Coklat Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⣀⣄⣀⣀⠙⠒⠠⠄⠉⠉⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠾⢏⣉⣉⠤⢠⣤⣓⠶⣤⣉⠙⠛⠉⠓⠀⠀⢀⣠⠴⠚⠫⢑⣈⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢯⣝⣳⠦⣤⣉⠉⠛⠻⠾⣍⣁⠈⢉⣀⡠⠤⠖⠒⠋⣉⣤⡤⠖⣋⣩⡤⡖⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠠⠝⡹⡟⠓⢮⣙⣓⠲⠤⣌⣉⢉⡏⣀⣁⡤⠶⣚⡋⠭⠀⢶⢺⠁⠁⠀⣀⡤⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣢⣤⣃⡐⠂⠳⠉⣿⠓⠦⣬⣍⡉⣉⠭⡖⢉⠋⢠⠀⠀⢈⣨⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠁⠂⠬⢭⣛⡳⢦⣌⡀⠀⠘⠇⢻⠀⠒⠁⣀⣠⣤⠶⢏⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢥⣌⣓⠦⣄⣀⠀⠀⠉⠓⠲⢭⣓⡲⠦⠼⠴⠾⣟⣛⣭⠭⠶⡚⠋⢳⡤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣀⡘⠀⣌⠙⢦⣍⣙⠓⠶⣤⣀⠐⠤⠉⠳⡖⡊⠉⠉⢀⣀⣤⠤⣖⣿⢿⡶⠒⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠞⠉⠻⣦⣄⡈⠀⠙⠉⠙⡓⢾⢿⣗⠢⠤⠥⠴⣒⣺⣋⣥⢶⠟⠋⡉⡜⠙⠋⣀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⡜⢆⠀⠠⡉⡛⠿⢶⣤⣒⡀⠈⠛⠉⠙⢲⡞⠛⠉⠁⠟⠀⣊⣀⣠⠤⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠈⠧⡳⡀⠘⣎⠂⠒⣀⣈⣉⣛⡦⣄⣀⣸⢀⣀⣤⠶⠞⢋⣉⣸⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠣⡤⢱⡝⢆⠊⠟⠛⠉⠉⢁⣀⣀⣠⠭⠿⠛⢛⣓⣻⣭⡭⢥⡶⠖⠚⢻⡀⠀⠀⠀⠀⠀⡠⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠉⠷⣀⠀⠀⢳⡈⠙⣎⢑⣒⣒⣚⣯⡭⠽⠖⠞⠻⠋⠹⠩⠃⠀⠀⠀⠊⢀⣠⣴⠾⠓⠀⠀⠀⠀⠎⠀⠀⣠⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠸⠦⣹⠂⠀⠀⠙⢆⢸⠙⠃⠘⢁⣊⣀⣭⣤⣤⣤⣶⠶⢾⣿⠿⠽⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠙⠟⢳⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠋⠀⠀⠀⠀⠈⠿⠾⠿⠟⠛⠉⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⣉⣳⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣖⣩⣏⣙⣦⠀⠀⠪⢨⣛⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠉⠉⠉⣿⠹⠟⠃⢰⣧⠀⠘⠉⣴⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣰⢀⣤⠀⠀⣧⠀⠀⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⡿⠚⢠⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠟⠷⠀⣿⢸⡷⠃⠀⣿⠘⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠿⠿⠿⣿⠶⠿⠿⢻⡟⠗⠻⠒⣟⠀⠀⠀⠀⠀⠀⢸⡗⠿⠿⠷⢿⠾⠶⠾⠖⡔⠲⠶⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡀⣷⡀⢸⡷⠋⠐⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠊⠋⠀⢸⡇⠄⠀⠀⣇⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣯⢤⣶⣤⣼⣥⣤⣤⠀⠓⠐⠄⠀⠀⠀⠀⢸⣧⣤⣤⣤⢘⣀⣠⣤⣄⢃⣠⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠀⠀⠈⠁⠀⠂⠠⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⣀⠀⣾⢠⠄⠀⠈⣷⢦⠄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡔⠀⠀⠀⠀⠀⠈⢛⢸⡇⠐⠋⠀⢿⠈⠠⠴⠀⡟⠁⠨⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠎⠀⠀⠀⠀⠀⢀⠔⠁⠘⣿⣯⣉⠉⣮⢙⣛⠛⢱⡎⢛⠛⠓⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠈⠀⠀⠀⣠⠄⠈⠀⠀⠀⠀⡟⣿⣿⠀⢻⣼⣿⠃⢸⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠘⣻⣤⣾⣿⣿⣿⣯⣶⡶⠟⠉⡇⠀⠀⠀⠀⠀⠀⡷⡶⠶⠶⡸⠶⠶⠶⢮⠶⠶⠶⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣤⠘⠒⠠⠂⠀⣀⣤⣶⣾⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⣿⠀⡠⠀⢸⡆⠀⠀⠀⡇⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⠀⣀
⠀⢀⣹⣷⡤⠶⠚⠋⢹⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⣧⣤⣤⣤⣨⣬⣥⣤⣈⣧⣠⣤⣀⡇⠀⠀⠐⠻⢿⣦⣀⣴⡶⠟⡻⠿
⠀⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⣙⠀⡀⡀⣈⣇⣀⣀⣀⡇⠀⠀⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⢷⣀⣀⣀⣙⣿⣤⣶⠶⠖⠶⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠔⢚⣷⣶⣤⣤⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢶⣟⠁⣀⢀⡀⠀⠀⠀⠀⠀⢿⣿⢋⣉⠁⠀⠈⠻⣶⢒⣀⣀⣤⣤
⠀⠀⢀⣠⣴⣀⣀⣿⣿⡟⣛⣓⣲⣿⣿⣿⣦⣀⡄⠀⠀⣀⡀⠀⣤⡶⢎⠀⠈⠓⣦⣠⢤⠶⠏⠹⢿⡃⠄⢀⣀⡀⠀⠀⠀⢿⢧⣾⣿⡿⣟⣛⡤⠭⠹⠿⠖⠁⠃
⠀⡀⠘⢿⣿⣿⣯⣽⣷⣶⣤⡤⣼⣛⠋⠉⠙⢛⣳⠖⢚⣫⡵⣀⠙⢿⣦⣖⠋⠉⠀⠙⢳⣄⣠⣤⠖⠋⠛⢭⡛⠀⢀⣀⡀⠘⠋⠉⠉
⠀⠀⠀⠀⠉⠻⢿⣿⣿⡛⠛⢳⣿⣿⣿⣳⣞⣩⡤⠚⠉⢉⣩⠥⠆⠀⠙⣿⣷⣴⡲⢿⠋⠀⠙⢶⣌⣢⡤⢴⣉⣾⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣈⠉⠉⠙⠿⠛⠛⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡦⢤⣶⣾⣿⣶⣶⣾⡯⠽⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠿⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⢳⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡁⠀⠈⠑⠂⠄⠀⠀⠀⠀⣀⡤⠤⠒⠉⠁⠀⠀⠀⢀⣀⠼⠇⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠢⢍⡓⠢⢄⡀⠀⠀⠀⢠⠉⠁⠀⠀⠀⠀⠀⠀⢂⣉⢥⡴⠾⠋⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡍⠙⠖⠦⡁⠀⠀⢼⣤⠴⠖⢈⣁⣀⡤⠊⠉⠃⠘⠀⠁⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠲⣤⣄⡀⠈⠀⠀⢸⡇⢠⡤⠖⠚⠋⠁⡼⠁⢀⣴⣊⣤⣴⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢿⠿⣶⣄⡀⠐⠀⢸⠀⠀⠀⣠⡿⠤⠚⠛⠉⠉⠀⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠸⣆⠈⢮⡙⠓⡤⣼⠶⠖⠋⠁⠀⠀⠀⢀⡀⠠⠤⠤⠶⢛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡄⠀⢹⡄⣿⠓⣄⠀⠸⠄⠀⣀⡀⣀⣀⣀⣤⡤⡴⠶⠒⠊⣹⠏⠀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠙⣇⠀⠈⠷⢶⠒⠛⠉⠹⠉⠁⠀⢸⡞⢁⠤⠂⠰⠃⠐⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣞⣻⠖⠋⢳⢀⠈⢦⡀⠇⢸⠀⢀⠀⠀⠀⠀⣠⣏⡴⠿⠥⠴⠓⠒⠒⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣱⡦⡀⠀⢀⠛⠀⠰⢏⡀⢹⢦⠙⠦⠼⠴⠖⠒⠒⠘⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠃⠀⠞⠀⠀⠀⠈⠳⣇⡏⠀⠀⠀⠀⠀⠀⣀⣈⣭⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡴⠀⠀⠀⢀⡀⠀⠀⠀⢰
⠀⠀⠀⠆⡀⠈⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣤⣀⠼⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⡙⠷⠂⠀⠈
⠀⠀⠀⣤⡉⠂⢄⠒⠠⠱⠲⠤⠤⠞⠤⢄⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠉⢻⠃⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊
⠀⠀⠀⠀⡐⠠⢄⠀⠀⠂⠈⠙⠢⣮⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡼⠁⠀⠀⠀⢿⠎⠀⢀⡤⠄⡂⢀
⠀⠀⠀⠀⣍⠒⠠⢤⢀⠀⠀⠀⠀⠄⠀⡈⠀⠛⠢⠀⠀⠠⠈⠒⠹⢲⠎⣅⣀⡀⢀⠎⠎⠀⠀⠈⠀⡀⠐⡌⡆⠀⠀⠀⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠉⠛⢿⠌⠀⠀⠀⠳⢄⣰⣀⠤⠃⠀⠀⠀⢄⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⡀⠀⢀⣀⠀⠀⢀⡾⠀⠀⠀⠀⢠⡟⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣿⣁⡀⠀⠀⢀⡎⠀⠠⣪⢟⡭⣿⣿⣆⠀⠀⠀⠀⡀⠘⠐⠊
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⡟⠀⢀⣄⠁⠊⠀⠀⠛⢉⣄⠀⠀⠀⢇⡀⡀⠀⠀⠄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠃⠂⠀⠉⠀⠀⠀⣤⠀⠈⠉⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠰⣄⢀⣄⣀⠼⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣾⢁⣀
⠀⠀⠀⠉⠑⠒⠀⠀⠀⠀⠒⠒⠀⠀⠀⠠⠀⠀⠀⡀⢀⠄⢀⡽⢞⣫⠝⢛⣡⣷⣀⠀⠀⠀⠰⣿⣦⣀⠈⠙⠯⣌⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⣋⣷⡦⣻⣽⣾⡯⣭⣭⣹⠿⠀⠀⠀⠈⠻⣝⠿⠁⠀⠈⠉⠒⠠⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠤⠐⠀⠀⠀⠀⠀⠉⠛⠓⠉⠉⠉⠁⠉⠙⠊⠁⠁⠂⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⢆⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⡀⠀⢏⡉⠁⣀⠜⠁
⠀⠀⠐⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⡂⠀⠀⠀⠰⠀⢀⡉⠓⠀⠀⠀⠀⠀⠐⠒⠢
⠀⠀⠀⠀⠠⠇⠀⡀⠀⠀⠇⡀⠀⠈⠂⠚⠀⠀⠀⠀⠀⢯⠀⢀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢷⣄⠡⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⣐⢁⠀⠀⠀⠙⣣⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⡆
⠀⠀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠛⠯⠉⠑⠂⢊⠕⠉⠢⣄⠑⡔⣀⠀⠚⠁⠀⠐⠂⠈⠀⢀⡀⠁⢀⣴⣁⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠻⠿⠉⠀⠀⠀⠀⠈⠒⠀⠄⠈⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢀⡀⠀⠀⠀⠀⠈⠁⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢝⡳⠶⠬⠤⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡽⠲⣶⢶⣬⣛⡿⣿⣭⠉⠀⠲⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠈⡹⢦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢹⣟⣶⣎⣉⠟⠻⢿⣿⣻⣦⣄⡀⠀⠉⠒⠽⠒
⠀⠀⠀⠀⢠⠔⠀⠀⠀⠈⠻⢦⣄⠠⠖⠁⠀⠀⠈⠛⢦⣄⣀⣠⣴⠞⠀⠀⠀⠀⢸⣿⣟⣟⣧⡜⠛⢲⣶⡉⢉⠻⢿⣝⢿⣷⡦⢤⡐⠂⠀⠈⢠⡀
⠀⠀⠀⣤⡻⣶⣄⠀⠀⢀⠠⠊⠛⠳⣦⡀⠀⠀⠀⢀⢠⣽⠟⠋⠁⠀⠀⠀⠀⠀⠀⢻⣿⣎⢿⣳⣴⠁⢨⠟⠳⣤⠖⠙⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⣠
⠀⠀⠀⠘⠻⣮⣹⢷⣆⡉⠀⠀⠀⠀⠀⠙⢷⣤⣾⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣝⢿⣷⣧⣠⡄⠉⡳⢯⣀⡼⢿⣿⣿⣟⣻⡭⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠹⠶⢿⣿⣶⣀⠀⢀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣬⣉⠛⠿⢿⣧⣴⡛⢳⣔⢿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣯⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⢶⣮⣍⣹⣩⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡆⢢⡦⣭⣞⣋⣻⣷⢎⡶⣶⡀⡤⠄
⠀⠀⠀⠀⠀⠀⠘⣤⡉⠛⠙⠷⠿⠥⠿⠿⠾⠏⢿⣶⡟⠴⠛⠋⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠈⢣⣄⣐⢀⣀⣲⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣤⠞⠉⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠉⠉⠛⠛⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢻⣧⣴⣿⣟⢳⣇⣦⡀⠀⠀⠀⠀⠀⡀⠳⠆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠐⣂⢴⣮⠔
⠀⠀⠀⠀⠀⠀⢈⠄⠒⠀⠤⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠹⢾⣿⣾⣿⣿⣿⢿⣿⣿⣿⣴⣾⠷⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠛⠒⠲⠖⠲⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠫⣟⢿⠟⣩⠧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠽⠋⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠄⡠⣤⣤⠀⠀⠀⠀⠀⠀⠄⠶⠶⠛⠛⠉⠉⡉⢉⡽⢣⣤⠒⢆⠀⢀⡖⢢⣄
⠀⠀⠀⠀⠀⠰⡈⠐⢄⣀⠀⢁⡤⠒⠀⢉⡟⠁⡀⠀⢀⣀⠁⠤⠄⠠⢤⣄⣲⣦⡵⠞⠋⣠⠟⣈⠆⠐⡄⡔⠀⢎⡘⢷⡀
⠀⠀⠀⠀⠀⡆⠈⠑⠂⠂⠤⠉⠀⢀⡴⠋⠀⠀⢡⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢠⡟⠂⠀⢋⠖⠁⠑⢎⠊⠀⠚⣧
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠚⠓⢮⠀⢈⠖⠛⠂⠀⢸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠊⠉⠀⠀⠀⠈⠉⠂⠀⠘⡇
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡆⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡆⣇
⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠀⣉⢒⠂⠀⠀⠐⠒⠒⠛⠛⠉⠉⢿⡁⠀⠀⠀⢸⠀⢸⠀⠀⠀⠐⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣠⡤⣶⣯⣶⢿⡷⢿⣿⢿⣺⠟⢋⡩⠭⠝⢛⣓⣢⠉⠛⠒⠂⠘⠀⠘⠂⠒⠒⠋⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠞⣫⠾⣭⢴⡭⢖⢭⣺⣧⣴⠋⢉⣠⡏⢳⡀⠀⢠⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⡟⢸⠁⢰⠁⣰⢁⠎⠀⠀⠀⢉⠉⠀⢀⠔⠉⠉⢧⢳⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠃⡾⢀⡇⠀⢀⡏⢰⠀⠎⢰⡆⠠⣸⡿⢸⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⢷
⠀⡼⠁⠀⠀⠀⠠⠤⠄⠒⠁⣀⠔⠁⡿⣇⡀⠀⠀⠀⠀⣧⡼⠀⠀⢸⠀⡇⠀⠀⠘⡇⢀⡜⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⠀⠔⢈⣀⠀⠀⠀⠈⠉⠉⠀⣂⠜⠁⠈⠙⠓⠒⠒⠒⠒⠒⠒⠒⠶⠶⠤⠤⠴⠶⠗⠋⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘
⣼⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠴⠤⠴⢖⣒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠
⣿⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⢰⠀⠀⠀⡐⣳⣤⠗⠚⠛⠓⠚⢭⣲⢞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠐
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠜⠀⠀⢰⡯⠗⠚⠉⠚⠿⠭⣙⠢⡀⠑⡙⡆
⠈⠓⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠊⠀⢀⠤⠒⠒⠦⣌⠑⣜⣆⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠳⡜⡜⡖⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⢳⡦⠙⠁
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠳⢤⣀⣀⣠⣴⢿⣀⢀⣰⣤⣤⠴⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢄⡀⠀⠈⠉⠁⠀⢢⣭⠟⠁⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠛⢶⣀⠀⢀⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⠙⣷⣟⡁⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⠞⠁⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡍⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠻⣶⣄⢄⠀⠀⡀⢀⣵⡿⠃⠀⠀⠀⠀⠀⡙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⡾⠷⣶⠟⠒⠳⣦⡀⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠙⢿⣦⣀⣵⡿⠋⠱⠀⠀⠀⠀⠀⢀⣼⣾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢉⣁⣀⠀⠤⢤⡄⠀⣎⠛⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⡿⢿⣷⡀⠀⠀⠀⠐⠀⣸⡾⢣⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⡛⠋⠉⠉⢛⣦⠤⠲⠄⡼⠃⠈⣿⠿⢷⡄⠀⠀⠀⠀⠐⣤⢾⠓⠀⠀⠙⠳⣼⡆⠀⢀⣾⣏⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢡⡆⠀⠀⠀⠀⠀⣻⢧⣤⡴⠞⠻⡳⣼⣀⠀⢻⢷⠶⢤⣤⣾⣝⠅⠀⡐⠄⠀⠀⠘⠟⣶⣟⣿⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⣏⠀⠉⠀⠈⠄⢸⠛⠿⣏⣀⣀⣙⡆⠀⠀⠙⠶⠶⣶⡄⠀⠀⣠⣾⣝⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡞⠀⠀⢸⡄⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡜⠀⠀⠈⠉⠙⣿⠀⠋⢠⠶⠆⠀⠘⢷⣌⣼⣿⣷⠟⠁
⠀⠀⠀⠀⠀⣠⡞⠁⠀⢠⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣾⠃⣴⢶⡄⠀⣠⣄⠀⠀⠻⢟⣿⢿⡄
⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠞⠁⠈⠳⡌⠁⠈⣀⡀⠀⣀⡀⠈⠻⣆
⢀⣠⡾⠋⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⣾⣿⣷⣿⠘⡉⠋⠀⢹⣷⣤⣼⠃
⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣿⡏⠀⠰⣿⡉⢸⣿⠿⠁
⠙⢷⡄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣠⡾⠉⠄⢠⡼⠛⣧⣀⣴⠿⢷⠾⠁
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣠⠾⡃⠀⢀⣴⠟⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⡄⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣴⠋⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠀⠀⠀⠀⠀⠀⠀⠑⣠⡞⠑⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣠⡾⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⣀⡀
⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡌⠉⡀⠙⣶⣂⠀⠀⢠⣄⣀⣰⡿⠃⢦⣄⣀⣘⣿⠆
⠀⠀⠀⢻⡇⠘⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⢸⠀⣿⡏⡆⠀⠀⠉⠉⠁⠀⣤⣤⡈⠉⠉⠀⠐⢲⡄
⠀⠀⠀⠘⢷⣤⠐⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⢸⠇⠀⠀⢸⠀⣿⣿⠀⠀⠀⠰⢥⣄⣴⡾⠟⠁⠀⡀⢀⣴⡿⠁
⠀⠀⠀⠀⠈⢻⣧⣌⠐⢀⠀⢂⠄⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⢹⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢻⣿⡦⡀⢪⠄⠐⡄⠀⠀⢀⠀⡄⠀⠀⠀⡇⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣜⠦⠀⠀⠀⠀⣆⣷⣆⠀⢸⣷⣿⡿⠀⠀⠀⠀⢀⡀⣹⠟⢻⣿⠷⠴⣾⡅⠄⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠦⠥⠀⠀⢻⣼⣿⡦⣸⣿⡿⠃⠀⠀⠲⣦⣀⠽⠃⢐⣿⡿⢶⣶⣿⣷⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⠄⢤⣤⣤⠄⢠⣤⢤⢍⠛⠿⠿⠛⠀⠀⠙⠲⢾⣿⣟⣶⣛⣻⣿⣷⣿⣿⡿⠟⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡰⠶⠂⣿⠠⠴⠆⢸⡅⠶⠦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡿⠀⠀⠀⢸⠇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⠛⠓⠉⣻⡙⠛⢂⣼⡇⠀⠀⠀⠀⠄⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⢠⡄⣀⡀⠿⣄⡄⣠⣿⣧⣤⣤⢽⢷⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣬⡇⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠛⠀⡤⠂⠀⠀⠀⠀⠠⠤⢦⣤⡔⠲⣶⠖⠚⠃⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣒⣶⣶⣶⣼⣥⣶⣿⠅⣀⡀⡛⠓⠶⣄⣲⣶⠶⠶⠤⣤⣄⣈⣡⣿⣿⣆⠀⣀⣤⡄
⠀⠀⣹⢦⡠⣄⣀⣾⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢙⠞⢿⡒⢦⣄⣈⡁⠐⠂⠚⠋⠁⠀⢀⣠⣼⣿⣿⣿⠃
⠀⠄⣠⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⠀⠉⢺⣍⠉⠉⣛⣳⣶⣤⣀⠀⣽⣿⣿⣿⣿⣿⣿⠄
⠀⠘⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠌⣱⣿⣿⣿⡿⠿⠿⠷⠿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠁⠀⣰⠏⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⣍⣀⣉⣉⣉⠙⠛⠒⠒⢐
⠀⠀⠀⠀⠀⣠⣾⣄⣀⣐⣀⣀⡟⢠⠍⠉⣳⣆⡤⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⠁⠀⠉⠉⠉⠳⢀⠉
⠀⠀⠀⠀⠀⢧⣦⣤⣬⣭⣍⣉⣉⣿⡷⠟⣋⠡⠒⠁⠀⠀⠀⠀⠞⠛⠻⠛⠛⠛⠛⠓⠒⠂⠒⠛⡁
⠀⠀⠀⠀⣠⣸⣻⣯⣛⢦⡴⠟⢋⣡⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠷⢿⠿⢿⡻⠿⠛⠛⠛⢉⠉⠟⠁
⠀⠀⠀⠀⠓⠮⢭⣛⡛⠿⢷⠞⡉⠋⠰⠦⠶⠀⠀⠀⠀⠀⠀⠀⠈⢂⣰⠁⣀⠤⠐⡀⢅⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠂⠐⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠤⠄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⠀⠀⠀⠀⠈⣦⣄⣀⡀⡀
⠀⠀⠀⠀⢀⣠⡤⣼⣿⣶⣷⣄⡀⠀⠤⠄⠙⠓⠀⠀⠀⠀⠀⠀⠀⠆⠛⠻⠗⢀⣀⣤⠤⠤⠀⢰⠃
⠀⠀⠀⠀⠻⣷⣾⣦⠙⠛⢿⢿⣿⡆⢀⣠⠤⠶⣦⠀⠀⠀⠀⠀⠀⠰⣦⠤⣤⣀⣀⣀⣀⠀⠀⠀⣹⠆⠄
⠀⠀⠀⠀⠀⣈⡙⠿⣿⣷⣢⡑⠎⠉⠉⢐⡚⠉⠈⠐⡂⠀⠀⠀⢠⡀⢻⣷⣝⢿⡂⠘⠉⠛⠉⠈⢉
