠶⣬⡙⠳⠦⣍⡛⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠂⠀⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠚⠉⠓⣲⣖⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠛⠁⣠⣶⠆⠀⠉⠀⠀⠀⠌⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⠐⡌⢧
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢳⡐⡈⣷⡄⢀⣠⣠⠤⠴⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠹⡀⠆⠁⣠⢞⢫⠍⠀⠀⢀⣉⣀⣈⣀⠒⠲⢭⣒⢤⡀
⠀⠀⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠁⢠⢞⠕⠁⠀⣀⠴⠚⠉⠈⠀⠁⠉⠙⠓⢦⠙⢳⣿⡄
⠀⠀⠀⠀⠀⢸⣇⣼⣿⠀⠰⠀⢀⢐⡆⠀⠁⠀⠀⠀⠀⠐⢠⣟⠊⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⢹⣿⡀
⠀⠀⠀⠀⠀⢈⣿⣼⣷⠀⠰⡄⢠⠈⡇⡀⡇⠇⣷⢠⡜⠄⡿⡼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⣩⣍⣁⣼⣿⣧
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⡁⢇⠈⡄⡇⣇⣷⣦⣿⢸⡇⡀⢰⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡎⣰⣾⡿⠟⡟⠋⠟⠿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡰⢸⣷⡀⣧⣹⠹⣿⢹⣼⡇⣴⡾⣿⡄⠀⠘⢇⠀⠀⠀⠀⠀⣸⠀⣿⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣧⣸⣿⣿⣽⣼⣿⣧⣿⣷⣿⣷⣀⠀⠈⠒⠒⠒⠒⠚⢁⣰⠏⠃⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⢹⣿⢶⣤⣤⣶⣾⣷⡾⡿⡏⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⢝⣦⣙⢮⡛⠻⡛⠀⠀⠁⠀⠀⣠⡆⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣓⣬⣀⣀⠀⠀⣀⣄⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠵⠋⠁




⣶⣶⣶⢶⠾⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶⡶⣶⣾⢶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠶⠴⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠉⣀⡤⠖⣋⣩⣤⣄⣈⠓⢄⠀⠀⠀⠀⣄⠹⣆⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣅⣠⠔⠋⠉⠒⠉⠉⠐⠒⠒⠾⣝⣮⣧⠀⠀⠀⢻⡄⢻⡀⠀⠀⢀⣼⣿⣇⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠈⣡⠞⣡⠔⠀⠖⠃⠀⠀⠀⠰⠘⠷⣼⣿⣿⠀⠀⠀⣤⠳⣸⡇⢀⣴⣿⣯⣿⣿⠀⢀⣴⢟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⡴⢁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣭⣑⠦⣿⠃⠀⠀⠀⣛⣆⣈⡇⣿⣿⣿⣿⣿⣿⣠⣾⣿⣼⡟⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢹⡟⠀⠀⢀⡆⢿⣿⣻⡇⡿⣹⣿⣿⡿⣿⣿⣿⣿⡿⢁⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡄⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠲⣦⣹⡇⠀⢀⣾⣿⠸⢟⣿⠇⢡⣿⣿⣿⠃⣿⣿⣿⣿⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠻⣄⠈⠳⢤⡄⠀⡄⠀⠀⣀⣴⣿⠿⠛⠉⠀⠀⢻⣿⣷⡀⠿⡿⢠⣿⣿⣿⠃⣸⣿⣿⣿⣿⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠛⠶⠶⠶⠶⠶⠖⠛⠛⠉⠀⠀⣀⣤⠰⡷⠘⢛⣋⠁⢰⢣⣿⣿⡿⢟⣛⣯⣿⣿⠛⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡀⣠⣴⡄⣿⣿⣹⠇⣠⣿⠏⠉⠓⠶⠌⠛⠿⣟⠽⡻⣅⣠⠅⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠙⢀⠻⣿⡀⢦⠻⣯⣇⠙⣿⣷⡘⣿⠁⣾⠛⠛⢦⡀⠀⠀⠀⠀⠑⠒⢦⣤⠴⠶⠖⢂⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣶⣿⣷⡌⢷⣿⣿⣷⡈⠻⣷⡘⢷⡙⢷⣄⠀⠙⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠊⠐⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠷⠿⠛⠛⠋⠀⠙⢷⣦⡠⢄⠭⣀⣀⠤⠤⠶⠾⢿⣿⣧⣺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣔⡋⠉⠙⠛⠛⠛⣛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⢸⣿⡄⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⢸⣿⡇⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠘⣿⣯⣳⣸⣟⣇⣾⣿⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠽⢿⣷⣽⣿⣷⣿⣿⣿⡏⢠⣴⡶⠦⠄⠉⠒⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⡠⠬⣀⣤⣙⣿⣿⣿⣿⣿⣿⣇⠘⣏⡀⠀⠀⠀⠀⠀⢄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢠⣤⣼⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣆⡈⠃⠀⠀⠀⠀⠀⠈⠛⣦⠘⢦
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠠⠜⡯⣿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣦⣀⠀⠀⠀⣱⣤⣱⣽⣷⠀⢧
⠀⠀⠀⠀⠀⠀⢸⠀⡠⠄⠀⠀⠀⠂⣡⣼⣷⣾⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣉⡙⠛⠋⢀⣸
⠀⠀⠀⠀⠀⠀⠛⣾⡿⡷⠒⠂⠈⠉⠉⢀⣭⣶⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣶⣶⣶⣿⣿⡟⠛⠿⣿⣿⣷⠦⡹⣿⣿⣿⣿⡿⣾⣿⣿⡟⠿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡹⠛⠢⠀⣀⣠⢚⣧⠙⢿⣄⠈⢪⣍⣉⠁⠀⣘⠟⠁⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣸⢏⣹⠿⠃⠀⠀⠻⢷⣿⣿⣻⣂⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠚⠛⠛⠛⠛⠒⠲⠶⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠙⠲⢦⣄⡀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠒⠒⠀⠀⠒⠒⠂⠤⣄⡈⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⠈⠻⣆⣠⠏⡁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⣷⠂⣹⠏⠀⢻⠀⡇⠀⢀⡠⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠐⠢⣙⠢⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠏⢠⡟⠀⠀⠸⡆⢱⡀⡎⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠈⠑⢌⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢷⣾⠃⡆⠀⠀⠻⡄⠱⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⢄⠈⢷⡀