⠀⠀⠀⠀⠀⠉⣅⣀⠈⠛⠻⢿⣷⠂⠁⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⣄⠀⠩⡟⠈⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠈⠁⢀⠀⠀⠀⠀⢀⢤⠀⡆⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣉⣉⡤⢬⣉⡉⠉⢉⣡⣈⡷⠁⠀⠀⠈⠒⠒⠦⠤⠦⠀⢶⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡀⠀⢀⣠⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠙⣿⣁⢄⣒⢐⡄⠐⠊⠀⠀⠀⠀⠠⠄⠈⠑⣀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⠉⣭⢄⣀⡀⠀⠀⠀⠀⢠⡄⢠⣅⡬⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠓⠈⠁⠀⠀⠀⠀⢠⡉⢩⠀⠠⠀⠄⢉⡐⡀⠀⠀⠀⠙⡜⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠈⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠘⣬⣆⠀⠔⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡠⠂⠊⡀⠀⠰⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣴⡺⠟
⠀⠀⠀⠀⠀⠀⠀⡅⠒⢢⣀⠙⢁⠀⠐⠺⣶⢤⠚⠗⠁⠀⠀⠀⠤⠄⣪⠀⠐⢒⡩⠂⠀⠀⠀⠀⠀⠀⠠⡤⠄⢀⠐⡀⠠⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠷⠤⠴⠛⠚⠛⠒⠚⠀⠀⠀⠀⠀⠀⢰⠡⣤⣴⠒⣭⠄⠲⠖⢤⠀⠀⠀⠀⠀⠇⡀⠀⠈⠙⠖⠲⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢢⣖⣀⡠⠴⠃⠀⠀⠀⠀⠈⠒⠒⠒⠒⠢⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⣁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠃⠀⠀⠀⢠⠂⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢃⠀⠀⠀⠀⠰⠈⡀⢄⡀⠤⠀⠀⠀⠀⠄⡤⠀⠀⠀⠀⠀⡐⠀⠀⠀⢠⡿⠁⠀⠀⠀⠸⡄⠀⣀⡠⠠⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠰⠆⠀⠀⠀⢀⢠⣤⡀⠉⠰⠂⣀⠀⢂⣰⠄⠀⠀⠀⠀⢀⡓⢀⡠⠴⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠀⠀⠀⠀⡀⠀⠀⠈⢃⠀⢈⢉⠰⠶⠤⠄⠊⠛⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⣀⡌⠗⠀⠀⠀⠨⠀⢠⣤⠠⠀⠴⠆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠤⠔⠂⠲⡌⠉⠉⢀⠙⠆⣀⣀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠺⡄⠉⠀⠀⠱⣄⣀⣤⣤⠴⣴⠖⠛⠛⠙⢧⡀⠠⠀⢐⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⢰⡀⠀⠀⠀⢠⡖⠠⠀⢤⢀⡀⠀⠀⠀⠀⠀⠙⡆⣀⣠⣤⠽⡶⠖⠛⠋⠛⠉⠀⠄⠀⢙⡄⢀⡠⠴⠌⠓⠒⠛⠉⢉⡄
⠀⠀⠀⠀⠐⡈⠑⠒⢀⡌⢀⡃⠀⠀⠀⠀⢀⢠⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⡜⡅⠀⠀⠀⠰⡀⢀⣠⠤⠴⠄⠐⠚⠋⣉⢀⣤⠆⠠⠴⠚⠐⠂⠈
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡽⡙⠚⠲⢿⠆⠉⠀⠀⠀⠀⠀⠹⣠⠔⠒⠛⠉⣉⣀⢠⡦⠤⠠⠖⠂⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⡂⠁⠀⠀⠀⠀⠀⠀⠙⠤⠐⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠒⠊⠙⠿⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠯⡀⠀⠀⠀⠀⠀⠀⠙⠟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠐⠊⠉⠀⠀⠁⠀⡈⠒⢄⠀⠠⠔⡈⠄⣂⠤⠌⡙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠈⠢⡀⠀⠀⠀⠀⢀⠠⢓⠀⠁⠒⢹⠀⠀⠀⠀⠀⠀⠀⠄⠙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⡏⠀⠀⠀⠀⠀⠀⠂⢀⠑⠄⠐⣨⡔⠂⠅⠒⠀⠂⠀⠑⠤⡀⠀⠀⢀⠠⠀⣈⣀⡼⠿⠃
⠀⠀⠀⠀⢀⡤⠦⠖⠛⠈⠐⠀⠈⠢⢀⠀⠀⢀⠠⠒⠈⠀⢀⠈⠀⢇⠀⠀⠀⠀⠀⠀⠁⣢⠈⠀⢈⣵⠾⠟⠋⢁⣠⠴⠂
⠀⠀⡏⠁⠀⠠⡀⠀⠀⠀⠀⠀⠈⣰⠄⠁⠠⠔⡾⠁⠂⠁⠀⠀⠀⢀⠁⠢⡀⠀⠠⢒⡠⣤⡤⠖⠋⢀⣀⣴⠟⠋⠁
⠀⠀⠳⣄⠈⠠⢌⠐⢄⠀⠤⢐⡡⢄⡢⠤⠄⡀⠑⢄⠀⠀⠀⠀⠀⡀⠜⠂⠀⣑⣾⣿⠟⢉⣀⣶⠶⠛⠁
⠀⠀⠀⠈⠻⢦⡀⠑⠠⡀⠂⢹⠀⠀⠀⠀⠀⠀⠐⠀⡈⠂⢀⢒⡩⢔⣪⠶⠟⠋⣉⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠐⢄⠑⠤⡀⠀⠀⣀⠄⠂⡉⠀⣠⡵⠚⠋⣀⣤⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠉⠢⣌⠀⠨⠔⣊⡤⠒⠋⡀⣠⡶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠑⠔⠋⢁⣢⡾⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣼⠞⠋⠉





⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣶⣿⣷⣦⣀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⠰⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⣿
⠀⠰⢿⣿⣦⣀⠀⢀⣈⣙⣿⣿⣯⣻⣶⣿⣦⣄⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠰⠿⠗⠒⠲⠶⡿⠶⠶⠒⠒⠂⢺⡷⠒⠒⠒⠒⣺⣿⡀
⠀⠀⠈⠻⠟⢿⡟⣛⠋⠉⠉⠀⠈⠛⠿⢿⣿⣻⢿⣶⣄⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⣿⣥
⠀⠀⠀⠀⠀⠛⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣨⣿⣿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢿⣿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⡴⡶⠞⠋⠹⠿⣛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢧⣀⣀⣀⣀⣠⣇⣤⣠⣤⣤⣤⣼⣠⣤⣤⣤⣀⣼⣿⠟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⠶⠽⣷⣀⠔⠊⠉⠉⠉⠓⠤⢐⡚⠹⠂⠀⠀⠀⠛⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡈⣧⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠤⠔⠊⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⡿⣿⣶⣤⣀⡀⠀⠀⠀⢀⡼⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣾⣿⣿⡷⢾⣽⣿⡷⢶⣰⠏⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡛⠻⢿⣙⡻⠿⣿⣿⣿⣇⠞⠉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣶⣤⣙⡓⣾⣿⠋⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢿⢿⣛⡹⠉⠋⠛⠛⠿⠿⢿⡇
⠀⠀⠀⠀⠀⣴⣿⣿⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠐⠛⠛
⠀⠀⠀⠀⢸⠁⠃⢸⠁⠈⢻⠘⣧
⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠄⠀⠙⠩⠄⠀⠈⠅⠀⠀⠀⠀⢤⣤⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠦⢄⡀
⠀⠀⠀⠀⢡⠀⠀⠀⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⡀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⣉⣦
⠀⠀⠀⠀⠈⣧⣠⠀⢰⡀⢠⣃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠘⠃⠀⢱⠀⢱⠀⠀⠂⠀⠨⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠈⢻⣦⣻⣧⣼⡟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡁⠘⢠⠐⠄⠰⠀⢁⡼⠀⠀⠀⢀⣠⣤⡤⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⣀⠦⠀⠧⢀⠁⠑⠀⢈⠀⢰⡀⡶⠌⠀⠀⠀⢰⣿⣯⠀⠀⠀⠀⠀⣠⡼⠂⠀⣠⣤⠐⠀⠀⠀⣀⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⢿⣤⡃⡁⢀⣄⣀⠆⡠⠖⠈⠉⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣶⡾⠿⠋⠀⠀⠀⠻⠿⠿⣶⡶⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠄⠀⠀⢀⣀⣀⣀⡀⠀⠄⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⢙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠁⠀⠀⠑⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢻⠏⠉⠒⠺⠋⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠱⢄⠀⠀⠀⠈⠰⢌⡀⠀⠀⠀⠀⣠⡞⣩⠖⠁⠀⢀⠄⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⢠⡶⢀⠑⢄⡀⠀⠀⠀⠉⠐⠀⠒⢛⣸⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠺⡃⠀⣈⠠⢄⠀⠀⠀⠀⢀⠜⠁⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠶⡥⢀⠂⠟⠢⢠⡴⠁⠀⠀⢀⡔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠑⢄⠚⡇⠐⠖⡀⢃⠀⢀⡴⠃⠈⠢⡁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠁⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠃⠂⠤⠀⢑⣤⡰⠆⡀⠈⠛⢩⣦⡀⠀⠆⠈⠑⠄⡐⠠⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⡤⠏⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⡀⠈⠳⡀⠛⣀⠚⢁⡝⢦⣀⠀⠀⠀⠀⠐⠠⠀⠀⢀⡴⠊⠀⠀⡴⢊⡀⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠁⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡚⠲⣌⡰⢤⡄⠨⠈⠕⢤⡀⠀⠀⠀⠀⠈⠁⠀⠀⣴⡼⡄⠠⢘⣏⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠞⠛⠿⣳⣞⠤⠰⠷⣀⠈⠒⢄⡀⠀⢰⢀⠄⠚⠃⣤⠂⣹⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠂⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠴⠊⠁⠀⣄⡴⠟⢡⣑⢄⠂⢀⠰⣿⢛⣈⠒⠼⠇⠲⠶⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠉⠁⠉⠓⢲⠒⠤⠒⠋⠀⠀⢀⡠⠖⠻⠐⢿⢈⣡⠞⠛⢦⣜⡋⢸⡄⢀⡘⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⣼⠀⠈⠀⣴⠂⢄⠄⢀⡀⠀⠀⠀⠀⢸⡄⢀⡠⠐⠋⠀⠺⢖⣤⠞⠋⠀⠀⠀⠀⠈⠻⣦⣀⠛⣁⡴⠋
⠀⠀⠀⠀⠀⠀⣿⠠⠻⠴⠉⢠⣤⡀⣼⠃⠨⠈⣒⡐⠾⠛⣉⠉⠰⠖⢋⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠤⠭⢠⣄⡐⠖⠀⢉⢀⢠⠠⠫⡅⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠲⣬⣤⠴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⢚⢼⠀⠳⠀⢾⠆⣠⣤⣶⣶⣤⣴⣦⣤⣄⡀⠀⢠⠖⠙⠠⠌⠕⢆⠀⣇⠀⠀⠀⠀⢈⡇
⠀⠐⠋⠓⠋⠛⠛⢌⡌⣄⡰⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠱⣌⣂⣁⣐⠤⡎⡔⣡⣤⣭⣭⣥⣤⣑⠆
⠀⠀⢀⠌⢩⠗⠠⠤⢉⣉⠀⢠⠖⢯⠿⢨⣿⣿⣻⣻⣟⢟⣿⠹⠿⣄⠱⣄⣀⣀⡠⠃⠉⢙⣛⣛⡛⠛⠛⠉⢩
⠀⠰⠁⡰⠁⠀⠀⠀⣀⡠⠬⠆⠓⠄⡑⠒⠡⠥⠈⠀⠁⠀⠭⠔⠊⡠⢇⡀⢄⡀⠀⠀⡘⠥⣀⣀⣈⠇⠀⠀⣠
⠀⢸⠀⡁⡔⠂⢉⣁⠠⠄⣒⡗⠀⠀⣂⢌⠉⢑⣒⠒⠒⠒⢂⡉⠁⠀⢯⠀⣀⠗⠒⢄⠫⣛⠲⠶⠶⠶⢖⡫⠇
⠀⠀⡇⡇⢈⠭⠐⣂⣈⠥⢔⣾⠀⣎⡸⠁⡴⠁⠈⠓⠒⢲⡘⢋⠤⠤⠠⠄⣘⠢⠠⠋⠐⣷⡈⠉⠉⠉⢀
⠀⠀⠸⢐⠀⣭⣛⣷⣬⠯⠟⣋⡈⠚⠃⢰⠅⠀⠀⠀⠀⠀⠃⢃⠀⠀⠀⠀⠀⠑⡢⣄⡀⢱⠳⠲⢄⡀⠺⠃
⠀⠀⠀⠙⢓⣈⢉⠀⠀⡴⠫⡑⠈⠳⡀⠸⣀⣀⣀⣀⠠⠔⠁⠈⠢⣄⠆⠀⢰⡾⠋⢻⡇⠀⠀⠐⠑⢌⠢⡀
⠀⢰⢎⠉⠙⣦⣠⡵⣄⢇⠀⠈⠀⢠⠇⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣬⣑⢤⣘⠧⣤⡺⠗⢠⠘⡀⠀⠄⢣⢡
⠀⠀⠣⡻⡋⠉⢳⣄⣬⢦⡑⠒⠛⠁⢰⣿⠶⣭⡰⡀⢶⢆⢸⣁⢻⣼⣿⡆⠈⠉⠀⢀⣠⣤⠣⡈⢆⠀⠀⢺
⠀⠀⣠⡑⣜⢟⠋⠙⣦⣀⡸⡆⠠⡦⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⢀⣠⣴⡾⠟⢋⠭⠰⠈⠒⠷⣤⡞
⠀⠀⠙⠁⠈⠢⣑⡨⠭⠒⠊⠁⠀⢀⡤⠒⢟⠉⢝⠉⢛⠲⣄⠀⡤⣒⠽⠟⠋⠁⠀⠀⠸⣀⠟⠉⠒⢄
⠀⠀⠏⢹⡎⠑⠆⢀⣀⠀⠸⠳⡀⡎⠁⠀⠠⣖⡚⣤⠀⡀⠈⢣⠈⠀⠔⠂⠀⢰⠒⢦⡀⠸⠀⢄⠀⠀⠑⡀
⠀⢀⠃⢸⠃⣸⠀⢀⠂⡇⢰⢠⠃⡧⣀⣀⠠⠈⠙⣛⠄⠀⢠⢺⠀⢠⠒⠒⠒⣺⠒⠒⠛⣲⠑⢄⠀⢠⡤⣁
⠀⢨⡁⢜⠀⡌⠀⠈⠦⠀⠈⠋⠀⠐⢄⠀⠱⢄⡀⠔⠐⢒⡡⠃⡎⠈⠑⢦⣄⡿⠄⠀⠠⣿⠀⣠⡌⢩⡡⠴⠃
⠀⢸⢀⡇⠐⢣⠒⢈⣉⣉⣩⣉⡁⠒⣄⡉⠐⠒⠒⣒⣊⠁⠀⠀⠈⡖⡖⠒⠀⠛⠒⡶⠴⢟⢢⡈⠀⢀⡤⡀
⠀⢸⣰⠂⣸⠈⡄⠀⠀⠀⠀⠀⠀⢠⢳⢹⠀⡴⢍⡂⠈⠫⣲⡄⢰⢠⠁⠀⠀⠀⠀⡇⠀⣨⠤⠇⢰⡁⠀⢳
⠀⠀⠉⢒⡂⠤⠵⡄⠀⠀⠀⠀⢀⣞⠥⢂⠸⡀⠀⠈⠁⠉⢀⡕⡌⠘⡄⠀⠀⢀⡴⠀⠀⠇⡤⠔⡆⠨⣍⣁
⠀⠀⠀⠘⠦⣤⣐⡻⣷⣶⣶⣾⢿⣂⣤⡤⠇⠈⠑⠢⠤⠔⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⣰⠀⠑⠤⠇⡆⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡐⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠘⠈⠂⠀⠀⠂⠚⠰⠰⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠳⠬⢒⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠻⠶⣂⢀⠀⠀⠀⠀⠀⠀⣇⠈⢙⣿⠃⠉⣱⠀⠀⠀⠠⣦⠀⣔⡀⠒⣶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣈⣉⣰⣤⢆⠀⠀⠀⢀⡟⠛⠻⣿⠛⠋⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠘⠻⠀⠀⠀⠸⣿⣷⣾⡟⠿⠻⠿⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⠀⠤⣤⣲⣤⣯⣽⣦⣠⣖⣀⡀⠀⠀⠀⠰⠟⠟⠋⠀⠀⠀⠢⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⢀⠁⠈⢋⣀
⠀⠀⠀⠀⠻⠟⡶⠶⠦⠤⣤⣤⡄⠬⢦⣵⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠁⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⢀⣄⠠⢀⠠⠐⠀⢀⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠚⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⡀⠀⣠⡄
⠀⠀⠀⠀⠐⠛⠲⢿⣤⣴⣶⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⠂⠀⠀⠦⠄⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡄⠉⠉⠉⣔⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠬⠠⠔⢀⡂⢀⡀⠀⠀⢀⡀⠀⠈⣠⠍⠐⠢⣴⡺⠟⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣀⢠⡀⡂⡠⠀⠎⠁⢉⠀⡓⢂⣀⣐⠦⠶⠛⠀⠐⠻⠯⢔⣠⡄⣾⠔⠉⠀⠀⠀⠀⠀⠦⠤⡀
⠀⠘⢇⡀⠀⠑⢌⢡⠄⠢⣓⣠⡵⠶⠚⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢐⡠⠄⠀⠀⠈⢣⡼⣈⠑
⠀⠀⠈⠋⣨⣀⣠⣷⠶⠛⠋⠁⠀⠀⠀⠀⢰⣴⠁⡄⠁⠀⠀⠰⠒⠂⠬⠃⠀⠀⠀⠀⣤⣀⣀⡎⠀⢀⡒⣸⢸⠆⣬⢠⣸⠾⠇
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠈⠀⠀⠀⠁⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⣤⠀⠀⠉⠈⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢒⠸⠿⣏⠳⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⢀⣀⣀⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢧⣄⡘⠺⣎⠄⣀⣀⣰⣶⣶⣶⣶⠾⣷⡴⠾⠖⠟⠛⠛⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠓⠣⠈⣏⢻⡌⢼⠋⠉⠉⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠑⠤⣀⣀⠉⣻⡜⣧⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢰⣷⣤⡀⠀⠀⠀⠑⢂⣉⢳⣺⡿⡼⡆⠀⠀⣀⣀⣀⣤⣄⣹⠆⠀⢐⣒⣫⡤⠥⢼
⠀⠀⠀⠀⠘⢿⣷⣯⡃⠀⠀⠬⠒⠋⠁⠀⠁⢲⣽⣤⠬⠭⠤⢖⣒⣛⣛⣭⡭⠵⠒⠒⠚⠋⠁⠂⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣕⢶⣄⠀⠀⠀⠀⡈⠩⠉⣏⠉⠉⣩⣐⠀⢁⠠⠀⠈⠢⣄⠀⣰⠂⠀⠈⣾⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣮⣁⠀⠀⠁⡀⠐⡃⠸⠀⠨⣷⣟⠳⡌⠀⠀⠀⣀⣼⠂⠁⠀⠀⠂⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⢙⠀⠘⠂⠁⠀⢠⡀⠈⠻⣿⣦⡄⢀⣴⣉⢿⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠸⠋⠀⠿⣷⣮⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠒⠚⠛⠉⠉⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠖⠛⠋⠉⠁⠀⠀⢀⣀⣀⣄⣤⣀⣀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠹⣆⠀⠀⠀⠀⠀⢠⡴⠛⠉⠁⠀⠀⠀⠀⠈⠛⢦⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⣆⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠘⢧⠀⠀⠀⠈⠃⠀⢀⣀⣀⣠⣤⡤⠴⠶⠖⠒⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢧⡀⠀⠀⠀⠉⠉⠉⠁⠹⣆⠀⠀⠀⠀⣠⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⢳⡀⠀⠀⠀⢀⣀⣀⣤⡼⠷⠶⠒⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢳⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠻⡄⠀⣠⠞⠋⠉⠉⠉⠉⠉⢹⠟⠓⠶⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢹⡞⠁⠀⠀⠀⠀⠀⠀⣠⢏⡀⠀⠀⢠⡶⠛⠛⠉⠉⠙⠓⠶⣤⣀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠹⣄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠙⣯⠙⠳⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠘⢧⡀⠀⠈⢷⠤⠴⠖⠚⠛⢉⣉⣀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡀⠀⠀⠀⠀⢀⣤⠞⢳⣄⣤⡤⠴⠶⠒⠛⣃⣀⠀⠀⢠⡴⠶⠚⠛⠉⠉⠈⠳⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⡞⠉⠙⣆⠀⠀⢠⡴⠶⠒⠛⠉⠉⠉⢷⡀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣽⡄⠀⠘⣦⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠹⣄⠀⠘⢧⣤⠤⠶⠖⠚⠛⠉⣀⣀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠘⢧⠀⠀⠙⢦⣤⡤⠴⠶⠒⠛⠉⠀⣀⣀⣤⡤⠴⠶⠚⠛⠉⠉⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢧⡀⢀⣀⣀⣤⡤⠴⠖⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢸⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣟⣀⣀⣤⡤⠴⠶⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠃⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡆⠀⠀⠀⠀⠀⠉⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣃⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠂⠈⠙⠶⣄⠀⠀⢀⠊⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⢤⣴⠋⠀⠀⠀⠀⠀⠀⠀⢱⣔⡁⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠅⢀⡾⠉⢠⡀⢄⡀⠀⠀⠀⣠⠂⡐⠊⠓⢤⡑⠄⠂⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠙⢆⠀⠉⠢⢌⠀⢀⡔⠁⠈⠀⠀⠀⠀⠉⢲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠱⠒⡆⠑⢤⡀⠀⠹⠯⢄⠀⠀⠚⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠔⠒⣄⠀⠛⠹⣠⠜⢦⣄⠀⠀⠑⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⠀⠠⢀⠗⣆⠈⠡⣖⠞⢦⠙⠒⢤⣀⢘⡟⣇
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠈⠫⠞⠡⣤⠄⠀⢠⣇⣀⠤⡤⢤⡉⠸⡉⠁
⠀⠀⠀⠀⠀⢠⠞⢡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢡⠔⠘⠁⠈⠀⡠⠊⠈⠙⠃
⠀⠀⠀⠀⠀⠙⠦⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⠀⠐⠐⠈⠉⠉⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢸⣷⠘⠆⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣀⠀⠠⣧⠀⠀⠀⠀⠀⣠⣤⣤⣤⣹⠦⣀⣠⣥⠽⠶⠶⠿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠰⢩⡉⢲⠨⣧⠀⣻⠿⠛⠛⠋⠉⠉⠁⠱⣇⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⠆⠀⠀⠈⠀⠻⣆⠨⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣽⣆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠠⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠸⡿⣯⡳⠤⠀⠀⠀⢀⡢⠄⠓⠚⠍⣎⢧⠀⠀⠒⠒⣂⣉⡹⠴⠥⠔⠒⣒⣈⣉⠭⠭⢋⠄⠀⡀
⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⠠⣀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡭⠭⠥⠴⢒⠒⠒⠋⠛⠁⢄⠀⠀⠀⣀⠀⠀⢊⡿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣮⣙⠢⠀⠀⠀⠐⠀⢀⠄⢳⠀⠀⣞⡳⣄⠀⠀⠀⠀⠀⠑⡄⠐⠃⠀⠀⠀⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣷⣦⡀⡤⠀⢀⠀⠄⠈⠀⠀⠫⣷⣬⡓⠀⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠸⠂⠀⠈⠻⣿⡆⠀⣾⠥⢨⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠁⠀⠈⠓⠚⠃⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⣠⠏⠀⠀⠀⠀⠼⠃⠀⠀⠀⠈⠓⢶⣀⠀⠀⠇
⠀⠀⠀⢀⠐⢄⠀⠠⣤⠠⢥⣀⣀⣀⡼⣀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠀⠀⠑⠶⣶⢁⠂⠀⠀⠀⠀⠀⠓⠨⠁⠀⡠
⠀⠀⠀⠉⠑⠀⡈⠑⠀⠉⠌⠀⠧⣄⡴⠀⠉⠉⢉⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢠⠏⠀⠀⠀⢰⣣⠃⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠲⢦⣉⠂⠀⠀⠀⠀⠀⠈⠋⠀⠀⠄⢸⣄⠀⠀⠀⠀⠄⣀⣤⣄⡰⡏⠀⠀⠀⢠⢒⠏⠀⠀⠬⡁⠀⢢⠐⡄⠀⠀⠀⠀⠀⢀⣀⡠⡆
⠀⠀⠀⠀⢾⠂⠀⠉⠃⠐⠠⠀⠀⠀⠉⠀⠐⠀⡀⠀⠀⠀⠠⠂⠀⠀⠈⡙⠁⠛⠶⢶⣤⡋⠎⠀⠀⠀⣄⠈⢦⠀⠇⡇
⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⣨⡋⠀⠀⠀⠀⠉⠓⠚⠂⠃⠀⠀⠀⠀⠙⠓⠒⠂
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠃⠀⠀⢶⣤⣀⣀⣴⠏⠀⠀⠀⠀⢠⠟⠀⠀⣠⣤⢶⣤⣄⠀⠀⠀⠀⠀⠀⢠⡄⢄⢄
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠻⠿⣦⣄⣀⠀⣴⡎⠀⠀⢪⠞⡵⠚⠿⣯⣧⠀⠀⠀⠀⠰⠀⠀⠉
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠀⠀⣴⣄⢘⢀⠀⠈⠁⣠⠦⠀⠀⠀⠸⣤⣠⣀⡀⡰
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠈⠀⠀⠀⠀⣴⠄⠀⠀⠉
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠏⠀⠀⠀⠀⠄
⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠂⠀⢦⣄⣠⣔⣺⡼⣷⣄⠀⠀⠀⠀⠀⠀⣠⠤⠂⢩⣿⡍⣀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠇⠀⠀⣄⠀⠀⠄⢀⡿⢟⣯⠾⠛⣫⠼⢆⡀⠀⠀⡀⢺⣿⣦⡀⠈⠙⢯⣌⠙⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢗⣋⣽⡔⢛⣯⣴⣿⣭⣉⣙⡿⠆⠁⠀⠀⠙⢯⡻⡯⠈⠀⠈⠛⠒⠤⣉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠰⠄⠀⠀⠀⠀⠉⠻⠻⠟⠊⠉⠛⠂⠓⠛⠋⠹⠁⠀⠀⠀⠀⠀⠀⠙⠂⠈
⠀⠀⠀⠀⠂⠀⠀⢐⡎⠀⠀⠀⡄⢀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⠀⠀⡟⠒⠂⠀⣸⠎⠀⠀⠈
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⣠⠄⠉⠍⠉⣇⠀⠈⠲⠗⡉⠁⣀⣀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⢲⠁⠀⠀⠀⠠⡀⠀⠀⠠⠄⢨⠇⠀⠀⠀⠀⢠⠦⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠓⠀⠀⠀⡀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠐⢄⣀⣤⣤⠤⠃⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠹⢦⡘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠢⡀⠠⠄
⠀⠀⠀⢠⣀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠈⠀⡖⠀⠀⢰⣦⡤⢄⡀⠀⣠⢟⠦⡀⠀⢄⠀⢀⠀⢀⡴⠀⠀⢀⡀⠀⠠⠀⠐⡇⠀⠀⠠⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⢈⠀⠀⠀⢀⣷⠄⠀⠈⠙⠣⠀⠈⢀⡴⠁⠀⠈⢢⣄⣧⣤⠆⠈⠀⠀⠀⢋⠀⠀⠀⠐⠔⣀⡀⠴⠤⠖⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠈⠁

⠀⠀⢀⠂⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⠀⠀⠀⡰⠁⠀⠀⠰⢤⡀⠀⠸
⠀⠀⢀⠐⠄⠀⠤⡰⣄⣀⣀⡸⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠀⠲⢦⠄⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠈⠉⠠⡈⠀⠐⠂⠒⢦⣔⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼⠆⠀⢀⠄
⠀⠀⠀⢨⠓⠠⠄⠀⠀⠀⠀⠄⠀⠁⠘⠂⠀⠀⠀⠐⠒⢲⠊⣄⣀⣀⠌⠎⠀⠀⠑⠀⠐⡘⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠠⠀⠈⠀⠀⢀⡄⠀⠀⠈⢙⠆⠀⠀⠈⠓⠼⠄⠂⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠰⣤⣀⣠⡞⠀⠀⠀⢀⠎⠀⢠⣤⢤⣤⡀⠀⠀⠀⠀⢠⡄⡠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⠳⢦⣤⣠⡟⠀⠀⠞⡕⠙⢹⠿⡀⠀⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠤⠄⠄⠀⠐⠋⠀⠀⡀⠙⠒⠒
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢦⢀⣔⣤⢾⢆⠀⠀⠀⠀⢀⡀⠀⢠⣾⣡⣀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣠⡴⢻⡿⢊⣭⢾⣧⣄⠀⠀⠸⣿⣦⣀⠉⠲⣬⡙⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠘⢧⣾⡿⠴⠿⠛⠿⢷⢶⠏⡀⠀⠀⠈⠳⠍⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢎⠀⢀⡠⠂
⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⢀⡆⠀⠀⠀⠄⠀⠉⠃⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠊⠀⠀⠀⠘⣄⠀⠈⠀⠃⠀⠀⠀⠘⣧⠀⠀⠀⣀⣀⡲⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⠠⠀⠀⢜⠳⣄⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃⠀⠀⠈⠀⠀⠐⠁⠀⠀⠳⢾⠞⠁⠀⠀⠀⠢⠀⠀⠘⠥⠒⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢆⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⢣⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠠⡶⠀⠀⠱⡄⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⢎⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠉⠀⠀⠀⡀⠀⠀⠀⠀⠣⡈⠊⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢰⠇⠀⠀⢀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠙⣄⢀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠈⢦⠃⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠳⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢶⠒⠒⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢀⡼⠓⠒⢒⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⣠⠴⠋⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠉⠓⠲⠤⢄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠒⠉⣀⣤⠶⠋⠁⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠚⠉⣁⣀⡤⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠠⢤⣀
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⢀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⢠⣀⢀⣜⡰⠠⠀⠀⠀⠈⢢
⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣻⡿⠏⠛⠛⠹⣿⠂⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣏⡀⠀⠀⣠⣼⡿⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢮⣿⣷⢟⣾⠛⠈⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠃⠈⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠻⡞⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⡀⣀⣀⣀⣀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠁⠀⠀⣠⡟⠥⠀⢀⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢯⢀⡤⡶⡏⠀⠀⠀⠈⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠉⠀⠉⠁⡀⠄⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠂⠉⠀⠀⢀⡰⠟⠁
⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠛⠋⠁
⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠸⠀⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠙⣮⡳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⠍
⠀⠀⠀⠀⠈⠹⠛⢢⢤⣤⠦⠶⠀⢐⣒⠋⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡾⡿⣿⣷⣾⣿⣿⣿⣿⣶⣶⣶⡖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⢿⣿⣿⣇⣤⣻⣰⣁⣉⣇⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠉⠉⠙⠙⠋⠉⠋⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠔⠚⠩⢤⣄⣀⡐⠂⠨⠉⠑⢒⣢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣴⡉⠧⠤⣶⣶⠮⠟⠶⠄⠉⢈⣁⡠⠔⢚⣉⡭⠴⡓⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢙⢳⡿⢟⡲⠤⣌⣙⠒⠲⠚⣋⣡⠤⢖⡛⢩⢴⠚⠋⢁⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣲⣤⣆⣂⠙⠹⡗⠪⣭⣉⣉⢽⠂⠏⠠⠀⣈⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢎⡀⠀⠐⠻⠽⣒⡦⣄⣈⢘⣀⣉⣤⣴⢶⣛⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠹⢓⠺⣝⡲⠤⣄⣀⠩⢑⠺⣭⠭⡝⠛⠋⣉⣩⣤⣾⣡⠵⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠙⠛⢶⣅⣈⠉⠛⠓⡻⣿⣖⠤⠬⠤⣶⣞⣫⢷⠿⠩⠝⠛⣀⣸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠫⡧⡀⢪⣍⣛⠶⠮⣄⡉⠁⠉⡿⠉⠁⣘⣀⡤⡤⣖⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡁⣝⣄⠳⡤⠵⠒⠒⠋⠓⢶⣷⣶⡿⣭⣔⣒⣺⣸⣦⠀⠀⠀⠀⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠙⢦⡀⠀⢣⡙⢮⣒⣀⣖⣶⣬⡽⠿⠳⠒⠚⠋⠉⢉⠙⣁⣤⡼⠆⠀⠀⠠⠋⠀⣠⣽
⠀⠀⠀⠀⠀⠀⠀⣡⠘⢓⣿⠀⠀⠑⣬⣉⣁⣁⣬⣬⣤⠶⠶⠖⠻⠿⠛⠛⠋⠋⠉⠀⣀⠀⠀⠙⠻⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠦⣄⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⣂⣛⣦⠀⠀⢜⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⡀⠀⠀⠀⠀⠀⠀⠈⠢⢝⡂⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⢣⣙⠂⢀⠀⠀⠉⠳⣌⡒⠦⠤⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⠄⠀⠈⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⡀⢐⠈⡉⠀⠀⠀⠢⣕⢦⠀⠀⠀⢤⡀⠠⠆⠦⠳⠳⠈⠁⢀⡔⠀⠀⠀⠀⠀⢀⣴⢋⠴
⠀⠀⠀⠈⠀⠘⠀⡁⠏⠼⣠⠀⠈⢦⢱⡀⠈⠳⣬⣑⡰⠤⠤⠤⠔⣚⠡⠊⠀⠀⠀⠀⢠⡷⣁⠋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢴⡀⠠⡆⣧⠀⠀⠀⠘⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⢣⠇⢐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠆⢈⡇⣿⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢄⣀⠀⠀⠀⠀⢻⢸⠀⠠⠖⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣸⡝⠀⠀⠀⡀⡀⠀⠈⠉⠉⠙⠒⢨⣙⢶⣄⠀⠘⡌⢇⠀⠚⣡⢀
⠂⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⠋⠀⠀⠀⠀⡄⠀⢠⡰⡆⢶⢰⢢⢄⡉⠢⠻⣃⠀⠐⠌⠀⠀⠀⠉
⠒⠈⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡘⠢⠃⠀⠀⠀⠈⠈⠠⠀⢣⢹⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣼⢰⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⢰⣿⢨⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰
⢀⡐⠆⡀⠀⠀⢿⡘⡀⠈⠵⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡆⠇⠘⣠⢀
⠃⠁⠰⠁⠀⠀⠈⢣⡱⣄⠀⠉⠰⠃⠇⠶⠘⡂⠊⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⢾⣌⢦⠀⠋⠞⠰⠆⡇
⣿⡿⠷⠷⠶⠶⢶⣶⢿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣾⣿⣷⣷⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠲⢏⡔⡠⢋⣝⠀⢄
⠀⠀⢰⣶⠤⢄⣀⠒⠀⠠⡀⠀⠀⠀⠻⢧⣴⣬⠉⠓⠎⠴⠠⠄⠀⠀⠀⠀⠄
⠀⠀⠈⢳⣝⢢⣄⡀⠓⠂⠀⠀⠀⠀⠀⠀⠉⠛⠳⠷⠾⠶⠴⠖⠒⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠙⠻⢮⣝⣒⣤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⢀⢀⡀⠱⣖⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌⠘⢃⠵⢹⣿⣭⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠆⠀⠀⠀⠀⠈⠋⠳⠂⢤⠁⠬⠻⠧⢄
⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⠀⢀⠀⠘⢒⣿⢁⠰⣖⢛⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠈⠁⠤⠄⠤⠤⠶⠒⡛⠿⢿⠚⢒⣶⠾⠀⠀⠀⠀⠠⠤⡂⣄⢦⣂⠆⡀⠀⠀⠀⠀⠀⠈
⠀⠀⢄⣤⣌⣀⡠⠀⠠⠐⣊⠭⠳⡇⠋⣸⠆⠈⠀⠀⠀⠀⠔⢀⡐⣓⠭⠖⣋⠑⠤⠀⠀⠉⠠⠔⣲⣿⠆
⠀⠀⠀⠈⠙⠫⡂⢤⣲⡹⠬⢒⣩⣠⡾⠃⠀⠀⠀⠀⠠⠤⣬⣨⣅⣤⣦⣿⠁⢀⠄⠈⠁⣠⡴⣪⡵⠋
⠀⠀⠀⠀⠠⢤⣍⣨⣤⣴⣦⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣤⣤⣖⣾⣭⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⡀⠦⣤⣀⡴⠟⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⠀⠀⠐⣤⢀⣿⠁⠀⠨⣴⣴⣿⣻⣧⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠞⢶⡀⠀⠴⣠⣬⡵⣾⣿⡆⠀⠀⠛⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⠀⠀⠈⢿⣸⠂⠉⢉⢉⣉⡛⢿⣦⡆⢠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠱⣟⡷⠈⣵⠶⢦⣐⡺⢴⡼⠊⣿⣿⠿⣿⣿⣾⢿⣷⠦⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠲⣠⠞⣋⣷⣂⠀⣤⣶⡄⠈⢳⣖⣸⠿⢋⢴⣿⡀⠀⠰⢿⣏⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⠃⠀⢠⡟⠉⠉⠈⠿⠀⣼⣛⡓⣶⢨⡟⢡⣾⣧⡘⣿⣿⠷⢦⡐⢻⣅⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢡⡄⢰⣫⡶⣶⡀⠀⣻⠀⡆⢠⣤⣾⣿⣇⢒⡳⢨⣿⡜⡏⠀⣠⣾⠋⣰⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⡆⣡⣈⣧⣅⣉⠳⣤⣥⣾⡗⠩⢍⠿⣿⣿⣭⣶⢟⣼⢃⡏⠘⠿⢋⡴⢫⣾⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣽⠣⢙⣭⣬⣻⠛⠟⢨⣿⡿⢿⣏⠀⠀⢀⣽⡿⠃⣿⡟⠉⣛⣽⣿⡿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⣀⣼⣿⣡⣰⣴⣿⣧⢙⣋⣉⢀⣀⣭⠉⣀⢀⢏⣯⣾⡿⣻⣡⣶⡿⠟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⣬⡙⠛⠮⠼⠿⡿⣉⣉⣉⢉⡉⠙⣛⣛⣾⣿⣿⣿⠿⠿⠛⢋⣁⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣇⠈⠉⣰⠲⠶⣦⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢻⡀⠀⢡⠀⠀⠁⠀⠉⠟⡉⢿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣧⢁⢸⣇⠀⠠⢠⣷⣤⢰⢾⣿⣿⣷⣿⣿⢟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠘⣿⠆⣽⢸⣿⣶⠰⢾⣽⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠂⣿⢆⠚⣺⣿⣿⡉⣿⣿⣿⣸⣿⡟⡿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⢸⠻⡀⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡗⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⣄⠔⠆⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⢀⣀⣾⣿⣷⣿⣿⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⢠⠏⠰⢣⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡄
⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⣸⠆⠀⡔⡆⢠⠀⡐⢰⡏⠰⡆⡋⢠⢂⠐⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡏⡁⣿⠻⠛⠿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⠤⠖⠹⠃⠆⠓⠧⠿⠔⠷⠃⠧⠛⠷⠷⠧⠎⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⠿⠛⠛⣿
⠀⠀⠀⡇⠀⣼⠀⠀⢠⡇⠀⠹⢿⡏⠀⣿⢻⡇⠀⠀⠲⠒⠒⠂⠂⠒⠒⠒⠒⠒⠒⠒⠚⠒⠚⠓⠛⠛⠀⠀⠀⠘⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡧⠀⠀⠀⠀⢸⡇⠀⠀⠈⡇⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⣶⣶⣶⣶⣾⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⡇⠀⠟⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠄⠀⠐⠃⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠠⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⡄⢶⠆⠀⠘⢿⣿⣿⣿⠯⠀⠀⢀⠔⠀⠒⠢⣄⠀⠀⠀⠂⣴⣶⣁
⠀⠀⠠⠚⠉⠀⠀⠀⡠⠔⠂⠁⠀⢆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⡸⣅⠐⠟⢀⠞⠹⡄⠀⠀⠊⣙⠛⠄
⠀⠀⠁⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⣶⣾⣷⣆⣤⣤⣄⠀⠀⠀⠀⠀⠀⠠⠒⠒⠆⠀⠀⡀⠈⠙⢶⠋⠀⣰⠂⠀⠀⠀⠈⠁⠀⠀⠀⠦
⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⢰⡏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠔⠉⠀⠀⠁⠀⠀⠀⡄⠀⠈⠲⣄⡘⣀⠔⠁⢀⣴⣾⣿⣿⣷⣦⡀
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠃⠀⠠⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠐⡀⠀⠀⡠⠔⠊⠁⣀⠠⠀⠀⠀⠀⠀⡀⠉⠛⠿⠟⠋⠀⠀⠀⠀⠙⠦⣀⣀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡟⠉⣿⠋⣿⠋⡿⠀⢀⡀
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠉⠁⠁⠀⠀⠘⣄⠀⠀⠀⠀⠀⠈⢦⡀⠀⠛⠀⢈⡴⠁⠀⠈⠁
⠀⠀⠀⢀⣄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⡔⡀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠓⠖⠚⠉⡠⠀⠤⠀⡀
⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⢀⡠⢆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠘⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⡇⠀⠀⠁⠀⠀⠀⠁
⠀⠀⣰⠠⠀⠀⠀⠃⢠⠐⠥⠒⠁⠀⠈⠳⢴⣄⠀⠀⠀⠀⠀⠰⠁⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⡇
⠀⠀⠅⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⡆⠀⠱⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⣆⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⢀⠆⠀⠀⠀⠈⠉⠀⠈⠑⢤⣀⣀⣀⠠⠲⠄⠠⠀⠂⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⢰⡶⠀⢀⣤⣤⣤⣦⡄
⠀⠀⢆⠀⠐⠀⠀⠀⠀⠀⢀⠜⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⢶⣶⣿⣿⣶
⠀⠀⠀⠳⡔⠀⠆⠀⠀⠰⢇⠀⠁⣄⠈⠀⡗⠤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠒⠐⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃⠸⠘⠚⠈⠃⢛
⠀⠀⠀⠀⠁⠀⢀⠐⠁⢀⠀⠈⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠐⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣀⣀⠐⠄⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣲⣦⣶⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⣩⡵⠶⣺⡽⣫⡟⣻⢻⡻⢿⡛⠭⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⢀⣴⠏⢀⣤⠞⢁⣶⠏⠰⣇⠀⢷⣀⠙⢦⡈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⢀⡿⠋⠀⣠⡾⠋⠀⣰⡿⠀⠀⡏⠀⠈⣳⠀⠀⢳⡄⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠃⠀⣶⠿⠁⠀⣴⡟⠋⠀⢀⡿⠀⠀⠘⣧⠀⠀⢹⣆⠀⠀⢹⡀⠀⢹⡷
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⣸⠏⠀⠀⣿⡟⠀⠀⠀⣼⣇⠀⠀⠀⣿⡀⠀⢸⣿⠀⠀⠈⣿⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⣰⡿⠀⠀⠀⣿⠋⠀⠀⠀⣾⡏⠀⠀⢀⣾⡄⠀⠈⢿⡄⠀⠀⢿⡇⠀⠈⣯
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢠⡿⠀⠀⢠⣾⡷⠀⠀⠀⢠⣿⠁⠀⠀⠈⣿⠇⠀⠀⢸⣦⠄⠀⢺⣧⠀⠰⣿⣤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢸⡷⠀⠀⣼⣿⠃⠀⠀⠀⣿⣧⠀⠀⠀⢀⣿⠆⠀⠀⢸⣷⡀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿⡇⠀⠀⢻⣿⠁⠀⠀⠀⢿⡇⠀⠀⠀⢸⣿⠀⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢾⡆⠀⠀⢾⡿⠀⠀⠀⠀⣾⣷⠀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢸⣷⠀⠀⣸⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣿⡀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠛⠀⠀⠿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣦⣤⣀⣀⣠⣤⣤⣤⣶⣶⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠶⣦⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⡾⠟⠀⣠⣶⠶⣶⣄⠀⠉⠁⠀⠈⠉⠛⠻⢷⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢯⣭⡛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣫⡞⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢌⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⠟⣡⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦
⠀⠀⠀⠀⠀⣸⠋⣼⠋⠀⠀⠀⠀⢠⣶⣶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣷⣄
⠀⠀⠀⢀⡴⢁⡾⠋⠀⠀⠀⠀⠀⢺⣿⣿⣷⣌⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣷⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⢀⢹⣦
⠀⠀⣠⡞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠉⠛⠋⠀⠀⠀⣼⣿⣿⣿⠿⣦⠀⠀⠀⠘⡇⣿⡇
⠀⢰⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⡿⠀⠀⠀⢰⡇⣿⡇
⠀⣿⠃⠀⢤⣤⣶⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⠀⠀⠀⠀⠹⣇⢻⣇