⠀⠀⠀⠀⠀⠶⢶⣶⡒⠶⠦⣤⣘⣆⠀⠈⣿⠀⠀⠀⠀⡀⠹⣆⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⢣⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⣄⠈⠛⢧⣀⣿⠀⢀⠀⠀⠇⠀⠈⠳⣄⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠇⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣳⡀⠀⠙⣿⡄⢸⠀⠀⠀⢰⠀⠀⠈⠳⣄⡀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠉⠢⣀⢸⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠈⠑⠲⢤⣄⣀⣀⣀⣀⣷⣀⣀⣠⠞⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠈⢿⡄⠀⢰⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠳⠠⢀⣀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠘⢿⡄⠈⠀⡇⠀⢰⠀⠀⠘⠀⠀⢀⠞⢀⠄⠈⠉⠛⠛⠛⠒⠒⠒⠲⣶⢾⡟⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠙⠀⠸⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠄⠀⠀⠀⠀⣠⠐⠋⣪⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⢠⠀⠀⢀⠎⠀⢀⡀⠀⠜⢀⠄⠀⢀⠜⠁⠀⡴⢁⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄⣀⠀⠒⠁⢠⠀⠐⠁⠀⠀⠁⠀⣀⣬⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣷⣶⣶⣶⣶⣶⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠉⠉⠛⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣠⣤⠶⠶⠶⣦⣄⣀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢰⡟⠉⠀⠀⠀⠀⠀⠈⠉⠻⣿⣦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢣⣿⣿⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠠⠤⠈⣨⢽⣷⠀⠀⠹⡄
⠀⠀⠀⣀⣴⣾⣭⠵⠶⠒⠒⠒⠒⠦⠤⢭⣙⠓⠦⣄⡀⠀⠀⠀⠀⠀⣿⣏⢹⣷⡄⠈⠙⠻⣦⣀⠀⠀⠀⠀⠀⠐⣤⣾⣿⠀⠀⠀⢻
⠀⣠⣾⣟⣋⡥⠤⠤⠄⠀⠀⠀⠛⠒⠢⠤⣄⣉⠒⠦⣝⣦⣄⠀⠀⠀⢸⣼⢸⠀⣽⢦⡀⠀⠈⠙⠿⣦⣀⣀⣤⣤⣿⠟⠁⠀⠀⢀⡿
⣰⣿⠟⠉⠤⠤⠤⠤⠤⠤⠤⠤⢤⣀⣀⠐⠤⢌⣉⠓⠲⢭⣛⣷⡄⠀⠀⢿⣧⣇⠻⢸⠟⣦⣄⡀⠀⠀⠉⠉⠉⠉⠀⠀⢀⣀⣤⡾⠁
⣿⣿⡳⠦⣤⣀⡒⠒⠒⠦⠤⢤⣀⣀⠈⠉⠙⠒⢦⣉⠓⠲⢍⡻⣿⣆⠀⠈⢿⣎⣧⠘⡇⠏⣸⠛⣳⠶⣤⣤⣤⣤⣶⣾⣿⣿⠟⠁
⣿⣯⡻⢦⡀⠈⠉⠓⠦⣀⡀⠀⠀⠈⠉⠙⠲⠤⣄⣈⠙⠲⣤⡙⢿⣿⣇⠀⠀⠻⣿⣤⣧⢎⡠⠎⢀⣊⠵⠚⣛⣭⣿⣿⠟⠁
⠹⣿⣿⢦⡙⠷⣄⠒⠤⣀⠉⠑⠒⠦⠤⠤⠤⣄⣀⣀⠉⠓⠦⢽⣷⣿⣿⡆⠀⠀⠀⠉⠻⠿⣷⣾⣿⣷⣾⣿⠿⠟⠋
⠀⠙⢿⣷⣬⡒⢬⣙⢦⣀⠉⣑⡒⠒⠲⠤⠤⠤⠤⠭⡭⠭⠥⠤⢛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠈⠻⣿⣿⣶⠤⣝⣮⣝⣒⠬⣭⣓⣒⣒⣒⣶⡶⠿⣿⣭⣽⣿⣿⡿⠁
⠀⠀⠀⠀⠈⠙⢿⣷⣶⣭⣳⡭⣟⣿⣶⣶⣶⡶⠶⠾⠿⣟⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣯⣽⣷⣶⣬⣭⣽⣿⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠦⣄⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⡟⠉⠉⠉⠉⠛⠛⠶⣦⣀
⠀⠀⠀⢠⠏⢠⡶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢠⡿⠀⣰⠛⠋⠉⠛⠶⣄⠈⠛⢷⣄
⠀⠀⠀⣏⣄⢈⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠙⢷⣄⠀⠻⣧⡀
⠀⠀⠀⣿⠟⠸⣯⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠉⢧⠀⠘⣷⡀
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⣷⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣷⡀
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠸⣧⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⣧
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⢦⣀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡄
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠉⠓⢦⣀⡀⣀⣼⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⣀⡈⠉⠉⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠶⠶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⠶⠶⠶⠖⠛⠉⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠶⠶⠦⠦⠴⠶⠚⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣻⣩⣙⣻⣉⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠱⢤⣀⣀⣀⣤⠏⠙⠿⣿⣿⠷⠂⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⢀⣴⣾⡿⢶⢶⣤⠀⠀⠀⠀⠆⢀⠀⠀⠀⠈⠻⣦⣤⣤⣤⡶⠏
⠀⠀⢠⣿⣛⢟⠀⢉⢜⠿⡇⢀⣀⣒⠠⠊⠀⠀⠂⠀⠀⠈⠉⠉⠉
⠀⠀⢸⡟⠡⠊⠐⠍⢨⣠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠈⢳⣆⠀⠀⠰⣫⡟⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠂⠀⠘⢻⣧
⠀⠀⠀⠀⠛⠙⠛⠉⠁⠀⡠⠒⠁⡖⠉⠹⡿⢿⣧⠌⠁⢀⣠⢼⣿⡆
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠀⢸⠃⠀⠀⣿⠐⣿⢷⢀⣠⡴⣿⣿⠟
⠀⠀⠀⠈⡄⠀⠀⠀⠀⠰⣄⠀⢸⠀⠀⢀⣿⡀⣼⣿⣿⣿⣦⣿⡋
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠂⣀⣾⣿⣿⣯⣾⠗⠿⠿⠿⠛⠧
⠀⠀⠀⠀⠀⢀⣴⢲⢶⠶⣦⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⢤⡀
⠀⠀⠀⠀⣰⠋⡟⠉⠄⠀⠈⣹⠂⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⢹⡄
⠀⠀⠀⢀⣿⡞⡐⠁⠠⢰⢂⣵⡇⠀⠀⢻⣶⣾⣿⡄⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠻⣾⣥⣬⣾⣽⣿⠟⠀⠀⠀⠀⠹⢿⣿⣿⣶⣤⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠙⠋⠉⠀⠀⢀⠀⠀⠒⠄⠀⢀⣀⣄⣈⣉⣀
⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠐⠀⠠⠔⠊⠀⢠⠁⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⣰⣿⢽⣍⣿⣿⣶⡄⠀⠀⠀⠀⠀⠸⣿⣶⠶⠶⠶⢛⡟
⠀⠀⠀⢰⣷⡄⡞⢡⣿⣞⣿⠗⠂⠀⠀⢀⡀⠀⠈⠛⠦⠬⠃⠋
⠀⠀⠀⠨⣿⣿⠳⣌⢣⢿⠁⠀⠀⠀⠀⠀⣷⣀⣀⣤⠀⠀⠀⡀
⠀⠀⠀⠀⠹⣿⣷⣄⡁⢿⣄⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠐⣌⠙⠛⠛⠋⠙⠶⣶⣶⠿⠟⠛⠛⠁⠀⠄⠀⠐⣇
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⡄⠀⠀⠀⠀⠀⠤⡀⠀⢀⣀⣀⣀⠀⠈⠐⠊
⠀⢀⡀⠀⠀⠀⠸⣧⡀⢰⣿⠀⠀⠀⠀⠀⡠⠁⣼⠿⠟⠤⠨⣟⠷⣄
⠀⠀⠹⣷⣄⡀⠀⣿⣧⣸⣿⣀⠀⠀⠀⠈⠀⢨⣿⡙⠀⠙⠒⠀⠑⢹⡀
⠀⠀⠀⠈⣻⣽⣶⣻⡿⣿⣽⣫⡟⠶⢄⠀⠀⠈⢿⣿⣲⡕⠤⠀⢀⣿⡁
⠀⠀⡴⠋⠀⠀⠀⠈⠛⣿⣯⣟⣿⡅⢸⡆⠀⠀⠈⠙⠿⢿⡶⠞⠋⠃
⠀⠀⡁⠀⠀⠀⠀⠀⢰⣿⢿⠻⡷⠠⣿⡇⠀⠀⠀⠀⠀⣠⠤⠶⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠚⠉⠛⠿⠿⠛⠷⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡧⠀⡴⠂⠀⢀⡀⠀⠀⠀⠒⢚⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠁⣶⡅⠀⠈⠁⠀⠀⢀⣮⣽⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠏⣛⢶⡭⠀⠀⠀⠀⢠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⡕⠀⠀⠀⠀⢘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣤⢦⣤⣤⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣤⠤⠴⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣯⣿⣀⠢⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⢠⣀⣠⣤⣤⠴⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠀⠀⠀⠤⠌