⠀⡿⠀⠀⠈⢿⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢰⠃⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣇⡇⠀⠀⠀⣠⣾⣷⠸⡆⢸
⣿⣸⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⢼⣿⠿⠋⠈⠀⠀⢀⣼⣻⣿⣿⢀⡇⣼
⣿⣾⡆⠀⠀⠀⠀⠀⢰⣿⣿⣿⣜⣿⠀⠀⠀⠀⠈⠻⢿⣿⠿⢟⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⣸⣷⡟
⠘⣧⢻⣦⡀⢀⣀⠀⠘⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡟
⠀⠘⢷⣾⣿⢷⣾⣿⠿⣶⣿⣿⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣰⣿⡇
⠀⠀⠈⠉⠲⣆⠙⠁⢠⡌⠉⠉⣿⠿⣷⣤⠀⢠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢶⡀⠀⠀⠀⢀⢞⣿⠇⣿⡏
⠀⠀⠀⠀⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⢿⣿⣿⣿⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⡇⠀⠀⣠⣵⡿⢋⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⣝⡿⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⣛⡫⠀⠀⣼⡿⣫⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠌⢻⡆⠀⠉⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣼⡟⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠢⣾⡃⠀⠀⠀⠀⢰⣿⣿⣥⣿⣧⠀⢀⣀⣠⣶⣴⠾⠷⠿⠟⣛⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⣽⣭⣤⣬⣙⢿⣿⣿⣿⠏⡰⠟⡭⣉⣭⣷⣶⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⢿⣶⣶⣶⣶⣦⣭⣭⣤⣶⣶⠿⠿⠿⠛⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣬⣿⣿⣯⣭⣤⣿⣿⣯⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠉⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⡤⠾⠃⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢉⡿⠷⠞⠁⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠽⡒⠊⢉⠽⠁
⠀⠀⠀⠀⣼⠋⠙⠓⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠖⠒⠫⠁⠂⡀⠌⢁⣀⠀⠒⢀⠠⢀⡀
⠀⠀⠀⢠⡇⠤⡀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣤⠤⠤⠤⠼⠀⠀⠀⠀⢀⠤⣪⣴⠾⠚⠥⢰⣀⡠⠦⢁⣀⠁⠃⢨⠀⠤⢃⠀⢠⠐⠙⡄
⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠈⢉⡇⠀⠀⠀⠀⠀⠀⣠⠵⣚⣿⠍⠂⣀⠤⠀⡀⣈⠙⠂⢠⠤⠔⣃⠠⢄⠀⠋⠀⠀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⠀⠉⠊⠙⣄⡀⠀⠆⡽⠺⠋⢠⣀⠀⠀⠀⠑⠂⣁⠠⣚⠢⠤⣀⠤⠋⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡤⠜⠀⠣⠳⣄⠀⠀⠀⠉⠉⠀⠠⠎⣀⠀⢀⠭⠒⠠⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠓⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠔⠒⢦⡀⠀⠀⠀⠀⠈⠉⠛⡶⠦⢤⣀⡀⠰⡟⢋⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠙⠲⠤⠤⠤⠵⠀⠀⠀⠉⠙⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣩⣍⢳⡴⢛⡛⢦⠀⠀⠀⢀⣄⣰⠏⣰⢸⣇⣰⠋⣹⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡘⢁⡏⡘⠁⢋⠍⣘⠓⠒⠚⠋⣸⡏⠐⢣⣿⣉⠁⢠⣴⣶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⣧⣬⡴⠁⠾⠶⢚⡻⡟⡛⠟⢫⠙⠀⡴⢋⠉⣹⢀⡟⣩⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⡿⠟⡁⢀⠀⠄⠸⢡⠀⠷⡀⠬⣰⠀⣀⣉⠀⣡⣘⣃⠱⣃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠞⠛⠚⠓⠛⢺⡟⠷⠾⠿⠛⠛⠀⠉⣤⣤⣶⠌⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠴⠖⠛⠉⠳⠦⡭⠤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡏⠁⠀⠀⢸⡇⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡇⣀⣀⣀⣈⣇⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⡏⠉⠉⠀⢠⡏⠀⠀⠀⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠇⠀⠀⠀⢸⠁⠀⠀⠀⢿⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡹⣤⠤⠤⢴⡧⣤⣶⠶⢾⡦⠶⠶⠦⣾⢿⡥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢍⠙⠷⠀⠀⠀⠀⠉⠁⠐⢬⣄⣀⣀⠔⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠰⠒⠀⠐⠂⠤⠄⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢐⠒⠒⠒⢦⡀⡴⠁⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣆⡈⢦⢹⡇⢸⠀⠘⣦⠀⠀⣸⠀⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠈⠉⠙⠻⢧⣸⡄⠀⣽⣤⠾⢃⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣴⠀⠀⠀⠾⠁⠀⠀⠀⠈⠑⣄⠻⠓⠚⠳⠶⠦⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⠀⣠⡤⠀⠀⠛⠃⠀⠀⠈⠡⠊⠀⣰⢂⠀⢻⡟⠛⠻⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠈⣧⠈⠦⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣴⠀⠀⢠⠆⡀⠀⠒⣃⠄⠀⠀⢚⡡⠂⠀⣀⠀⡇⢻⢿⣦⢄⣀⢙⡂⠄⠀⠀⠀⠀⠀⠀⠀⢀⡞⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠫⠂⠀⣿⠄⢹⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⣤⣀⢸⠀⣿⡜⢉
⠀⠀⠀⠀⠀⠀⢸⠛⠃⠀⢞⠄⠀⠰⢆⡄⠀⠀⠻⠷⠂⠀⠴⢖⡠⠀⢀⠄⣼⠃⠀⠂⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠈⠻⣆⠘⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠀⠁⢠⠶⣀⠀⠀⠀⢀⣈⣡⠴⣊⣵⠞⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠐⢦⣀⠀⠀⠀⠘⣧⣁⣾⣀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠘⠁⠂⠀⠀⠀⠨⢴⣒⣺⣭⠭⠶⠞⠛⠉⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢄⣠⠽⠛⠉⠀⠀⢀⠀⠀⠈⠻⡶⢬⡉⠉⠒⠒⣂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⡶⠊⠁⣀⠄⠀⣠⠶⠋⢀⠀⠀⢀⠹⡆⠈⡓⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⠝⢋⡠⠖⢋⣤⠶⠋⣁⣤⠖⠹⠀⠀⣸⣸⡿⠦⠤⠤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠁⢠⣶⣭⠶⢛⣩⠴⠒⢻⠁⠈⠁⠀⠀⢀⣵⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⡠⠀⡤⠈⠀⠞⠀⠀⣀⣀⣠⣤⠴⠖⠋⠉⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣤⣤⡤⠴⠶⠶⠶⠚⠛⠛⠏⠛⠒⠈⠉⣀⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠴⠒⠚⠉

⠀⠀⠀⢸⣿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⢿⣿
⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠘⣿⡄⠀⢹⣧⠀⠀⢺⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠂⠀⢠⣿⠁⠀⣼⡟
⠀⠀⠀⠀⢹⣧⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⢠⣿⠁
⠀⠀⠀⠀⠀⢿⣇⠀⠈⢿⣦⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⢠⣾⠏⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⢀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠈⠻⣷⣄⡀⠀⠀⠙⠃⠀⠀⠀⣿⡇⠀⠀⠀⠛⠁⠀⠀⣀⣴⡿⠋⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠙⠿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠉⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⠀⠀⠉⠙⠛⠿⠿⠿⠶⠾⠿⠿⠟⠛⠉⠁⠀⢀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣦⣤⣄⣀⣀⣀⡀⣀⣀⣀⣀⣤⣤⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐
⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⢄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠈⠉⠉⠉⠉⠉⠉⠙⠓⠒⠾⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡀
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢄⠀⢠⡀⠠⠀⡀⢠⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠂⠤⣔⠩⠉⠷⠶⠶⠷⢛⠤⣤⣀⡀⠤⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡠⠔⠒⠫⢂⠀⠀⠀⠀⠀⠉⠺⠱⠢⠄⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠢⣀⠀⠀⠀⠀⠀⠠⠒⠊⡰⠐⠤⢴⣲⣶⡊⡔⠬⡑⠒⠒⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢆⠑⢄⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠙⠒⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡾⠁⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠲⠤⠼⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣠⠞⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣀⡤⠤⠔⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣾⡿⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣾⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⣠⡞⠁⣠⢾⣿⣿⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⢀⣴⠏⢠⡾⠁⢸⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢿⣦⡀
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡁⢠⡟⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠻⣷⡄
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠻⣷⡟⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⣿⣆
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⣦
⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠈⣿
⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⣀⣾
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣷⡄⠀⠀⠈⣉⣁⣠⣤⣶⣾⡿⠛
⠘⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⢿⣿⡿⠿⠿⠟⠛⠋⠉
⠀⠀⠈⠙⠿⢷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠆⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠟⠋⢁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡟⢟⣙⠛⣻⢛⣻⢿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠁⠀⠀⠀⠀⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⡀⢄⠀⣠⠆⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢠⡀⢑⣨⢀⡏⠀⡄⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣀⠁⢤⠙⠉⠁⠒⠰⡯⠐⠊⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠠⠀⠀⡘⠂⠀⠀⠀⠀⠲⣏⠠⠥⠄⠀⠀⠀⠀⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⢀⣭⡁⠀⠀⠀⠀⢁⠒⠀⠒⠂⠀⠀⠀⢀⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠤⢃⠠⠄⢀⡠⡌⠁⠠⠤⠀⠀⠀⢀⣾⢢⢺
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠈⠁⠀⠉⠞⠘⠈⢥⠀⠳⠀⠀⠀⠀⢀⡾⣻⡤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠴⠃⠀⠀⠈⠃⠈⠁⠀⠀⠀⠀⣰⡿⠟⣟⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢛⣳⣾⠳⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡝⡿⣶⣶⢻⠿⢿⣛⠷⢡⣵⣯⣇⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠾⣧⡥⢞⣿⡯⣶⣥⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢹⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣞⢀⣷⡦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣿⡷⢿⣿⣿⣿⡿⢹⡛⠛⠲⢦⣌⣙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⡟⠉⣰⣿⠋⢸⣿⡇⢸⣧⠀⠀⠀⢈⠻⣷⣮⡳⣄
⠀⠀⠀⠀⠀⠀⣰⢋⣴⣿⠋⠀⣾⣿⠃⠀⣸⡿⠁⢻⣿⡄⠀⠀⠀⠀⠈⠻⣧⡈⢳⡀
⠀⠀⠀⠀⠀⣰⠃⣾⣿⠃⢠⣴⡿⠋⣀⣴⣿⡇⠀⠸⣿⣧⠀⠀⠀⠀⠀⠁⠹⣿⡀⠹⡄
⠀⠀⠀⠀⢠⠇⣴⣿⠇⢰⣿⣿⡇⠀⢹⣿⣿⠀⠀⠀⣿⣿⠈⠁⠀⠀⠀⠀⠀⢹⣷⣀⠹⡀
⠀⠀⠀⠀⣼⠀⣿⡟⠀⢸⣿⣿⠆⠀⢸⣿⣿⡀⠀⠀⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⢿⣿⡀⢧
⠀⠀⠀⠀⡇⣰⣿⡇⠀⢸⣿⡿⠀⠀⢘⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢸⡄
⠀⠀⠀⠀⡇⢹⣿⡇⠀⢸⣿⣇⠀⠀⣸⣿⡿⠀⠀⠀⣿⣿⡇⠀⠀⠒⠀⠀⠀⠀⠀⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣄
⠀⠀⠀⠀⡇⢸⣿⡇⠀⣻⣿⡏⠀⠀⢿⣿⡟⠀⠀⠀⢻⣿⡇⠉⠀⠀⠀⠀⠀⠀⡀⢿⣿⡀⡇⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁⠀⠀⢸⡄
⠀⠀⠀⠀⢷⠈⣿⡇⠀⣿⣿⡇⠀⠲⢾⣿⣇⠀⠀⠀⣸⣿⡇⡀⠀⠙⠀⠀⠀⠀⡃⣸⠿⠶⠗⠒⠉⠉⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠘⡆⢺⣿⠃⠈⣿⣿⠀⠀⢹⣿⣿⠀⠀⠴⢿⣿⡁⣁⠀⠤⠀⠐⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠹⡜⣿⡀⢀⣿⣿⡁⠀⢼⣿⣿⠀⠀⠀⡎⠉⠁⠀⠀⠀⠀⠀⡀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢁⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⣿⣿⡇⠀⢺⣿⣿⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⢠⡀⠀⠀⠇⠀⠀⠘⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⣿⡇⠀⠀⣿⡇⠀⠀⢾⣿⣷⡈⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣷⣄⠀⣿⡇⠀⢠⣿⡿⠙⢿⣦⣀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠷⠤⠴⠿⠧⠶⠒⠛⠻⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠤⠤⣄⡀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠙⠲⢤⣙⠀⡧⠒⠉⠑⢶⣴⠞⢳⡀⠀⠀⣠⠔⠋⠉⠉⠉⣒⣦⣤⠉⠺⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡤⠛⢛⡿⠛⢀⡠⠀⠈⠀⢀⡀⠀⠠⠴⢿⣆⠀⢳⢀⡾⠁⠀⠀⢀⣴⣯⣥⣤⣤⣤⠀⠀⠘⠙⠓⠶⢤⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠰⣯⠴⢚⠏⢀⣦⠀⢱⣄⠉⢳⣶⣤⣄⣹⡆⢸⡾⠀⣀⠀⠀⠧⠀⠀⠀⢀⣞⡡⠚⡀⢸⡀⠑⢦⡄⣈⡒⢄
⠀⠀⠀⠀⢠⡏⠀⣟⡆⠀⠀⢸⣠⠏⢸⡀⢸⣨⠟⠉⠀⠉⠙⠫⣽⢸⠗⠉⠀⠉⠓⠂⠤⡀⠀⠟⢋⠀⠀⡇⢸⠈⢦⡀⠹⡌⢿⡉⠃
⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠸⠇⡴⢄⣳⠞⠉⡽⠋⢉⡠⠄⡀⠀⡀⠤⣀⠐⠒⠒⢖⡚⠻⡄⠀⢸⡄⠀⢸⣸⠀⠀⠙⢦⣿⠘⣇
⠀⠀⠀⠀⢸⡇⠀⠀⣠⢤⠀⠀⠀⠙⡼⠁⣀⠸⠷⠚⢹⠁⡰⣇⠀⠹⢦⡈⠻⡓⠶⢤⣵⡄⠙⣆⠀⠀⠀⠈⠿⠀⠀⠀⡶⠟⠀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠘⠎⠀⠀⠀⢸⠃⠀⣯⠇⠀⠀⣾⡼⠁⢹⡀⢸⠀⠻⣦⡹⡄⠀⠀⠣⠄⢹⡆⠀⡌⠀⠀⠀⠀⠀⠘⠁⠀⡿
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡤⣾⠀⠀⠀⠀⠀⠀⠘⠁⡞⡆⠳⣼⠀⠀⠈⠙⠷⢠⠄⠀⠀⢀⡇⠀⠀⠀⢰⢳⠄⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⢹⡆⠀⠀⣶⢦⠀⠀⠀⠉⠀⠀⠉⠀⣖⢲⠀⠀⠈⠒⠃⠀⢸⡇⠀⠀⠀⠈⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⡵⠀⠀⠀⢿⡀⠀⠈⠃⠀⢰⢦⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⠀⠀⠀⡾⠰⣉⠀⠀⠀⠀⢰⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⣀⠀⠈⣷⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢬⠃⠀⣼⠃⠀⠁⢀⠀⠀⠀⢈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠓⠀⠀⠸⣧⠀⢀⡀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⣰⣏⠀⠀⠀⢨⠇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⠦⣄⣘⣧⠸⠜⠀⠀⠀⠀⠀⠈⠁⠀⠀⢾⡷⠀⣰⠏⢯⠃⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⣧⡀⠀⢄⠀⠀⢀⣀⠀⠀⠀⠈⠀⣴⠷⠤⠤⠖⠡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠉⡀⠀⠘⠜⠀⢀⣄⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠾⠲⢤⣄⣴⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡆⢰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⢰⠖⠒⠒⠒⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⢷
⠀⡇⠀⠀⠀⠀⠀⣤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸
⠀⡇⠀⢀⣀⣀⣀⣿⡦⠴⣦⣤⣀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⡤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸
⠀⡇⠀⢠⣿⣿⣿⣧⡄⢾⣿⠟⠟⠁⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢠⣤⣼⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢸
⠀⡇⠀⠀⠀⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⡇⠀⠀⠺⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⡴⢻⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⢸
⠀⡇⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣰⠋⢰⡟⢻⣿⢿⡀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⡇⢸⠂⠀⡴⠁⠀⠉⠀⠀⣿⠁⢧⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢠⣄⣤⣼⣿⢋⡿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⡾⠁⠀⠀⠀⠀⠀⡙⠀⠘⡆⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢩⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠐⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠹⣀⠀⣇⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⠀⠀⠀⠀⠀⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠄⠐⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠒⡒⠀⠀⠈⡉⠩⠙⣿⡄⠀⠀⠈⠀⠄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢻⣆⠀⠀⠀⠁⠌⠐⡐⡡⠁⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢊⢆⠠⠀⠈⠌⠔⠔⡀⠁⠠⠘⢿⡄⠀⠀⠀⠈⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡄⢂⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠘⡿⣄⠀⠀⢐⣒⣪⣥⣥⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠛⢿⡌⢆⢤⣤⢬⣭⣿⣶⣶⡶⠿⠽⠕⣎⡵⠛⠛⠉⠉⠉⠉⠉⠀⡈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢥⣄⡀⠀⠀⢱⡈⢆⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣖⠚⠼⠈⢹⠐⠪⣷⠈⢜⡄⠀⠀⠀⡀⠁⠠⠀⠂⠀⠘⣽⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢉⡗⡦⢤⣀⡘⠃⣦⣧⠈⡿⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⣀⡠⠤⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠇⢨⠙⢲⣿⢧⠸⣄⠀⠀⢀⣀⣠⡄⢠⣤⢤⣄⢸⠓⠀⣀⣉⣉⠥⠤⠤⠴⠶⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠈⠉⢀⠀⢣⠹⣄⣀⣀⣀⣤⠭⠄⠖⠒⠒⠚⣉⣉⣉⡤⠤⠤⠖⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢻⢷⠀⢷⣯⠭⠤⠤⠶⠒⠒⠚⢋⡩⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠺⠑⠀⢿⣗⣤⡑⡀

⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⡀⠀⣀⠀⠀⠀⣠⢄⡄⢠⣤⣄⠀⠀⢤⣤⠀⢀⡀⠀⠀⣤⡄⢠⠤⢤⣤⣄⠀⣀⣤⡤⡤⢤⣄⡀⠀⠀⠀⠠
⠟⠀⠀⣀⡤⠤⠤⣤⣄⣀⣀⠀⠉⠉⢩⣄⣙⡷⠋⡀⢠⡏⡞⣹⣟⠀⠈⢳⣦⣞⠉⡾⢸⠁⠘⠛⠉⣰⣋⣹⣿⢿⠉⣀⣿⣯⣿⠀⣿⣹⣿⣷⣤⣀
⣠⣾⣏⠀⠀⠀⠀⠀⠀⣙⣿⣟⠛⣇⣄⠉⠉⠀⠀⠅⣰⣹⡿⣇⠈⠲⣶⣾⠋⢉⡿⢡⠞⠀⠀⠀⣰⢥⣼⣿⠛⠀⣦⣿⣿⣾⣿⡹⣿⣿⣻⣿⠉⠻⣷
⣾⠿⠿⢿⣿⣿⣶⣿⣿⣿⣿⠿⣿⠿⣿⣀⣀⣠⠀⠀⣿⡽⢧⣤⡿⣿⠥⠾⣛⣭⣒⠁⢠⣠⡿⢠⠷⣾⢿⠉⢦⣼⣿⣿⡿⠦⣼⣱⣹⢿⣇⠈⠳⡀⠈
⣿⣤⣤⣴⣾⣿⡛⢻⣭⣤⠽⠷⣟⠓⠾⡻⢿⡿⣄⣀⠘⣿⣿⣯⠟⠲⠶⠛⠑⡋⣁⣀⡈⣉⡀⢸⣻⡟⣦⣷⣿⣿⡟⡼⠇⠤⣾⣉⡇⣼⣿⣦⡀⢹⡆
⢷⡿⠫⠤⣤⣈⣿⠿⠛⠓⠢⣄⣈⣻⣶⠿⢾⣻⢏⡏⠀⠈⠉⢁⣠⠶⠟⠛⣡⣴⠾⠋⢉⠅⣹⢨⠟⣷⠿⠛⣿⢻⣇⣷⣄⣠⣿⣈⢷⣧⣿⢿⣧⠀⢳
⡞⢛⢒⣶⣾⣿⠟⠒⠲⣤⡴⠾⢿⡁⠈⢷⣀⡟⣸⣷⠀⠀⡴⠋⣁⣤⠶⠛⢋⣡⣤⣾⣿⣾⠅⠘⠊⠁⠀⠀⣡⣸⣿⠧⠤⣼⣇⡼⣾⡾⣿⣄⢻⣄
⣀⣽⣿⣿⣿⣧⣤⣤⠞⠛⠳⡀⠀⢳⣄⣨⡟⢠⢏⡟⢀⡾⣁⡾⠋⠀⠀⢠⡾⠟⢛⣿⠏⡿⠀⢀⡀⢠⡀⠀⢸⣿⣿⠦⢤⡾⣼⡿⣿⠁⠈⠪⣵⣿⣶
⣿⠿⣯⣿⢣⣄⣴⣛⣳⣤⣤⣿⣤⡾⠟⢋⣴⣧⠞⠀⡿⣿⡿⠀⠀⣠⡴⠋⠀⣠⡿⣡⠔⠁⣤⣌⣽⠟⠋⠀⠘⣿⣿⡶⣾⢶⡟⣽⠏⢀⣤⠤⠀⠉⠓
⣏⣀⣿⣧⣬⢭⣭⣭⣭⣭⣭⣥⠤⢒⡾⣿⡟⠁⠀⣤⠞⢡⣴⡾⣛⢁⣀⡤⠞⢉⠞⠁⠀⠀⠀⠁⠀⠰⠽⠿⠂⠹⣿⣟⣵⡯⠞⠁⠀⠻⠇
⠉⠉⠉⠁⠀⠈⠙⠿⣭⣙⣛⣛⣯⠥⠞⠉⠀⠀⠀⠷⠶⣥⢶⠿⠿⠿⠭⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠟⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠋⠉⠉⠉⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠉⠒⠠⠀⠀⠀⢀⣠⡤⠖⠊⠁⠀⠀⢀⣀⠼⣃⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠨⣍⣒⠤⢀⠀⠀⢰⠁⠀⠀⣀⠀⠀⢀⣩⠤⡶⡺⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢀⠢⠈⡏⠂⢀⣀⠚⠖⣋⣡⢤⢤⠞⠁⣈⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣀⠀⠀⡇⢸⠋⠁⠀⣤⢋⣠⠴⠿⠞⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡍⠻⡷⠦⣄⣸⣤⡤⠚⠉⠁⠀⠀⠀⣀⣁⣤⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠀⠹⣄⡿⠢⡈⠰⠧⠄⣀⢀⢀⣀⣠⣤⡤⠴⠒⢒⠖⢩⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢀⠀⠙⢇⠀⠙⢶⠒⠛⠉⠟⠋⠀⢸⡟⣀⡔⢀⠊⠐⣀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠴⠯⡿⠉⣹⠂⣌⠢⡘⢸⠀⠠⠀⠀⣠⢤⠮⠚⠛⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣟⡆⠀⡐⠀⠀⠑⢆⡜⡇⠉⠈⠉⠉⠉⠀⠠⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠁⠈⠷⠁⠀⠀⠀⠐⠀⠒⠿⠟⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢷⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠘⣧⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠸⣇⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠹⡆⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠸⣇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢹⡆⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⢷⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⣧⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣧⠀⠀⢀⢞⣷
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⢫⡞⢹⡆
⠀⠀⠀⠀⠀⣼⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣷⠏⣰⠏
⠀⠁⠀⠀⢰⡏⠳⣮⡑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣥⠞⠹⣶⠋
⠀⠀⠀⠀⠀⠙⢦⣄⠙⠳⢮⣝⡒⠢⠤⢄⣀⣀⢀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠖⣚⣩⡴⠞⠋⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣈⡉⠛⠲⠶⠶⠶⠭⠭⠭⣭⣭⣭⡥⠴⠶⠖⠛⠋⣉⣠⡴⠖⠛⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⠦⠤⠤⠤⠤⠤⠤⠶⠶⠶⠚⠛⠋⠉
⠀⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⢳⣄⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢷⣝⢦⡀⠀⠀⠀⠀⢀⡾⣏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⠙⣯⣻⣆⠀⠀⠀⣼⠁⣿⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠘⢧⡈⢿⣽⣧⡀⣸⠁⠀⢸⠀⠈⡇⢀⡤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡀⠓⢦⣿⣿⣷⡏⠀⡀⣾⣷⢰⣿⠋⡴⠁⠈⠉⣹⣭⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⣧⡁⡠⣌⢿⣿⣇⣷⣷⣿⣿⣿⠇⣼⠇⠀⣠⣾⠟⠋⠙⠳⠶⣦⠴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣶⣿⣿⣾⣿⣧⣿⣿⢟⣫⠁⣀⣈⠛⣯⣶⣖⣯⣶⣿⠗⠂⠀⣠⡔⠛⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣯⣷⣾⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣾⣿⠶⠿⠿⢿⣦⡀
⠀⠀⠀⠀⢀⣤⣶⣶⡟⠀⢰⠋⠁⣴⣥⡾⣻⣿⡟⣻⠏⣝⣿⡳⡝⢿⣿⣙⠉⠀⠂⠈⠉⢢⡀⠀⠈⠁
⠀⠀⠀⣴⣿⢝⣽⣿⡇⠀⢼⣀⠀⣿⣿⣿⢯⢿⣼⣿⣄⠈⠙⢳⡀⠀⢿⣿⣦⣴⣶⣿⣿⣶⣿⣦⣀
⠀⢀⣴⣿⡷⣋⣿⣿⣷⣴⡘⣜⡀⣿⣿⣿⠀⣾⠏⢠⠟⢦⡀⠂⢧⠀⣸⡇⠻⣶⠈⠡⠞⢷⣿⡭⢻⣷⣄
⠀⢾⣯⠵⢚⣿⣿⣙⡟⠻⠿⣮⠇⣿⣿⡸⢸⡏⠄⡀⠈⠀⠛⣆⠘⠀⡟⠀⠊⠁⠰⠆⠳⠌⠠⢞⣹⡿⠹⣆
⠀⠀⠀⠀⣾⠓⠮⠐⢇⠁⡒⠝⢷⠟⢻⣧⣸⠃⠁⣿⡆⠀⠀⢹⡄⢸⡗⠂⣿⣷⠀⢸⡇⠴⠾⣿⢯⡩⠽⠻⣆
⠀⠀⠀⣸⣿⠵⠠⠆⣾⠀⣩⡄⠙⠻⠋⠿⠏⣿⡆⠘⠁⠀⠀⠀⡙⠻⠀⢀⠁⠁⠈⢀⡀⠀⢶⣯⡀⢂⣴⡀⣿
⠀⠀⠀⡇⠐⠊⠈⢷⠄⡌⢧⣿⠀⠦⠀⠀⠀⠉⠀⠀⠐⣶⡄⠀⣁⣀⠀⠿⠇⠀⠀⠀⣄⠀⢬⡷⠢⣗⡻⠂⢻
⠀⠀⠀⣿⣾⣖⣛⠃⢨⣀⠀⠀⣠⣶⡄⠀⠀⣶⢶⠀⠈⣷⠇⠀⠘⠋⡀⠀⠀⢂⡀⠀⠛⠀⠈⠔⠃⢖⣴⡄⢻
⠀⠀⠀⢸⠀⠲⡜⢳⢸⡅⠀⠀⢿⣿⠀⠀⠀⠹⠾⠀⠀⠀⠀⢰⡀⠀⢸⣧⠀⠿⠇⠀⡄⠀⣦⡭⣀⡐⠉⠩⢼
⠀⠀⠀⠘⣧⠀⠾⠤⠀⢡⠃⣰⡄⠀⠀⣴⡄⠀⠀⢘⣷⠀⠈⡾⠃⠀⠀⠀⠀⢀⠀⠀⠠⡏⠕⢂⣛⢠⣶⢠⡗
⠀⠀⠀⠀⢿⣀⡄⢉⢲⢶⣃⣿⡷⠀⠈⢷⣿⠀⠀⠸⠿⠁⠀⠀⠀⣿⠁⠀⠘⢿⠃⠀⠀⠀⠀⣸⢂⡄⣁⢰⡇
⠀⠀⠀⠀⠈⢿⡿⠀⠘⠾⣖⡀⡀⢴⣦⠀⠀⠀⣂⠀⠀⣸⣧⠀⠀⠀⢠⣄⠀⠈⠀⠀⣰⡄⢀⣁⠈⣱⠇⣾
⠀⠀⠀⠀⠀⠈⢷⡀⣶⡔⠈⣴⡧⠘⠿⣠⠀⢰⣟⡇⠀⠻⠼⠀⠀⠀⠴⠋⢀⣰⡆⠈⠉⢡⠎⠙⠀⣈⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠻⣎⣡⣖⠙⡿⠃⠀⣽⣷⠈⠙⠁⣴⡄⠀⠀⣼⡆⠀⠀⠈⠙⠃⣀⣠⡕⡐⡁⣸⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣏⢱⡄⢰⠔⢈⣩⣦⠀⠀⠿⠟⠀⠀⢉⠁⠀⢠⡦⠀⡀⣛⡶⠰⠷⣄⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡓⢎⠀⣤⠚⠟⠀⠀⠀⣦⠀⠀⢸⣧⠀⠛⠃⢀⡃⣠⣀⣦⣌⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⡄⠻⣅⢀⣽⡆⠀⠙⠁⠀⠀⠀⠀⠀⠠⠙⡁⠻⢁⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣣⡂⠻⠯⠀⣸⣷⠀⣸⣧⠀⣷⡴⠛⠀⠿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣶⣦⠀⢈⡋⠀⢨⠅⡜⠉⠤⠰⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡀⠠⠀⢠⣾⠀⡀⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠦⢾⣥⠶⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠀⠀⠀⠀⢸⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⡓⠤⣀⠀⠀⠉⠀⠀⢀⠴⠒⠋⠁⠀⠀⠀⠀⠤⠐⣒⣩⠔⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠢⢬⣐⠀⠀⠀⢸⢀⣀⡠⠄⠀⠀⣠⠖⠖⠩⠋⠉⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⣀⣈⠀⠐⠀⠁⢠⡄⢈⣉⡥⠴⠚⢋⡟⠁⢠⡤⣀⣀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠀⠀⠁⢸⠁⠀⠀⣰⣎⡠⠖⠛⠛⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡀⢧⠈⠫⡛⠲⣄⣸⡤⠶⠊⠉⠀⠀⠀⠀⠀⠀⠤⠤⠿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⡀⠈⢧⢸⠗⢦⠀⠸⠥⠀⣀⣀⡀⣀⣀⣤⢤⠴⠒⠒⢩⠏⠁⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠈⠻⡀⠀⢱⢲⠒⠉⠁⠙⠉⠀⠀⣷⠋⣠⠊⠀⠃⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠎⣿⠊⠉⡗⢀⠑⢄⡈⢸⠀⠀⠀⠀⢀⣀⡴⠥⠾⠁⠐⠒⠒⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠗⡄⠀⠠⠁⠀⠘⣤⠀⢓⠌⠓⠚⠒⠒⠉⠉⢉⡀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠃⢀⡀⠀⠀⢳⡜⠀⠀⠀⠀⠀⠀⠤⣴⣶⢿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠖⠂⠈⠉⠉⠉⠉⠙⠶⢶⣲⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⢿⠛⠛⡟⠟⢱⢢⣦⣀⠀⠀⢀⠀⠈⠛⣷⣄⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠚⠷⢧⣲⣀⠄⠘⢻⣦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⢀⣠⡤⢊⠀⠢⠀⣡⣢⠠⡀⠤⡀⢀⠄⠀⠀⠀⠉⠙⠀⣄⠈⠻⡄⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⠛⠉⠀⠀⠁⠁⠀⠀⠀⠀⠃⡦⠺⠿⢾⢶⣵⣄⣠⡀⠀⠀⠑⠂⠡⠀⠈⣷
⢀⡟⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⣀⠠⠀⣠⣀⢀⡀⢠⡀⣀⠀⡀⠀⠀⠀⠀⠈⠁⠙⠶⢶⣤⣄⡑⢿⡼⢈
⢸⠃⠀⠀⠀⠈⠉⠉⠑⠢⠤⢄⣸⠉⠁⠈⠉⠀⠙⠉⠉⠉⠁⠋⠃⠋⠋⠉⠁⠢⠀⠲⠀⠠⠀⠀⠀⠀⠤⠈⣻⣷⢿
⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠑⠂⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⡤⡐⠴⠤⢒⠘⢹⣽⣿
⣿⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢷⠠⠠⢔⡤⣶⣲⠿⠎⠝⠊⠙⠀⠀⢀⠄⠃⢀⡿⣼⣷
⢻⡀⠀⠀⠀⠐⠀⠀⠈⢀⠀⢀⠀⢀⠀⠂⠀⡄⠀⠀⢠⠟⢾⠆⠓⠀⠐⠀⠀⠀⠀⠀⣀⣠⡤⠾⠋⠀⣤⣾⢇⡇⠏
⠈⢧⡀⢀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⢀⢀⡏⣰⢸⠀⠀⢀⣀⣠⣠⣶⢶⠞⠋⠁⠀⠀⠀⣼⠟⠠⢸⠋
⠀⠈⠣⡈⠢⡀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⡠⢡⠞⡴⣿⣸⣶⣰⠶⠞⠚⠛⠀⠀⠀⠀⠀⣠⣴⡿⣛⡰⠙⠁
⠀⠀⠀⠙⢦⣈⠂⠀⡀⠀⠀⠀⠀⠀⢀⠄⢀⣴⣾⣾⣷⣟⢁⠀⠀⡠⡀⠀⢀⢀⠀⢀⣰⣿⣟⠿⠓⠉
⠀⠀⠀⠀⠀⠙⠻⢶⣤⣬⣁⣈⣈⣥⣤⡾⠿⠛⠋⠁⠀⠈⠉⠛⠚⠚⠒⠺⠒⠓⠛⠋⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠈⠋⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⠄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠨⠀⠀⠀⠀⠀⣀⣀⣀⠹⣦⡀⠀⢀⣒⣢⣠⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠛⢧⠡⢤⣤⣽⣿⠿⠿⠿⠛⠻⣵⠛⠋⠉⠉⠉⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣙⣳⠤⡄⣈⣆⢸⡅⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠞⢷⢬⣁⠓⠬⣹⡆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠘⠏⡝⢲⡿⠌⣧⠀⠀⣀⣠⣄⡤⠤⣄⠹⢀⣀⣈⡩⠥⠤⠴⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣄⠈⣜⡦⠤⠤⠶⢒⣒⣊⣩⠭⠭⠄⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢻⠇⠈⠋⠉⠉⠉⣭⠀⢰⡆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠙⣏⠐⠀⠃⠁⠀⠀⠀⠄⠸⠧⣄⣀⣿⡵⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠶⠝⠛⠀⢠⠈⠑⠒⠂⠁⠀⠠⡽
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠷⠤⠄⠈⢀⣄⠃⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣯⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⣵⠟
⠀⠘⠀⠀⠂⡀⠀⢀⠀⠀⠀⠀⠠⠂⠁⠂⠀⠀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⢀⡼⠁⠐⣀⠤⠒⠋
⠀⠀⠀⠠⣶⢋⣀⣠⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠁
⣾⡆⠀⢠⡕⣎⢉⡀⠀⠀⡠⠀⠄⠀⠀⠁⠀⠀⠀⠀⠰⠿⠀⠀⠂⠉⠘⠛⠀⠁⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰
⠚⣁⢀⣐⣾⠛⢷⣶⠾⣎⣀⠀⠐⠄⡀⠾⠷⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⡄⠀⠑
⣄⡨⢫⠏⠸⣆⣼⠁⠀⣘⢽⣇⠀⠀⠀⠀⠠⠀⠀⡡⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⢠⡽⠂⠀⠀⢠
⠉⢁⣿⠟⡓⠀⠉⠀⠀⠅⣼⠇⠀⠤⠄⣴⠀⣰⠏⠀⠀⠸⠀⢀⡀⠀⠂⠠⠔⠀⠀⠀⢀⡀⠀⠁⠀⠀⠁
⢠⠋⠀⠀⠀⠀⠀⠡⠤⠞⠁⠀⠀⠀⠰⢷⢸⣏⣠⢖⣹⡷⠚⠭⡛⢷⡄⠀⠀⠀⠈⠂⡀⠈⢠⡄⠀⠀⠆⠀⠸⡶
⠁⠀⠀⣠⣴⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠶⢸⣿⠙⠻⡆⠀⠀⢆⠸⡇⠀⠀⠇⠀⠀⠘⣤⠀⠠⠎⠀⢀⠀⠀⠀⢀
⠀⠀⠙⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⢷⣦⠀⠀⣭⣏⠳⠶⠝⠂⠄⡀⢈⠇⠀⠀⠘⢦⡀⣀⣈⣿⡟
⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢐⠊⠀⠙⣛⢻⣤⡞⠂⠀⠀⠀⠁⠀⠀⠀⠂⠈⠈⠁⠉⠙⠛⠒⠊⠀⠀⠀⠙⠃
⠀⢸⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠉⠁⠀⠀⣠⠾⠀⢹⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠂
⡕⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⡠⠀⢸⡀⠀⢷⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⣤⣠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠪⣟⢳⣦⠀⡇⠀⠀⠣⡀⠀⠀⢀⣼⡃⡀⠀⠀⠀⠈⠁⠀⠐⠀⠀⢠⡴⠞
⢀⡴⠂⡀⠀⠀⠠⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠈⠥⠁⠀⡀⠀⠀⠀⠢⠄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠁⠀⠀⡇⠀⡀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡤⡀⠀⠀⠐⢀⠄⢀⠠⠤⣴⠀⢠
⡤⢂⣾⠖⠺⢛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠎⠀⠂⠀⠀⠈⠁⠀⠀⠀⠲⣾⣸⣏
⡟⠛⢿⠀⠀⠸⠁⢿⠀⠀⠀⠀⠄⠀⠠⡀⠀⠘⠛⠀⠀⠀⠀⠋⠀⠀⠀⡴⠁⠀⠀⠀⠀⢠⣤⠀⠀⠘⢀⠀⠀⡾⢹
⠳⠦⠬⠶⠠⡀⠀⣹⠀⠀⠆⠀⠐⢦⠀⢠⠄⠠⠀⡄⠀⠡⠁⠀⠀⠀⣿⠃⠀⠠⠈⠀⠀⠀⠉⠀⠀⠀⢷⣭⠄⠀⣉
⠇⠴⠲⠀⠀⠀⠈⠁⠀⠀⠆⠀⠀⠸⠆⠨⠠⠂⠀⠂⠀⠀⠀⠀⠀⠘⠋⠈⠀⠀⠐⠀⠠⠀⠀⠠⠀⠀⠡⠸⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⡠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠈⠑⢄
⠀⠀⠀⠀⠂⠀⢸⠁⠀⠀⠀⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢈⠇⠐
⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⠀⠘⠃⠈⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢋⠙⠳⣄⠀⠀⠀⠀⠀⠀⣴⠟⢉⠙⠳⣄
⠀⠀⠜⣃⡀⢀⠤⣄⢑⣄⣀⣀⣀⣀⡊⢀⠤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢺⠺⡁⠸⠀⠀⠀⠀⠀⠠⠇⠐⢪⠮⡁⠿
⠀⠀⠀⠉⠁⠹⢤⠜⠈⠉⠉⠉⠉⠉⠁⠸⠤⠜⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢠⠄⠀⠀⢀⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘
⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⡠⠤⠦⠤⢦⡬⠤⠤⠤⠄⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢦⣤⣤⣀⠀⠀⢀⣴⠞⢻⣇⠀⠀⠀⠀⢀⣠⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠈⠉⠛⢦⣾⡃⠀⠀⢻⡆⠀⣀⣴⠟⠋⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠹⣷⡀⠀⠀⠀⠠⣈⢧⡀⠀⠀⣧⢞⣩⡴⠞⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠤⡄⠈⠛⢦⣄⣀⣀⣀⣑⣷⣴⣴⡷⠿⠷⠶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠳⠾⠃⠀⠀⣠⣾⠿⠋⠉⠭⢿⣿⣿⠿⣄⠉⠀⠀⠉⠻⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡔⢲⡄⠀⠀⢠⣤⣴⡿⠋⠁⠀⠀⢀⣠⡾⣿⡀⠑⢀⠑⢦⣤⣤⣤⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠘⠗⠋⠀⠀⠀⣀⡈⠛⠿⠷⣶⣶⠿⠟⠋⠀⠹⣷⣄⠀⠁⠈⢿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣞⢁⠇⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠘⠻⢿⣶⣤⣬⣧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠒⡄⠀⠀⠀⠀⠙⠉⠀⠀⠀⣼⠁⣽⠀⠀⠀⢰⡏⣹⠀⠀⠀⠀⢩⡤⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠻⠾⠃⠀⠀⠀⢀⡔⢲⡀⠀⠀⠘⠛⠁⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⢸⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⠀⠀⠸⣷⡾⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣠⠒⡄⠀⠈⠉⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣾⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣠⠇⠀⠀⠀⠀⣷⡴⠃⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠁⠀⠀⠀⣠⠤⡄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣀⣄⠀⠀⠀⠀⠀⣯⣴⠇⠀⠀⣠⠴⢦⠀⠀⣰⠊⣩⠂⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⡃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠞⠀⠀⠙⣋⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡉⠉⠀⢀⠔⠆⠀⠀⢀⡴⢲⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⢿⡴⠃⠀⠀⠸⠶⠞⣀⣤⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣤⣤⣶⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣏⣩⣬⣩⣿⣹⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉⠉⠉⠉⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠷⠤⠤⣀
⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⡀⠀⠀⠀⠀⠀⠉⠢⣄
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⢿⡀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠔⠀⠄⠀⠀⠈⢆
⠈⢷⡀⠀⠘⢦⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣤⣤⡴
⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⠚⠛⠋⠉⠁⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣠⣤⡴⠶⠚⠋⠁
⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠈⢿⡄⠀⠀⠀⠀⠀⣾⠋⠙⣷⠀⠀⠀⠀⠀⢠⡿⠁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠸⣷⠀⠀⠀⠀⣸⡏⠀⠀⢹⣇⠀⠀⠀⠀⣾⠇⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⡆⠀⠀⠀⣿⠁⠀⠀⠈⣿⠀⠀⠀⢰⡿⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢠⣿⠀⠀⠀⠀⣿⡄⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣸⡇⠀⠀⢸⣿⣀⣀⣀⣀⣿⡇⠀⠀⢸⣇⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣉⣉⠉⢹⡇⠀⠀⢸⣿⣉⣉⣉⠉⣿⡇⠀⠀⢸⣏⣉⣉⡉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠁⢸⣧⠀⠀⣸⡟⠛⠛⠛⠀⢹⣇⠀⠀⣼⡟⠛⠛⠋⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠛⠛⠛⠛⠛⢻⡟⢻⣿⠛⠛⠛⠛⠛⠛⣿⡟⢻⡟⠛⠛⠛⠛⠛⠛⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣶⣶⣶⣶⣶⣾⣷⣾⣿⣶⣶⣶⣶⣶⣶⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠻⠛⠛⠛⠀⢿⡅⢀⣿⠟⠛⠛⠛⠃⠐⣿⡀⢨⡿⠛⠛⠛⠛⠃⠸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠾⠿⠶⠿⠿⠿⠇⠸⠿⠶⠿⠿⠿⠷⠶⠿⠇⠸⠿⠷⠿⠾⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⢸⡄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠠⠤⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠈⠁⠀⠈⠀⠀⠀⠀⠉⠁⠀⠐⠄⡀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣠⣴⠀⠀⠀⠀⢀⠀⠀⠘⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠆
⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⠓⠚⠛⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠠⠤⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠤⠀⢀
⠀⠀⠀⠀⠀⢄⣀⡀⠈⠁⠀⠀⠀⡀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣁⢀⡀⠀⠀⠁⠒⠁⣄⡤⠄⡀⠈
⠀⠀⠀⠀⠀⠀⢆⢀⠠⣄⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠈⠋⠉⡁⠀⠀⣀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠖⠃⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠠⠀⠂⠀⠤⠄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠤⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⣩⣭⣉⣤⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣉⣉⣭⣍⣥⣴
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣈⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣈⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⢀⣴⠊⠙⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⡴⠆⠀⠐⠃⠀⠀⠐⠚⠂⡀⢀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⣀
⠀⠀⡘⠁⠀⣠⣄⠀⠈⠓⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⠀⠐⡻⠁⠀⢰⡀⠠⠟⠂⠀⠀⢠⣄⠉⠁
⠀⠀⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠋⠀⠀⣀⠠⠁⠀⢾⠦⠐⠉⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡇⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠰⠦⠀⠀⢀⡤
⠀⠀⠻⠄⠀⢀⡀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠁⠘⠃⠀⢀⣤⢤⡄⠀⣤⣤⣤⣤⣀⣰⣏⡼⢀⠀⠀⣠⢤⠀⠀⠀⠘⠺⢇⡀⠀⣉⠠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⣾⠇⢈⣋⠀⣨⢍⢩⣿⢭⡄⣾⣰⢒⠛⢮⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠸⠿⢠⣿⢸⣾⣧⣸⣾⣿⣞⠱⠧⠻⠄⢺⣆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣠⠿⣏⠟⠙⠳⢋⣈⣥⡿⢷⣋⣉⣱⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠘⠿⠿⠛⠋⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢤⡀⠀⠀⠀⠀⠀⠀⣠⢇⣈⣉⠠⠄⣄⠀⠂⠀⣀
⠀⠀⠀⠚⢱⡄⠘⠁⠀⢀⣠⡀⠀⠘⠿⠀⠀⠀⠀⢀⠠⠞⠁⠠⡶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⣿⠞⣉⠀⠀⠤⠀⠀⣀⠀⠁
⠀⠀⢸⣇⠀⠀⣀⠀⣤⡄⠁⢠⣤⣄⠠⢢⠆⠀⢠⡇⠐⠂⠀⠀⠀⠘⠀⠈⠉⠀⠙⠂⠀⠀⠀⣾⣶⡿⢷⠛⣛⠛⠛⠻⣄⣠⡗
⠀⠀⣾⣿⣿⣦⣦⣤⣠⣤⣄⣀⣀⣤⠴⠏⠀⠀⡰⠀⠈⠉⠀⠀⠀⠄⠰⣆⠀⠂⠀⠀⠀⠀⠀⣿⠋⢠⣄⠈⠋⠀⠠⣤⠀⠙⢆
⠀⠀⠙⣾⣶⣤⠆⠈⠉⢉⠀⣀⣰⣿⣧⡾⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⡆⢀
⠀⠀⠈⣛⡛⠛⠉⠙⠛⠛⣻⡏⠉⠁⣀⣀⡤⠀⠀⠀⠀⠲⠀⠀⠀⠀⠘⠀⠈⠁⠠⠒⠂⠀⠀⣷⠉⢀⡀⠀⠀⠙⠀⢀⠀⡆
⠀⠀⢘⡹⠋⢹⣗⠛⠛⡿⢓⡖⠚⠛⠙⣋⡀⠀⠀⠀⠀⣀⠀⠠⠔⠒⠀⠂⠀⠀⢀⡀⠀⠀⠀⠘⡆⠈⠋⠀⠤⠀⠀⠀⠁
⠀⠀⢾⡿⣻⡗⢶⢤⡶⠶⠶⠶⠚⢋⣍⠡⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⣶⡆⠀⠀⠈⠁⣰⠂⠀⠀⠈⠲⠄⣀⡀⠐⠖⡠⠖
⠀⠀⠀⠛⠻⠷⠦⠍⢁⣀⣠⠤⠤⠤⠽⠚⠁⠀⠀⠀⠀⢤⠀⢤⠄⠀⠀⠀⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⡞⠉
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠖⠢⠀⠐⠊⣿⠃⢠
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠴⠄⠈⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠂⣀⡠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠃⠄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠳⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⠰⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡲⠀⣀⠀⠀⠀⠈⠀⠱⠀⠀⠀⠠⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠰⠒⢻⠷⣄⡈⠀⢐⠻⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⡄⠀⠤
⠀⠀⠀⢠⢦⡤⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠐⡶
⠀⠀⠀⠀⠗⢦⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠈⠓⠠⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⢠⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣦⢀⣀⡀
⠀⠀⠀⠀⠀⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠐⠠⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠻⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡤⠀⠘⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠴⣠⣿⠖⢲⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣤⣄⣟⠃⠀⠀⠀⠀⠀⠀⢤⣴⣄⣁⡀
⠀⠀⢠⣍⠀⠀⠀⠀⠂⢿⠀⠀⠀⠀⠀⠀⠐⠰⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠇
⠀⠀⠘⡇⠀⠀⠀⠀⠈⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠣⡄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⠉
⠀⠀⠀⠀⠀⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⠟⠁⢀
⠀⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡸⣿⣫⣉⣉⣛⠂
⠀⠀⠤⠞⠃⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡅⠻⢿⣗⣳⣂⣁⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠑⠂⠀⠀⠀⠐⠀⠀⠀⡃⠀⠀⠈⠛⠶⢌⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠯⣅⡀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⠦⢄⡀⠈⠁⠀⢀⠤⠒⠊⠁⠀⠀⠀⠤⢐⣂⡭⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⡒⠢⢅⡀⠀⢀⣄⡤⠄⢂⣀⡠⠒⠛⠙⠙⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⣶⣤⡈⠀⠀⢾⠀⡴⠒⠋⢉⠜⢀⣰⣦⡤⣶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢟⠻⣶⣤⣀⢰⣆⣀⡤⠟⠒⠉⠀⠀⠀⢀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⢲⡸⡧⡈⠂⢜⠉⠉⠁⠀⠀⣀⣀⣠⠬⠭⣽⠓⣪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠈⠻⡁⠈⠶⡔⠒⠋⠙⠋⠉⢹⠞⣠⠆⠰⠁⠀⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠤⠾⡗⠉⣹⠠⡑⢄⠃⡇⠠⠀⠀⣀⣤⠯⠞⠃⠒⠓⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢉⣟⡶⠀⡐⠀⠈⠱⣄⢻⠆⠉⠉⠉⠉⠀⠠⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠀⠘⠋⠀⠀⠀⠀⠀⠚⠛⠋⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀
⠀⠀⠀⠆⢴⣂⡐⣔⢖⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⡠⠶⠃⠻⣆⣴⠃⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⡇⠈⠉⠁⠉⠁⢹⡇⠀⠀⠈⠁⠀⠈⠀⠈⢹⠀⠀⢳⣉⣈⡦⠄⠀⠈⠁⠀⠀⠀⠒⠀⠐⠂⠀⢺⡀
⠀⠀⠀⡅⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠂⠀⠒⠀⠀⢾⠀⠀⠀⠁⣀⠀⢨⠀⠀⣼⠀⠀⠀⣀⠀⢠⠄⠀⣸
⠀⠀⠀⠇⠀⡆⠐⢲⡐⢿⡇⣠⡆⠀⡀⠀⣠⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⢲⣁⡄⣮⣫⣼⡇⠈⠇⠀⠀⠀⢀⠀⠀⣸⠁⠀⠀⠀⠉⠀⠈⠁⠀⢹⠀⠈⠀⠉⠀⠈⠁⠀⢹
⠀⠀⠀⣿⢡⠴⡖⢟⢻⣼⡇⠀⠈⠀⠁⠀⠉⠀⠈⣹⠂⠀⠀⠀⠒⠀⠐⠂⠀⢺⠀⠀⠀⠒⠀⠐⠂⠀⢺
⠀⠀⠀⡏⠀⡀⠗⢙⣿⣸⡇⠀⡏⠈⠢⠀⠐⠤⠾⢻⡇⠀⠀⠀⠀⠀⠠⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠃⠀⡇⠈⢹⣿⣿⡇⠀⣟⣠⡤⠄⢀⣠⡀⢙⠃⠀⠀⠀⡀⠀⢀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣇⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡿⠟⠛⠛⠛⠛⠛⠛⠿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡈⡄⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠠⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣤⠀⠄⢸⣿⣧⣤⣴⣶⣾⣾⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠂⣤⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⡄⢰⡄⢠⡇⢀⡞⢠⠆⠀⠀⠀⠈⠹⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⡇⢀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣾⠟⠁⠀⢄⠘⣆⢻⠘⡇⣸⢁⡞⡰⢋⡴⠊⣀⡠⠀⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⣿⣿⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⣠⣿⠋⠀⠀⠢⣌⠳⠘⣢⠴⠷⠿⠛⠻⢷⣏⡴⠞⠋⣀⡀⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡀⠀⢂⡄⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠐⠲⠦⢌⣃⡾⠋⠀⠀⠀⠀⠀⠀⢸⣿⢚⣋⣉⣀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⢰⣿⣇⠀⢯⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⣼⡿⠀⠀⠈⣋⣛⣻⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣩⣤⣀⠀⠀⢀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⣰⠀⠆⠻⡤⠁⡄⠀⣄⠀⡤⠀⠀⣿⡇⠀⠈⣉⣉⣡⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠶⠤⣤⡀⠀⠀⣼⡿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠁⢰⡔⠆⡰⢀⠅⡀⠈⠰⠀⠀⠀⣿⡇⠀⠀⢉⣠⡤⠾⣷⣤⡀⠀⠀⠀⠀⠀⡀⢾⢿⡝⠓⠶⠄⠀⠀⣴⡟⣥⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⣤⣁⠈⠙⠘⠁⠈⠀⠀⠀⢀⣿⣷⠀⠈⠉⢀⣴⠞⣫⢟⡿⣾⡶⠶⠶⠖⣷⠘⠇⠙⠦⠀⠀⠀⣴⡿⣀⣛⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣦⣤⣤⣤⣴⣾⡿⠿⣿⣆⠀⠀⠉⠀⡴⢋⡞⣸⠁⡟⢸⠘⡇⠘⠇⠈⠁⠀⠀⣠⣾⢛⢈⡵⢁⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⠉⠀⠀⢹⣿⣷⣀⠀⠈⠁⠈⠀⠁⠈⠁⠈⠀⠁⠀⠀⠀⠀⣠⣾⠟⠃⠦⠬⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠿⣫⠁⠒⠐⡀⣤⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⠉⠉⠛⠛⠛⠛⡛⠉⠭⠑⡄⢉⠂⢀⠁⠈⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⣀⡀⠰⠀⠑⠀⠈⠐⠁⣀⣡⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣷⡶⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠁⠀⣴⣠⢆⣶⣦⣴⣶⣤⠤⣤⣤⣤⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⣴⣤⣤⣾⠟⠛⠋⠉⠀⠀⠀⠁⠀⠀⠉⠉⠘⢧⣄⣿⣷⡄⣀⡠⠆
⠀⠀⠀⠀⠀⠀⢀⡏⢀⣼⡿⠛⠁⠈⠀⠀⣀⣀⣠⣤⣾⣷⣶⡿⢭⠴⠾⣶⣿⣭⣵⣾⡁
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⣰⣷⣤⣿⡿⣿⠋⠙⠀⠀⠀⠀⠀⢠⣴⠏⣿⢿⡻⣷
⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⢠⣴⣼⡿⠛⠻⠁⠀⠀⠀⠀⠀⣄⣀⣠⣶⠇⠁⢰⡧⢸⡃⣿⡀
⠀⠀⠀⠀⠀⠀⣯⣀⣸⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠇⠀⣙⣿⡗⢾⣿⢹⠇
⠀⠀⠀⠀⠀⠀⢻⣾⠏⠈⠀⠀⠀⠀⠀⠀⠀⣶⣴⣾⣿⡿⠟⠏⠀⠰⣶⣿⣿⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⡀⠀⢠⣤⣷⣾⣿⣿⠋⠁⠀⠀⢠⣤⣾⣿⡿⣽⣽⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄⣠⣿⣷⣿⠻⠋⠀⠀⠁⢀⠂⣶⣴⣿⡿⠟⣙⠳⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⠉⢉⠀⠀⠀⠀⣶⣤⣼⣿⣿⣟⡋⠡⠌⠿⠿⠿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣼⣶⣾⣿⣿⡿⠿⣧⡀⣒⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠭⣿⣴⣤⣴⡏⡆⢹⡄⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣀⠂⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢼⡀⠧⠀⠀⢠⡾⢀⡄⢀⠂⠀⠃⠐⠀⣌⠁⣤⡀⠙⠃⡈⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣷⡐⢦⡀⠀⠀⠟⢡⡿⠀⣾⡄⢸⡆⢹⡇⠙⠃⠀⣰⠁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣌⠻⣆⢀⠀⠈⠁⠀⠙⠁⠘⠃⠀⠀⠀⢀⠔⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣌⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠄⠉⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣈⣉⡘⠛⠙⢀⣁⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡁⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⡆⢸⣏⡝⢄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⠘⡇⡀⠀⠀⠀⠀⣠⠟⠀⣼⠃⡈⣯⢂⠉⠉⠱⠒⢂⢄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠖⠒⠊⠉⠁⠀⠸⠁⠀⡇⢹⡆⡑⠀⠀⠀⠈⠀⠉⠑⠂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠚⣿⣛⡻⠟⠋⠀⠙⠀⣠⠀⠀⠀⡆⢸⠇⠳⣤⠤⢀⠈⠀⠈⠑⠀⠘⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣠⡴⠞⠁⠀⣀⠀⠁⠀⢠⡏⣶⠀⠀⡇⢸⠀⠠⡟⢀⠀⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠠⣾⠷⠋⠀⠀⣠⡜⠁⠀⠀⣿⣿⣷⠿⠀⠸⠀⣿⡄⠀⠁⠘⢦⡀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣿⡴⠃⠀⠀⢀⡴⠋⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠘⣿⣇⠀⠀⠀⠈⢳⠄⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣎⡁⢠⡟⠁⠀⠀⣠⠊⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⢄⣄⡀⠻⣿⡄⠀⠀⠄⡀⢢⡀⠀⠰
⠀⠀⠀⠀⠈⠛⠶⠾⣿⡾⠿⣷⡟⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⠟⢁⢈⡈⠁⠀⢐⣋⣡⠰⢿⣷⣄⢠⠀⡇⣾⢓⠦⢭⡆
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠉⠀⠀⠀⣶⠃⠀⠀⠀⢤⣼⠋⠠⠀⣨⠄⠀⡀⣺⠤⣼⠀⢿⣿⣿⣦⣇⣰⣄⣹⣿⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡰⠁⠀⠀⢀⢰⣾⠃⠀⠀⠀⠴⠀⠤⢤⡟⠲⠖⠀⢸⢹⣟⢻⣿⣿⣝⡛⠻⠛⠛⢓⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⣠⠁⠀⡄⠠⢄⣾⡏⠀⠀⠄⣴⠂⠀⠀⣼⠛⠓⡏⠀⠈⣼⣏⢀⠿⡄⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡉⠐⠤⠀⣠⣾⣿⠃⠀⠂⠠⠈⠀⠐⢤⣌⠉⢻⠃⠀⠀⢿⣿⣇⢰⣷⣦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡁⠄⣠⣾⣿⣿⣿⠀⠀⠐⠲⠉⠀⠒⢾⡅⠉⡋⠀⠀⠀⡞⠈⠙⢾⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⣿⠀⢉⠐⢊⠈⠀⠲⠅⣀⡸⠁⠀⡴⡼⠁⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠋⠁⠀⡄⢨⢨⠄⠀⢀⡾⠦⢤⠃⠀⣰⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠰⣴⠂⠢⣼⣃⡒⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠃⠶⠗⠋⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⣠⣤⣤⣀⣀⣀⣀⣀⠀⠀⣠⣴⡾⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠖⠲⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠓⠒⠋
⠀⠸⣿⣿⣿⠿⠟⠋⠉⠰⢿⡟⠁
⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠔⢲⣀⡀⡄
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣠⣦⣀⠈⡟⠀⠀⠀⠀⠀⣸⠁⣴⣦⣤⡀⢳⠆
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠻⠿⢏⣠⠃⠀⠀⠀⠀⠀⠱⡀⠙⠻⠛⠁⢀⡧
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠢⠔⠉⠉
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢢⣤⣤⡄⠑⠆⠀⠀⠀⠀⠀⢰⠎⣡⣈⠣⡤
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⠸⠿⠿⢏⠔⠓⠀⠀⠀⠀⠀⢽⡀⠿⠿⢃⠇
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛⠊⠉
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⡠⠴⠔⢆⡀
⠀⠀⠀⢸⢿⡧⠤⠤⣼⣿⣯⡧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⣾⣿⡆⠀⡇⠀⠀⠀⠀⠀⢼⢰⣿⣿⡆⢸
⠀⠀⠀⣼⣸⡇⠀⠀⢸⣿⡧⡇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣈⣉⠤⠎⠁⠀⠀⠀⠀⠀⠀⢇⣙⠛⡡⠼
⠀⠀⠀⠛⠿⠿⢿⣶⣶⣶⣶⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⢲⣞⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢦⣤⠞⠉⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⢠⣶⡾⠟⢋⠩⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣤⣴⣶⠿⠟⡋⣃⡈⠐⢂⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠄⢀⣀⣤⣶⡿⠷⠜⠋⠡⠀⠈⠀⠀⠘⢷⡄⠈⢂⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣾⠿⢛⠉⠁⠒⠙⣶⡄⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⢆⣀⣠⣤⡶⠟⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣀⣠⣼⣿⣦⠸⢛⣩⢥⡲⣯⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⢀⡶⠿⣛⠫⢭⣤⠶⣾⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣤⣶⡾⠿⣛⣭⣿⡶⠿⣞⣗⣥⠬⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡐⢨⣿⣷⣾⣿⣏⡦⠽⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠾⠟⠛⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠄⠀⠁⢄⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠂⠀⠀⠀⠀⠠⠀⠀⢀⡄⠀⢤⠀⠀⠐⢒⣶⡶⠀⠀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⠲⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠒⠚⠒⠒⠖⠁⠀⠀⠄⠀⠀⠰⠞⠈⠃
⠀⠀⠀⡄⠉⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⡅⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠉⠉⠅⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⠀⣠⣶⣾⡶⣶⡶⣶⣶⣶⢶⣦⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⣀⠀⠠⣄⠀⠀⠀⠉⠀⢿⣿⣧⣼⣼⣿⣧⣿⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⢤⡀⠘⠣⡀⠈⠳⣄⠈⠳⠄⠀⠀⠀⢈⠉⢋⡉⠉⠉⠉⠉⠉⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠙⠆⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣴⠆⢀⣤⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠀⣠⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⢠⡶⠘⢃⣄⠾⠋⠀⣴⣦
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠼⠃⠀⢸⡏⡠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠄⢀⠀⠀⠘⠀⠀⠿⠁⠀⣾⣷⠟⠁
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢉⣉⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣧
⠀⠀⠀⢼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡿⠀⢿⡄⠀⠀⢀⣠⡴⠶⠶⠲⠶⠶⣤⡀
⠀⠀⠀⢸⡈⠛⠶⣤⣄⡀⠀⠀⣠⡴⠖⠛⠛⠳⢦⣼⠛⠦⣄⣼⣁⠀⠘⣧⢀⣴⠟⠉⠀⠀⠀⠀⡀⠀⠀⢙⣧
⠀⠀⠀⠘⣧⠀⠀⠀⠈⠉⣹⣞⡁⠀⠀⠀⠒⠢⣄⣿⠀⠀⠀⠈⠉⠙⠓⢿⣿⠃⠀⠀⠀⢀⡴⠋⠀⣠⣶⡋⠁
⠀⠀⠀⠀⠘⢷⣄⡀⠀⠐⠋⠉⠙⠳⣦⡀⠀⠀⠀⠙⢦⡀⠀⠑⢦⡀⠀⠀⠙⢧⣀⣠⠴⠋⠀⣠⡾⣯⣀⠙⠲⠦⠤⠴⠶⣶⠟
⠰⣶⡶⠶⠶⠶⠾⠛⠛⠛⢋⣉⣡⡤⠾⠿⣷⣤⣄⣀⣀⣹⣆⠀⠀⠙⣦⠀⠀⠈⢿⣁⣠⡴⠞⠻⠶⠶⢦⣤⣤⣤⠴⠶⠛⠁
⠀⠈⠛⠶⢦⣤⣤⣀⣀⣈⣀⣉⣠⣤⠶⠛⠉⠀⠉⠉⠉⠉⠻⣦⣄⣀⣹⣆⣤⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⢀⡶⠋⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠳⡄
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⢹⣄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠢⠀⠀⠀⠀⠀⠀⢿
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠤⢀⠆⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⣿⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠎⠂⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⢀⠀⡓⠀⣸
⢸⡇⠀⠐⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢰⢒⡄⠀⠀⣠⡀⠀⠐⠀⠀⡀⠤⠀⠀⠀⠀⠆⠀⢀⠐⠀⠈⠀⠃⢠⡿
⠀⢿⡄⠄⠀⠀⠀⠇⠀⢐⡂⠀⠀⠀⠣⡼⠀⠀⠀⠀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠀⡜⠐⢁⡤⠀⢀⣿⠃
⠀⠈⢷⡈⠀⠀⠄⠀⠠⢈⠁⠀⠀⡀⠀⠀⠀⠀⠐⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠚⠀⠀⣾⠃
⠀⠀⠈⢻⣄⠈⠂⠀⠀⢫⡇⠀⠀⢰⠳⡀⠀⠀⠀⣧⣹⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⢠⡌⠄⠀⠔⠃⠀⠈⠂⠀⣼⠇
⠀⠀⠀⠀⠹⣦⠀⠀⠀⡄⠀⠀⠀⠀⠓⠃⠀⠠⢄⡈⠁⠀⠀⠀⠁⠈⠠⠀⠘⠲⠃⢀⡀⠀⠀⡀⠀⠠⠄⠀⠠⢄⣽⠃
⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⠀⠀⠀⠰⡄⠀⠀⠈⠰⠇⠀⠠⠤⣄⠀⠀⠀⣠⠔⠂⠘⠁⠀⠀⠀⠀⠀⠃⣡⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⠀⠀⠑⠁⠀⠀⠒⢤⠀⠀⠀⠐⠈⠁⠀⠘⠀⠃⠀⡴⠓⠀⠀⢀⠒⠀⠈⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠀⠀⠀⢄⠀⠠⡀⠘⠀⠀⠀⠒⡄⠀⠔⡒⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢢⡈⠀⠀⢁⠀⠀⠒⣀⠈⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠁⢀⠤⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡁⠀⠀⠄⠀⡀⢀⠁⠀⠀⠈⠉⠑⠀⢀⣀⠀⠀⠀⠀⠃⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⡄⠀⠀⠁⠀⠉⠀⠀⠀⡀⠑⠀⠀⠋⠠⠄⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠙⡀⠀⠀⠠⠂⠈⠀⠀⠒⠂⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠠⣄⠀⠐⠒⢄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣤⡶⠾⠛⠁
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣰⣿⣿⠀⠀⢠⡏⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⡿⣿⣿⠀⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⡇⠀⠀⠠⡇⣿⣿⡇⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣦⠀⠀⠀⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⡇⣿⣿⡇⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⠀⢀⡼⣿⣿⣿⡀⠀⠀⣿⠀⣿⣿⣿⣿⡇⠀⠀⢰⢸⣿⣿⡀⠀⠰⡇⣿⣿⡇⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣧⠀⠀⢰⣸⣿⣿⣿⠀⠀⢸⠁⣿⣿⣿⡇⠀⠀⣿⠀⣿⣿⣿⣿⡇⠀⠀⡏⢼⣿⣿⡇⠀⠐⡇⣿⣿⡇⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⡴⢻⣿⣿⠀⠀⢸⠉⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿⡇⠀⠀⣿⠀⣿⣿⣿⣿⡇⠀⠀⡇⣸⣿⣿⡇⠀⠠⡇⣿⣿⡇⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⡇⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿⡇⠀⠀⣿⣀⣿⣿⣿⣿⡇⠀⠀⡇⣿⣿⣿⡇⠀⠀⡇⣿⣿⡇⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⡇⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿⡇⠀⠀⣿⠀⣿⣿⣿⣿⡇⠀⠀⡇⣿⣿⣿⡇⠀⠀⡇⣿⣿⡇⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⡇⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿⡇⠀⢸⠀⣿⣿⣿⡇⠀⠀⣿⠀⣿⣿⣿⣿⡇⠀⠀⡇⢿⣿⣿⡇⠀⢐⡇⣿⣿⡇⠀⢸⡇⣿⣿⣿⣿
⠀⠀⠀⣷⣿⣿⣿⠁⠀⢸⣶⣿⣿⣿⠁⠀⢸⣶⣿⣿⣿⡇⠀⠠⣿⣶⣿⣿⣿⣿⡧⠀⠀⣷⣿⣿⣿⡏⠀⠈⣷⣿⣿⡇⠀⠠⣿⣿⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡄⠀⠄⠀⠀⠀⠀⠀⡀⠀⠒⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠒⢀⡐⠛⠒⠒⢂⡘⡤⠀⠀⠐⠥⠴⢀⣄⠀⣤⣄⠄
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⢀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⢇⣔⣤⣠⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠖⠰⠦⠀⠀⠀⠀⢢⠠⠶⠊⠀⠀⠀⠠⠤⠠⠀⠀⠠⠀⠀⠀⠰⡄⣀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠁⠀⠐⠓⠀⠀⠀⠈⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⠂⠀⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠔⢃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣤⡴⠏
⠀⠀⠀⠀⠀⢠⡒⣂⡄⠛⢀⠀⠒⡶⠤⠻⠂⠀⠀⠀⠄⠀⠀⠐⣂⠅⠀⠀⠀⠀⠀⢠⠄⠀⢀⡀⠠⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠑⠂⠊⠉⠉⠀⠁⠀⠀⠀⠀⠀⠊⡶⠖⠡⠆⠐⠒⢢⠀⠀⠀⠀⢦⢀⠀⠈⡉⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠾⠖⠂⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠰⠀⠙⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⢶⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠶⠀⠀⠘⠀⠀⠀⠀⠤⠀⠀⡀⠄⠁⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢘⡀⠀⠀⡤⠀⣠
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠲⠀⠀⠀⢠⠤⢄⡀⠀⠀⡀⠀⡴⠀⠀⠀⠀⠈⣀⣤⢔⡜
⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⢀⠀⠀⠈⠄⠀⠀⠐⠂⢐⠉⢋⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠐⠈⠀⠀⠀⠁⠐⠓⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠠⠔⠒⢖⠉⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠒⠀⠘⡄⠀⣀⣬⣄⡤⠶⠖⢶⡉⠉⠉
⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⢀⠄⠠⠠⠀⡀⠀⠀⠀⠀⠹⡄⣀⣤⠭⠶⠖⠛⠛⠋⠉⠀⢈⣆⢀⡠⠤⠱⠒⠒⠋⡀
⠀⠀⠀⠀⡄⢉⣀⠤⠀⠁⠀⠀⠀⣠⣀⡀⢀⠀⣀⠀⠀⠀⠐⡟⠄⠀⢀⣠⡀⠤⠤⠐⠀⠈⠉⣩⠠⠴⠀⠔⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠄⠉⠛⡋⠄⠀⠀⠀⠀⠘⣖⠉⣁⡠⠴⠀⠒⠓⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠠⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠁⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢰⠀⠀⠀⠀⠀⠀⡀⠉⣆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢃⡀⠠⢀⠀⠀⠀⠀⠈⢀⠈⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠆⠈⠙⠲⣄⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣰⠏⠀⠐⠀⠀⠀⠀⠀⠙⢢⡀⠎⠠⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡚⠃⢈⡿⠷⠀⣀⠀⠀⠀⠀⠀⠀⢀⡜⢉⡛⢦⡀⠂⢄⠀⡤⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢿⡀⠀⠙⢦⡙⠢⡀⠀⠀⣠⠎⠠⠊⠀⠀⠈⠓⢤⣑⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⠀⡙⢦⡀⠀⠉⠒⢄⣀⡴⠃⠀⠀⣀⠀⠀⠀⠀⠄⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠈⠋⢻⠀⡉⠢⣄⠀⠀⠻⠶⢄⠀⠀⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠔⠉⢂⡀⠈⠉⢹⣠⠞⠳⣤⡁⠀⠀⠑⠂⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠄⠠⠀⡵⢢⡀⠈⠡⣴⡾⢧⡈⠓⠦⣄⡀⠘⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⠞⣡⠏⡉⣄⡀⠈⠀⡸⠀⢀⣄⣀⣉⡙⠁⡟⠛
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠆⢘⠸⡟⠙⠋⠈⢁⡜⠱⠦⣷
⠀⠀⠀⠀⠀⠀⣬⡁⠠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⡁⢅⠆⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣭⡥⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⢰⣿⣿⣿⡆⠀⣁⣘⢶⠃⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⣿⡝⣿⡇⠀⠺⡩⠡⠂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⡖⡶⣄⡶⣖⠂⠀⣀⣀⣀⣀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣀⡄⠀⠀⣴⣾⠳⢻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠓⠃⠙⠀⠓⠂⠀⠨⠭⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠻⠿⠶⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣾⡏⢀⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢃⡞⠁⠀⠀⠈⠁
⠀⠀⠀⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⢤⡄⢀⣀⡀⠶⠆
⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠠⣤⠀⢤⡄⠉⢠⡤
⠀⠀⠀⠀⠃⠀⠀⠐⠁⠀⠀⠀⠀⠰⠦⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣷⣤⡀⠀⠀⠀⠀⠀⣠⣶⡟⠁⠀⠀⠀⠉⠉⠓⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇
⠀⠀⠀⠀⠸⢿⡿⠏⠀⠀⠀⠙⠿⠇⠀⠙⠟⠀⠀⠿⠛⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⢸⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠸⠇⠈⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠻⠋⠙⠟⠁⠀⠈⠛⠁⠘⠛⠀⠀⠀⠀⠀⠆⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁
⠀⠀⠀⠈⠁⠀⠀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠀⢠⣤⣤⣤⠀⠀⣴⣦⣤⣄
⠀⠀⢠⣀⣀⡀⠀⠙⠛⠛⠁⠀⢲⠶⣶⠆⠀⠀⠀⠈⠀⠀⠀⢸⡋⠈⢻⠀⠀⠉⣭⣍⠉
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⢀⠀⠀⠀⠀⠈⣷⣶⡿⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠾⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠥⠶⠤⡀⡀⠀⠀⠀⠀⠀⢻⣤⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠠⢀⡽⠛⠦⡀⠀⠀⠈⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣾⣤⡈⠁⣠⣀⡀⠀⠀⠅⣈⠻⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⡻⢻⢻⣿⢟⣾⣿⣿⣿⠿⣧⣦⣄⠙⠓⠦⣉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠃⠈⡾⠇⢼⡏⣿⠋⠀⠀⠈⠙⢟⠀⠀⠀⠈⠑⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⡀⠀⠀⠄⠀⠻⠀⠘⠀⠀⠀⠀⠈⠀⢢⠀⠀⠀⠀⠀⠑⣔⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠓⠲⠶⢶⡶⣶⠇⠀⠀⠀⠀⠀⠐⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢊⠧⠠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠇⠀⠀⠀⠀⠠⠀⠀⠠⠗⣦⠱⡄⠂⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣌⡃⠀⡹⣆⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣿⠀⠀⡞⠀⢠⣠⣞⠀⠀⣣⠁⠐⠈⡿⣷⣄⢄⢀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣰⢃⣴⡿⣏⢩⡀⠀⠦⠄⠰⠀⠇⢨⠙⠳⢷⣝⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣿⡿⠛⣄⠹⣆⡦⠀⢺⡆⡀⠈⢀⠆⠀⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠘⢆⠙⣿⣆⢸⠃⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠻⣾⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣩⠞⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢰⠀⠐⠀⠠⠄⢀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠗⠀⠀⢀⣴⡆⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠛⠁⣀⡀⠀⠻⠃⠀⠀⠀⢀⣶⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⡄
⠀⠀⠀⢸⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠰⣿⠃⠀⠀⠀⣀⠀⠀⠈⠿⠁⠀⠘⢿⠇⢠⣦⡀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⣿⣆⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⣴⠀⠀⢀⡀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣶⡄⠀⡀⠈⠻⠃⠀⠀⠀⠠⠁⢠⠇
⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⠻⠋⠀⠀⣿⠇⠀⠀⠀⠉⠀⣴⡄⠀⠀⠛⠁⢸⣿⠀⠀⠀⠀⠀⡠⠀⢠⠏
⠀⠀⠀⠀⠀⢻⣿⣧⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠻⠇⢠⣶⡀⠀⠀⠉⠀⠀⠀⠀⠈⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣤⣀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⣀⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠛⠛⠛⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠚⠓⠒⠲⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠲⠦⠤⣴⣯⣓⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢉⣑⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⣹⠋⠙⡿⣿⠙⠲⠦⡤⠖⠒⠉⠁⢀⠀⣘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣨⠞⢽⢷⣄⠀⠁⠤⣔⡢⠭⢴⠞⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢠⠎⠀⡀⣼⣿⠀⢸⡾⠋⠓⡆⠉⠁⠀⢀⣮⡴⢎⠁
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡜⣰⠃⢸⣠⣿⣷⣦⣄⣀⡤⠶⡾⠟⠉⠀⠀⣻⡆
⠀⠀⠀⠀⢀⡾⠳⠤⢤⣀⣀⠀⠀⠀⠀⠀⣠⢎⣾⠉⢣⣿⣁⡀⠀⠀⠈⠉⠑⠆⠀⣠⠔⣡⢰⠁⢃
⠀⠀⠀⠀⣾⣕⣒⠠⠀⠀⠈⠉⠓⣆⢀⡴⢡⡏⢸⣴⡟⠛⠛⠫⠭⢭⣄⣀⡀⠀⢈⡴⢺⠡⣋⡴⠋
⠀⠀⠀⠀⠘⡄⣌⠉⡙⠦⢤⣀⡀⠚⠛⣱⠛⢇⣼⣿⣦⣤⣄⣀⣐⠉⠉⠀⠉⠉⢻⠄⣸⡟⠋
⠀⠀⠀⠀⠀⠈⠉⠒⠛⠓⢄⣙⠻⠉⢻⣧⡀⣼⡏⠀⠀⠀⠀⠀⠉⠉⠛⠒⠷⠤⢼⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠳⠿⠋⠀⡠⠶⣤⡀
⠀⠀⠀⠀⠀⠐⠒⣶⣷⠄⢈⡉⣹⢷⡀⠀⠀⡠⠊⠀⢠⣸⣿⡆
⠀⠀⠀⠀⠑⠶⠥⠾⠇⡈⠁⠀⠉⣂⡼⠁⠘⠅⣀⡀⣋⣠⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠉⠐⠋⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⣀⡰⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⠛⣦⣀
⠲⠤⠤⠀⣲⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡖⠂⠀⠀⠁⠀⠀⠴⠦⠄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣌⣨⡉
⣦⣰⣷⠿⠋⠀⠀⠀⠀⠀⠀⣀⢤⡀⠀⢠⡶⠷⠶⠀⠀⠀⠈⠀⢀⠀⡔⠉⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠺⡿⢍⡿⠃⠀⠀⠀⣠⢀⣠⡄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠉⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡷⠯⠽⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢶⣾⠁⠀⠀⢠⡾⠟⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠙⣼⡷⣤⡤⢾⡏⠀⠀⢀⡎⠀⠈
⠀⠀⠀⢀⡠⠀⠒⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠈⠉⠫⠁⠀⠀⣠⠟
⠀⠀⡐⠁⠀⠀⠀⠀⠆⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣤⣤⠤⠴⠚⠉
⠐⠚⠂⠀⠀⠀⠀⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⡄⡀⠀⣒⡀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠌⢢⠀⠀⢃⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠡⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢰⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⣀⠆⠠⠄⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠈
⠀⠆⠀⠀⠸⠄⠀⠁⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢀⠆⠀⠀⠀⠀⡐⠋⠉⠀⠀⠀⠐⠁⠀⢀⡀⠀⠀⠀⠀⠂⠀⠉⠀⠁⠀⢀⣰
⠐⠤⠄⡀⠉⠠⢀⡀⠀⠀⠀⠀⠊⠀⠐⠚⠋⢉⡉⠁⠀⠀⡀⡼⠇⠀⠀⠀⠀⠀⠁⢀⣔⠉⠀⠀⠀⠀⠀⠀⠐⠐⠂
⢀⠀⡔⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠡
⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣇⡆⠀⠀⢀⠄⠀⠀⠀⠀⠀⠘⠀⠠⠗⠂⠙⣧⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠰⢄⡀⠀⣀
⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠰⣄⠉⢀⡀⠀⡞⠀⠀⡢⣄⣀⠀⢠⢖⠀⠀⠀⣰⡍⠀⢀⡇⢬⣿⡆
⠀⠈⢀⠔⠀⠀⠀⠀⠀⠀⠀⠣⡙⢷⣷⣿⣿⡇⠀⠀⣿⢿⠀⠀⠀⠚⠿⢶⠨⠀⠀⣠⣞⠁⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠙⠻⠿⣿⡀⠀⠘⠾⠷⢿⣦⠓⠂⠀⣠⡴⠿⠓⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⠀⠙⠁⠀⢀⣽⣴⣉⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠄⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠄⠄
⢀⡁⠛⠹⡦⣄⣾⠟⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠠
⠈⠛⢞⡀⠈⠛⠁⠀⠀⢀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⠀⠀⠠⡿
⣄⡀⣀⢶⡀⠀⢰⠖⠚⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢼⣿⢧⡀⠐⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢱⠀⠀⣰⠊⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠀⠀⣧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⣤⠴⠶⣶⣶⣲⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠲⣶⠒⡒⠒⠒⠒⠒⢶⣶⣶⣒⠦⢤⣀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠉⠻⣖⢤⡉⠓⢤⡀
⠀⠀⠀⠀⠀⢀⡤⠖⣋⠍⠉⡠⢊⠄⠀⡀⠈⡆⠈⠀⠄⠀⠀⠀⢱⡀⠉⠙⢶⣌⠙⢢⣄⠀⠀⠀⢳⠀⠀⠀⣠⡄⠀⠱⡈⠢⡀⠙⢦
⠀⠀⠀⢠⠞⠁⡰⠁⠀⢀⠎⠀⠘⠀⠀⠇⠀⢘⠀⠀⠀⠁⠀⠀⠀⢣⢀⣤⠀⢣⠱⣌⢋⢣⡀⠀⠈⡇⠀⠀⠉⢀⡠⡄⠈⢆⠙⡄⠀⢳⡀
⠀⠀⡴⠁⢀⠎⠀⠀⠊⠁⠀⢠⠂⠀⢀⠆⠀⠀⢇⠀⠀⠀⠑⠀⠀⠈⢏⠁⠀⠀⢣⠘⡆⢣⠹⡄⠀⢹⠀⠀⠀⠈⠉⠀⠀⠀⢢⠘⡄⠀⢳
⠀⡜⠁⠀⠁⠀⢐⠁⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠈⢆⠀⠀⠀⠃⠀⠀⠘⡆⠛⠃⠈⡆⠸⡄⢆⢱⠀⠘⡆⠀⠶⠂⠀⠴⠴⠀⠀⠆⢰⠀⠘
⠸⠁⠀⠌⠀⠀⠎⠀⠀⠀⠀⠄⠀⠀⠀⡆⠀⠀⠀⠘⡄⠀⠀⠀⠄⠀⠀⢹⠀⡠⡀⢰⠀⢧⠸⠀⡇⠀⣇⠀⠒⠒⠀⠀⣀⡀⠀⢸⠀⡆
⡇⠀⠀⡆⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠈⠄⠀⠀⠀⠀⢣⠀⠀⠀⢀⠀⠀⠀⡇⠈⠁⠀⡀⢸⠀⢆⡇⠀⢸⠀⢀⣀⡀⠘⠂⠁⠀⢸⢀⠃⢠
⡇⠀⠀⡁⠀⠀⡅⠀⠀⠀⢀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠰⡀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠇⢸⡆⠈⡇⠀⢸⡄⠀⠀⠀⠠⡴⠀⠀⡄⡘⢀⡞
⡇⠀⠀⠡⠀⠀⢁⠀⠀⠀⠀⡇⠀⠀⠀⢘⠀⠀⠀⠀⠀⡃⠀⠀⠀⢱⠀⠀⢸⡄⠙⠃⡀⢸⠀⢠⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⣱⣡⠞
⢹⠀⠀⡘⢄⠀⠘⠀⠀⠀⠀⢣⠀⠀⠀⢀⠀⠀⠀⠀⠀⡕⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠇⡸⠀⡼⠀⠀⠀⡇⠀⠀⠈⠣⠂⣠⣿⠟⠁
⠈⣇⠀⠀⠈⠀⠀⠰⠀⠀⠀⠸⡀⠀⠀⠈⡆⠀⠀⠀⠀⢣⠀⠀⠀⡨⠀⠀⠀⡇⠘⢁⢠⠃⡸⠁⠀⠀⠀⡇⠀⠀⠀⣀⡴⠟⠁
⠀⠘⡄⠀⠀⢢⠀⠀⠇⠀⠀⠀⢃⠀⠀⠀⢃⠀⠀⠀⠀⢆⠀⠀⠀⡇⠀⠀⠀⡇⠀⢂⢎⡜⠁⠀⠀⠀⠀⢧⣤⠶⠛⠉
⠀⠀⠘⢆⠀⠀⢢⠀⠸⠄⠀⠀⠈⢆⠀⠀⠘⡄⠀⠀⠀⡆⠀⠀⢰⠀⠀⠀⠀⣇⣼⡿⠋⢀⠀⠀⢸⠓⢄
⠀⠀⠀⠀⠳⣄⠀⠣⣀⠐⠄⠀⠀⠘⡀⠀⠀⢡⠀⠀⢀⠃⠀⢀⠃⠀⠀⠀⢠⡿⠋⠀⠀⢈⠟⡆⠸⣄⡼
⠀⠀⠀⠀⠀⠀⠙⠦⣄⡣⡘⡄⠀⠀⠐⢄⠀⠘⠀⠀⢐⠁⡀⠁⠀⣀⡤⠚⠉⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠦⣤⣤⣤⣱⣤⣤⣤⣶⠴⠖⠚⠉⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠅⠀⠀⠀⠀⠉⠉⢢⠀⠉⢰⠁⡠⠀⠈⢢⡀⠀⠀⡰⠁⡠⠆⠄⠀⡝⠌⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠐⠈⠆⠸⡠⠁⠀⣀⠤⠄⡤⢤
⠀⠀⠀⡀⠀⠀⠠⠄⠲⢥⡁⠀⠐⣄⠀⠁⠤⡀⠰⡀⠀⡅⢀⡀⢀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⡐⠀⠀⠀⠁⡜⠀⢠⣈⠁⠘⠗⠤⠤⠍⡏
⠀⠀⠀⢰⣐⠀⠀⠀⠀⢂⠽⠀⠀⠈⠢⢄⠀⠌⠢⠇⠀⠀⢎⣕⡲⠀⠀⠀⢀⠂⡀⡀⢸⠀⠀⡐⠀⠀⠀⣡⠊⡔⠀⠀⠈⠢⠀⡄⠀⠀⠀⡇
⠀⢠⠀⠀⠄⠀⠐⠈⠁⣠⠤⠤⡠⠠⠀⣄⠉⠐⠀⢠⣞⡃⢨⣊⠼⠀⠀⢄⡠⠃⠀⢱⠄⠈⢠⠠⠄⢀⠔⠁⠀⠸⠓⠤⠴⠄⠀⠁⠐⠒⠁⡀
⠀⠈⠃⠀⠨⠇⠀⠴⡃⠠⠀⠐⠡⢁⣂⡠⢕⡄⠀⠘⠋⠀⠀⢷⠇⠀⠀⠲⢇⠀⠀⢰⠦⣐⠈⠂⠐⠁⡐⡠⠀⠐⠦⠤⠀⠀⡀⠴⠈⡀⠀⠈
⠀⠀⡔⠲⡄⠀⡔⣀⡒⢒⣢⢁⣁⠼⠃⢊⡍⠀⣔⠒⠓⠼⢄⠘⠀⠀⠀⠀⢐⠀⡍⠀⠉⠀⠀⠀⠀⠀⠐⠁⢴⠄⠀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣷⠀⠘⠄⠀⠢⠄⠄⠤⠤⠴⠒⠚⠉⠀⢄⡇⠀⠀⠀⡇⠀⠌⢀⠁⢀⠼⠰⠁⠀⠀⡠⣶⠿⣿⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⠚⠐⠆
⠀⠀⣇⠨⡁⢸⠀⠀⠀⢤⠤⢄⠀⠀⢀⣀⣤⠈⢧⠠⢄⡘⠁⠀⠈⠨⠆⠀⠀⠀⠂⠀⠈⠉⢻⡒⠛⠛⠛⠳⠀⠁⠀⠀⡍⠀⠈⠓⠒⠊
⠀⠀⠘⠦⠴⠊⢀⠄⠀⠈⠂⠤⠀⠤⠄⠔⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠑⠒⠁⠐⠠⢖⠒⠒⠁⠀⢹⠉⠀⠀⢀⠤⠄⠠⠄⡀
⠀⡠⠀⢠⠀⡰⠁⠙⠀⠘⡀⠀⠀⢀⢀⣄⢠⢤⢰⡿⠞⢱⠀⡠⠩⠐⠒⠐⠒⠪⠔⠁⠀⠠⠄⠀⠈⠀⠠⠀⣀⠒⠀⠐⠀⠰⠃⠀⢈⠤⢤⢃
⠀⠙⠣⠁⠠⠁⠀⠀⠀⠐⢀⢤⠀⠠⠀⠐⠚⠈⢉⠠⠒⡱⠘⠏⠙⡠⣲⠖⠁⠀⠀⠀⠄⠀⠴⠀⠀⣀⠀⠀⣁⠀⠀⠀⢠⠃⠀⡔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠈⠐⠂⠀⡈⠀⢀⣊⡭⡴⠦⠒⠋⣡⡀⠀⠀⠀⠀⡜⠀⠀⣠⠐⠇⠩⠠⠅⠩⠈⠣⡀⠑⣀⠽⠆⢀⡀
⠀⢀⠀⠂⠐⠙⢄⠀⠀⠀⠀⡲⠁⠤⠄⠀⠀⠊⠀⠈⠀⣠⡀⠀⠀⡺⠭⠃⣄⢀⠨⠊⣀⠀⠀⡀⠀⠄⠈⠉⠉⠀⠈⡀⠁⠀⠀⠀⡜⠀⠈
⠀⠘⠤⠀⠀⠈⢀⡄⠀⠀⠐⠚⡞⠠⠀⠀⣰⠶⠞⠛⠀⢛⡧⣤⡀⠉⢀⠔⠈⠀⠀⠀⠈⠀⠀⡆⠁⠀⠀⠀⠁⠈⠀⠈⡇⠀⠀⠠⢃⠐⢀⡁
⠀⢀⡀⠐⢊⠔⠃⠠⡀⠀⠂⠁⠉⠀⠀⠜⠁⠀⠀⠀⠐⠌⠈⢁⡀⠈⠀⢄⠆⠀⠀⠒⢀⠣⠈⠑⠀⠀⠐⠒⠒⠒⠊⡊⠝⢀⠀⠀⠀⠀⢀⠁
⠀⠰⠀⠉⠀⠘⠀⠠⢂⠄⣀⠐⠠⠀⠀⡀⠀⠀⠀⣀⣄⠀⠌⠀⠀⢂⠀⠀⠀⠀⠐⠀⢁⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡮⡆⠀⡒⠒⠊
⠀⠀⠣⠬⠄⠂⠁⠀⢇⢸⣁⡐⠀⠢⠀⣁⡀⠀⠉⠉⠀⢌⠀⠀⠀⢸⠀⠘⠀⠀⠁⠊⡀⠁⠀⠁⠠⠐⢒⠂⠠⡎⠈⠂⢀⠈⠁⠀⠧
⠀⠀⠄⡠⡀⡠⢆⡀⠀⡆⢀⠤⠄⠊⢀⠇⠈⢁⠁⠠⠁⠀⣄⠀⠀⡾⠀⠰⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠂⠀⢉⢱⠤⣀⠤⠊⠀⣀⢀⠀⠆
⠀⠠⠂⠂⠃⠓⠀⠖⠀⢈⠥⠤⡀⠀⠢⠄⡶⡇⠀⢀⠀⠐⠈⠀⠀⡜⠀⠈⠀⢤⠀⠀⡰⠋⠁⠀⠀⠀⡔⠁⠀⠀⡴⢁⠀⠀⢀⠹⠗⠎⠈
⠀⠀⠀⠀⠰⠀⠄⠒⠀⠀⠐⠒⠊⠀⠀⠀⠀⠠⠀⠀⠑⠄⠠⠔⠚⠀⠀⠀⢄⡀⠠⡘⠄⠦⠄⠠⢭⠒⠤⣤⠤⢚⡀⠝⢀⠀⢈⠀⢀
⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠘⣠⠠⠁⠀⠁⠀⡠⠤⠴⢆⠀⠀⢄⠀⠠⠉⠈⠑⢊⠉⠐⠒⢒⡀⠉⢀⡀⠈⢁⡀⠀⠐⠀⠀⠁⠀⠀⠜⠔
⠀⢀⢀⠐⣀⢀⡀⠄⠀⢠⠁⡠⠤⠀⠁⠀⢎⣉⠆⠱⠀⠀⠚⠀⠀⠊⠀⢠⡀⠀⣀⠀⠀⠀⠐⣃⠟⢰⢁⠘⠐⢁⡑⠀⢀⣀⠄⠤⠤⢀⠄
⠀⠈⠚⢀⡀⠄⣀⠀⠀⠀⢨⠀⠀⡠⠤⢄⠈⠀⠀⠐⠒⠒⠂⠀⠐⠀⣤⠄⠀⠈⠉⠀⠠⡄⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠨⠉⡀⠀⠀⠀⠈⡹
⠀⠀⡔⢽⢃⢴⠋⠂⢠⠦⠈⡠⠂⠀⠀⢨⠅⠀⡠⠂⢁⣈⡰⡄⠀⠀⠀⠠⠰⡆⠀⠀⢀⠠⠐⠀⠐⡴⢶⠖⡂⠀⠀⠀⠈⢢⠄⠀⠀⢀⠔⠁
⠀⠀⢯⠴⠐⠁⠀⡄⠀⠀⠈⡀⠀⣀⡠⢊⡀⢰⢀⠜⠁⠀⢄⠈⠂⠤⠤⠔⠊⠀⠀⠂⢁⠀⡀⠀⠔⠁⠀⠐⢄⠀⠀⠀⠠⠄⠁⠀⠀⠀⡠⡲
⠀⠀⠀⠁⠒⠒⠒⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢉⣩⣭⣤⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣉⣉⣉⣉⣉⣿⡟⢉⣉⣉⣉⣉⣽⡇⠈⣿⠸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠃⢀⡸⡆⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣉⢻⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠁⣧⢸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠃⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠐⢸⣾⣿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡏⣥⣭⣭⣭⣭⣿⡏⢨⣭⣭⣬⣥⣿⣿⢉⣭⣭⣭⣭⣽⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⡟⠀⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠁⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢀⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⠛⠷⣶⣶⣶⣶⣶⣿⡇⢰⣶⣶⣶⣶⣾⣿⢠⣶⣶⣶⣶⣾⠷⠖⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠠⢍⡙⠻⢿⣿⣷⣾⡿⠿⠿⠿⣿⡿⠾⠛⢋⣉⠥⠆⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣄⣀⠉⢛⠛⠾⠁⠀⠀⠤⣤⡤⣤⣀⣠⣭⠁⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠉⠉⠑⠉⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⠤⢤⠤⠤⠤⠤⠤⠤⠤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠼⠃



⣿⣿⣿⢿⣿⠿⢿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣶⣷⣼⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣻⠏⠀⠀⣀⣤⡴⠖⠛⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡆⠀⠀⠀⣠⠞⠋⣰⢏⣠⡶⠛⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠃⠀⢀⡾⠁⠀⢰⡿⠟⠁⠀⠀⠀⣠⣴⠟⠛⠓⠲⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⣿⡸⡇⠀⡼⠁⠀⣰⠟⣠⠖⢁⣠⠶⢛⣉⣀⣀⣀⠀⠀⠀⠀⣈⡟⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡙⠻⢿⣇⢳⡼⠃⠀⡼⢁⡼⠁⠰⠿⠛⠛⠉⠉⠉⠉⠉⠉⠙⢋⣩⡟⠱⣦⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣠⣿⣎⢷⡄⢸⢃⣾⠁⣠⡶⠚⠉⠉⣀⣀⣠⣤⣴⡶⠾⠛⠁⠀⠀⠉⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⢉⣁⣀⣿⣆⠹⣆⢸⣷⠟⠁⣠⠴⠖⠛⠋⠉⠁⢠⣄⠀⠀⠀⣦⡀⠀⠀⢠⣄⠀⢸⣇
⠀⠀⠀⠀⣠⠞⠁⢠⠴⠛⠉⠉⣉⡥⢹⡿⠛⠘⠁⠀⠀⣿⠀⢀⡀⠀⠀⠀⠈⠻⠂⠀⠀⠙⠁⠀⠀⠘⠿⠀⠀⣿⡄
⠀⠀⠀⢰⠏⠀⢀⣠⣴⠶⣺⡿⢋⡴⠋⠀⡖⠀⠀⠀⠀⣿⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢠⢏⣴⠾⠋⡿⠁⣰⠏⢠⠞⠀⢀⡾⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⡀⠀⠀⢸⣆⠀⣿⡇
⠀⣠⣿⠟⠁⠀⣼⠃⢰⡏⠀⠘⠀⣠⠏⠀⢿⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⣿⡄⠀⠀⠋⠀⢻⣧
⠴⠋⠀⠀⠀⢠⡟⠀⢼⡇⠀⠀⣴⠃⠀⠀⠈⠻⣦⣀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣸⠏⠀⠀⠸⣷⠀⠈⠙⣷⡈⡇⠀⠀⢸⣷⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰⣄⠀⠸⣿⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⢷⡀⡿⠀⠀⠀⠀⠈⠀⠀⠀⠈⠻⣿⠀⠀⠀⠉⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠘⠿⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢿⡇⢷⡄⠘⣿⡇⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠸⣿⡈⠟⠀⢻⠀⠀⣀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠘⠀⠀⠹⢷⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠰⣷⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠻⣶⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⢼⣦⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣦⣤⣀⡀⠀⠈⠛⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠸⣷⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⡀⢀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⣴⠉⠁⠀⠉⠐⠀⣀⠀⠈⠁⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣄⠐⠤⠤⠞⠀⡀⠉⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠛⠶⠶⠲⠞⠇⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡼⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠓⠀⠀⠂⠀⠀⠀⡴⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠹⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠐⡌⠑⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣀⡀⠀⠀⠀⢀⠀⣀⡀⠐⠁
⠀⠀⠀⠈⠠⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢀⡀⠠⠄⠐⠈⠉
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠐⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠭⠁⠠⠤⠄⠍⠦⠀⠁⠀⠀⠘⠉⢱⠒⠂⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⣀⣀⡄⠸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡃⠀⠀⠙⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⢚⠀⠀⠀⠀⠠⢄
⠀⠀⢸⠉⠉⠉⢉⡉⣉⠉⠉⠉⠉⢉⢀⣀⠀⠀⡀⢀⡐⢲⠀⠀⠀⠀⠀⠀⠀⢠⠄⠰⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢸⠀⢠⠊⠁⠀⠀⠉⠢⡀⢰⠁⠀⠈⡆⢌⠀⠀⢘⢘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢱⠈⠓⠤⠐⠁⠘⢂⡐⠊⢸⠀⠀⠈⠀⠁⠀⠀⢸⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠂
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⠙⡆⠜⠁⠈⢱⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⢸⠀⠘⢆⡀⠀⠀⠀⡠⠃⠈⠢⠄⠴⠁⠐⠤⠤⠚⢸⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠤⠤⠤⠬⠭⠬⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢐⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡠⠄⠀⠒⠂⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⢻⠁
⠀⠀⠀⠀⡀⠀⠀⢃⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠲⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢸
⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⣼⢁⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⡒⠒⠲⢌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⢘
⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠰⠁⡀⠈⠂⡀⠄⠀⢱⡀⠀⠀⣠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡇⠈⠈
⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠑⠄⠀⠀⢘⡀⢃⠀⠀⠠⠀⠀⢠⡇⠀⡎⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢀⠄⠀⠀⠀⠣⣀⠀⠀⡄⢊⠀⠔⠀⠀⢇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⠀⠁⠀⠀⡠⠒⠢⡈⠑⠉⠈⠂⠁⠀⠀⠀⠈⠓⠲⠔⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠒⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⡄⠀⠀⡁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⢁⠀⠀⠀⢀⠄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠐⠀⠀⠀⠤⠠⠠⠀⠀⠀⠈⠢⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠃

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⢛⡛⠓⠲⠶⢤⣀
⠀⠀⠀⠀⠈⢻⣿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟⠋⠁⠒⢤⣀⣭⣽⠿⠶⠶⠶⠾⣿⣦⣄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⣉⠉⠉⠉⠉⠉⢉⡁⠀⠀⢒⣲⣶⢶⠟⠉⣡⠏⠀⠀⢀⣠⡴⠶⠾⢿⣷⣦⡀⣴⠿⠈⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣍⠓⠲⠶⠶⠶⠾⢒⠿⠋⠉⡰⠋⠀⠰⠃⢀⣤⡾⠋⠁⠀⠀⠀⠀⠈⠙⣿⠏⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⠀⠁⠀⠀⠈⠀⢀⣀⣤⠾⠛⢁⣀⣀⣀⣀⣀⣀⣀⡀⣰⡟⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟⣛⣻⣿⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠁⢀⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣼⣇⣠⡿⠻⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠛⠛⠦⠀⠈⠙⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣶⡀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣤⡻⣇⠀⢀⡤⠴⠦⣤⡀⠀⠀⠀⠀⢀⡠⠴⠶⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⢰⢷⣙⣿⠁⣠⡶⠒⠶⠽⣲⣤⡀⣰⡉⠀⠀⠀⠀⠀⢀⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠰⠃⠛⠉⢀⡼⠛⣳⣶⢀⡴⠋⢹⠷⠾⣷⣖⣶⡁⠀⣠⠏⠀⠀⢀⡈⠳⣄
⠀⠀⠀⠀⠀⡴⠃⠀⠤⠶⠓⢼⡀⣾⠏⢀⡄⠊⠁⡼⠧⣾⠁⣀⠖⢁⣸⠿⢿⣷⡉⠠⡈⠒⢯⢤⣀⣀⠙⠂⢤⣄⡠⢤⡀
⠀⠀⠀⠀⡼⠀⠀⠀⢀⡗⠀⠀⠛⠋⢹⡟⢀⡤⠊⢀⠴⠛⢹⣇⣤⠊⠀⡀⠾⣷⣹⡄⠰⡄⠘⠃⠀⠉⡟⠓⠚⣛⠟⠊
⠀⠀⠀⢸⠁⣀⠀⠚⢋⠁⠠⠄⡆⢶⠁⠸⠟⣧⣴⠋⠀⡴⠎⠀⣸⠶⣿⠀⢀⣼⣇⢳⡀⠃⠀⠀⡄⠀⢀⣤⠞⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠐⡆⠀⠀⢻⡜⣷⢀⡔⠉⢹⡶⡶⠁⣠⡼⠃⢀⣵⣾⢁⣈⣿⢨⠃⠻⣧⡘⠛⡛⣯
⠀⠀⠀⢰⠀⠀⠀⡤⠐⢧⠤⠄⠀⢳⣜⢿⣄⡤⠋⢀⠿⠛⣯⣤⠞⠈⢁⣨⣟⢉⡝⣸⠀⠸⠈⠹⣍⠁⢸
⠀⠀⠀⠈⣇⠠⠀⠀⠀⢸⡀⠀⠉⠁⢻⣧⠙⠷⣴⡁⢀⠞⢛⣧⣴⠟⠉⣉⣽⢛⣇⡟⠠⠀⠀⣤⢿⡀⠸⡄
⠀⠀⠀⠀⠘⣇⠀⠀⠀⢘⡇⠀⢀⡀⢨⠁⠈⠐⠠⢝⡛⠶⣾⣀⠿⣶⠋⢠⣤⣿⣽⠉⠙⠦⣄⠋⠀⠑⢦⡛⣄
⠀⠀⠀⠀⠀⠘⣆⠀⠴⠀⣦⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠙⠢⠽⣶⢾⣇⣁⣠⣿⡏⠀⠀⠀⠈⠉⠀⠘⠂⠩⣌⡆
⠀⠀⠀⠀⠀⠀⠈⢧⠀⣰⡋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡙⠻⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢳⠁⣣⡞⠁⠀⠀⢀⠀⠀⠀⣀⣽⠃⠀⠀⠀⠀⠀⠙⢦⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢺⠀⠀⠀⠀⠀⠳⠶⠛⣩⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠦⣤⣄⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⢦⣄⡀⢀⣀⠀⠀⢀⠀⢀⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠒⠀⠒⢤⣥⡀⣈⣙⠋⠉⠀⠻⠦⠆⠚⠏⢶⠀⠈⢉⣀⣀⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⣽⣾⡯⠶⠷⠚⠛⠙⡾⣟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠒⡐⠚⣡⠀⣠⡦⣥⣼⣯⣁⣀⠀⠀⠀⠀⢰⡆⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡴⠃⠀⠀⠛⣤⡇⠐⠀⠈⡇⢸⡄⢳⠀⠀⠀⡾⠀⢰⡄⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢎⡄⠀⠺⠀⠀⠀⠀⢠⣾⠁⡇⠀⢾⡃⢸⡀⣼⠀⠀⢸⠃⢀⠜⠁⢦⣄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⣾⣄⡀⠀⢀⡿⠃⠠⠇⠀⠸⡇⢸⡇⠸⡄⠀⠸⡇⠋⠀⠀⢸⣦⡀⠁⠷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⣠⠔⢻⠀⠉⢰⡿⠀⠀⡀⠀⠀⠀⠃⠀⠇⠀⠙⢄⠸⣇⠀⠀⣠⠊⠈⣧⣀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⣧⠀⣻⠀⠀⠘⠀⠀⠀⢠⠇⠀⠐⠀⠀⠈⢂⠙⡆⠰⠁⠀⠀⡈⠡⠉⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣽⠉⣛⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠀⠀⠀⠘⢤⡆⠀⠀⠀⠀⠁⠀⠳⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡴⠹⠀⢹⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢠⡆⢱⡄⠀⠀⠀⠀⠀⣸⡇⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⣦⣀⣧⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⡸⠁⠈⠇⠀⠀⠀⠀⢀⠇⣵⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡾⠁⢸⡟⢢⡄⠀⠃⠀⠀⡌⠀⣸⠀⠀⢰⠇⠀⠀⠀⠹⣆⠀⣴⠃⣀⣼⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⠴⠋⠀⠀⠙⢦⡀⢦⠀⠀⠰⠁⠀⣰⠃⠀⠀⠀⠀⠀⠈⠓⠇⣀⠋⢹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠹⣞⡀⠀⢞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⡋⠉⠉⠉⠉⠙⠒⠲⢤⡀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡡⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡴⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠔⠀⠔⠈⠀⠀⢀⠀⠀⠀⢀⠀⠈⠁⠀⠀⢺⢷⣾⡀
⢀⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡐⢁⠀⠀⠀⡀⠐⠀⡀⠀⠂⠀⡀⠀⠂⡠⠀⡁⠠⠀⠙⣿
⡼⢰⠃⠀⠀⠈⠉⠉⠓⠒⠲⠤⢤⣀⡀⠀⠀⡞⠀⠠⠀⠀⡀⠊⠀⠀⠁⠀⠠⠐⠀⡀⠐⠀⠠⠊⠠⠁⠀⠄⡇
⡇⣦⠀⠀⠷⠂⠀⠰⠟⠀⠀⠀⠀⠀⠉⠉⠚⠳⠤⣅⣀⠐⠀⠈⠀⡀⠀⠁⠀⠄⠈⠀⠀⠀⠀⠀⠀⠐⢀⠀⠇
⡇⢋⠀⠀⢀⣠⠀⠀⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠉⣝⡳⢤⣈⠀⠀⠊⠀⠀⡠⠀⠀⡀⠀⠀⡐⠀⠀⠀⡄
⢱⠘⠄⠀⠈⠉⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢰⡄⠈⠁⠀⠈⡷⡄⠀⠄⠀⢀⠄⠈⠀⠀⠄⢀⠀⠀⡜⡸
⠈⢧⠩⣄⠀⠀⠾⠇⠀⢠⡆⠀⠀⠀⠻⠂⠀⠀⢠⣄⠀⠀⠀⠀⡸⣸⠁⡀⠄⠀⠀⠀⠀⠐⢁⠐⠁⢠⠞⡴⠁
⠀⠈⠳⡑⢦⡀⠀⠀⠀⠈⠀⠀⣦⠀⠀⠀⣦⠀⠀⠉⠀⠀⢀⡴⣱⠋⠀⠀⠀⠀⠄⠊⠀⠂⠀⠀⠒⣠⠞
⠀⠀⠀⠙⠦⡙⠴⣄⡀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⣀⡴⢋⡔⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⣀⠥⠊⠁
⠀⠀⠀⠀⠀⠈⠓⠬⣁⡁⠤⠤⣠⠤⠀⢤⡀⠤⠖⣋⡥⠖⠉⠛⠺⠦⠤⠤⠤⠤⠴⠶⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣶⣶⣶⣶⣶⣶⣾⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡖⠂⠀⠀⢰⡆⠀⠀⠀⢰⡆
⠀⠀⠀⠀⢠⣴⣦⣄⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⢠⣄⠀⠈⠻⢿⣿⣿⣶⣤⢺⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡷⠀⡀⠀⠈⣇⠀⢀⡀⢸⡇
⠀⠙⢿⣷⣦⣤⠴⠾⠟⠳⣿⣿⣷⣦⣀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡏⠋⠉⠉⢉⡏⠉⠉⠀⣾⣷
⠀⠀⠀⠉⢿⣾⣦⠀⠀⠀⠀⠈⣙⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠙⣿⣦⠖⠛⠉⠻⠋⠃⠈⠀⠀⠀⠀⠀⠀⢀⠻⣤⣤⡤⢤⣧⣤⣤⠦⢼⣧⣤⠤⢄⣼⣿⣣⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢍⠙⠷⠂⠀⠀⠀⠉⠉⠉⢭⣁⠀⢀⡡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣦⣤⣀⡀⠀⢠⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡷⣧⠾⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⣻⠿⣽⣿⢋⣡⡾⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠘⠿⢟⡟⠋⠛⠻⠿⢿⡆
⠀⠀⠀⢠⢻⢿⠟⢻⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⡆⠀⠈⠀⠀⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⠒⠂⠐⠂⠠⠄⠀⣀⣀⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠑⠢⢄
⠀⠀⠀⠰⡀⠀⡀⠀⡀⡆⠀⠀⠀⠀⠀⠀⣀⠀⠆⠘⡉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠖⠚⠚⠁
⠀⠀⠀⠀⠙⢧⣺⣦⡟⠀⠀⠀⠀⠀⢠⡀⠄⢐⠈⠄⠁⠠⠈⡰⠃⠁⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⡀⠀⡜⢂⠁⠀⠈⠀⢀⡀⠄⠓⠀⠀⠀⢾⣿⣀⣀⣀⣠⡴⠃⠀⣴⣆⣀⣀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠉⠁⠂⠚⠒⠁⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠰⠅⡆⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣛⡛⠢⢍⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢘⠗⣸⢀⠀⠣⢠⢠⢸⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠻⠦⡉⠁⠀⠀⠈⠀⡊⡈⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣮⠑⡄⢀⠀⠀⠀⠀⠀⠐⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢾⠀⠁⠒⡡⠂⠀⠀⠀⠀⠀⢀⠁⣁⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⣢⡀⠀⣿⣻⢰⠍⡦⠂⠀⠀⠀⣀⣴⣶⣾⠿⠛⠃⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⡄⣶⢾⣿⠹⡄⠘⣾⣆⠈⢁⣠⠴⠚⣽⡿⠋⠀⠀⠀⠀⢀⣞⡟⢉⡽⢧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠽⠓⣺⣦⣧⡿⣿⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⠾⣥⠤⢚⣷⡀
⠀⠀⠀⠀⠀⢀⣿⣷⠸⣿⠿⢷⠘⣄⣱⢳⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⢞⡽⡖⢉⢞⣷⡀
⠀⠀⠀⠀⠀⠸⣿⡟⢐⣾⣯⡘⠣⣻⣿⣏⡆⠘⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⣀⣯⢟⡿⣯⠔⢻⡄⢊⡿⣧
⠀⠀⠀⠀⠀⠀⠙⢧⣿⣿⠛⠀⠀⢹⣟⢻⣧⠀⠀⠀⠈⠀⠀⠀⢺⠀⠀⠘⢫⣹⡲⣧⡷⣂⡠⢷⣊⠀⣻⣀
⠀⠀⣠⣶⢿⣿⠛⣷⡺⣿⣦⣠⢄⡀⠈⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢋⣾⣟⣥⡤⠼⢃⠀⠁⠸⠧⡄
⠀⢸⣲⠏⣨⣍⢡⠟⠛⢙⡺⣽⣿⢽⣦⣻⣿⣴⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠏⠆⠈⠘⢻⣧⡴⠚⠑⢻⣅⡠⠴⠿⡀
⠀⠸⡟⣷⡰⢆⣜⣛⠷⣶⣖⣿⣿⠿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⠀⠙⣯⡗⣦⠁⠀⢹⡆⠀⠐⠛⢀⣀⣀
⠀⠀⠙⠺⠷⠾⠿⠛⠋⠉⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⠶⠤⢿⣽⣧⠤⠤⣿⡁⢸⣻⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠉⠛⠲⢧⣸⠯⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⣀⣤⣴⠶⠾⠟⠛⠶⢦⣄⠀⠀⠀⠀⠀⣀⡴⠛⣉⣠⣄⡀⠌⢿⣆
⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠉⠉⠛⠛⣷⣤⡀⠀⠸⣯⡉⢰⣶⣿⣿⣷⣶⢶⣒⠛⠓⠲⠦⣿⣷⡀⠀⠀⣰⠋⣀⣸⠟⠋⢹⡧⠥⣼⡿⣇
⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠈⠳⣄⠙⠻⣿⣿⡿⣷⣦⣍⡙⠒⢤⡈⠻⣇⠀⠀⡏⠀⠘⢿⣶⡶⢿⣂⣼⣿⣷⣿
⠀⢸⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⠛⢦⡀⠙⢿⣎⠻⣿⣿⣶⣄⠙⢧⣸⣧⠀⢻⣶⣤⣬⣤⡶⠾⠛⠉⠈⣿⡟
⠀⢸⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡿⠀⠀⠀⠀⠀⢀⡕⠙⢦⡀⠻⣧⣘⡜⢷⠈⠳⣄⠹⣿⠀⠀⠙⢿⣯⣉⡀⡀⣀⣀⣴⠟⠀⠀⠀⠀⠐⣆
⠀⠀⠻⣿⣿⣿⣧⣤⣤⣴⣶⣿⣿⣿⣿⠟⠀⠀⣀⣤⣤⣤⣮⣀⡀⠀⠹⡄⠘⣷⣿⣼⡆⠀⠈⢿⣿⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⣸⣷⠈⠀⣿⡆
⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣠⣿⣿⠿⠿⣿⣿⣿⣿⣦⠀⢻⠀⠈⢻⣿⣷⢀⣧⣼⠏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠨⣿⣶⢿⠏⠁⠈⢠⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣸⢏⠋⠁⠀⠀⠀⠈⣻⣿⣿⣧⢸⡀⠀⠀⠈⢿⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⠂⠀⠁⢀⣠⣯⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣶⣾⠽⠾⠋
⠀⠀⠀⠀⣠⠞⠋⠉⠉⠙⠛⢦⡀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⠟⠋⠉⠛⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⣼⠁⠀⢀⢀⣱⣂⠀⠈⢻⡄⠀⣿⣧⡀⠀⠀⢀⣿⡟⡟⠁⠀⠀⠀⠀⠀⠛⣿⣿⣷⠀⠀⠀⠀⢀⣤⠾⠋⠉⠱⠿⢿⣭⣿⣷⣆
⠀⠀⢠⡇⠀⢀⣰⡟⠙⣿⡇⠀⠀⣿⠀⠹⣿⣷⣤⣄⣸⣿⡧⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢠⡟⣁⣠⣠⣤⣤⣤⣤⣝⣿⣿⣿⠄
⠀⠀⢸⠀⠀⣸⣿⠂⢀⣿⠅⠀⢠⡇⠀⠀⠘⠻⢿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⠀⠀⣾⠛⠁⠀⠀⢀⣤⣤⣬⣽⣿⣿⣿⣷⣄
⠀⠀⢹⡄⠀⠉⢿⣷⣾⡓⠀⢠⡞⠀⠀⠀⠀⠠⢲⠋⠽⠃⠘⣿⣶⣄⡀⢀⠀⠠⣮⣿⣿⣿⠇⠀⢸⣿⣧⣤⡴⠾⢛⣿⣿⣿⣿⣿⠟⢿⣿⣽⡆
⠀⠀⠈⠻⣄⡀⠀⠈⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⢀⣿⣿⣯⣥⣶⣶⣿⣿⣿⢿⣿⡟⠀⠘⣻⣿⡏
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣻⣿⠻⢳⠂⠀⠼⣿⣭⣥⠄⢀⣰⡿⠿⢉⣾⡟⠁⠀⢺⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠉⠀⠀⠀⠀⠉⠛⠶⣿⣇⠀⣠⣿⣏⣀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠂⢄⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷⣠⡀
⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⣁⣁⣀⠂⠀⢠⠌⠀⠀⠀⠀⠀⠙⢳⡀
⠀⣀⣠⢰⣮⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⢁⣤⠀⠀⠀⠀⢤⣄⠀⢠⣼⡿⡇
⠚⠉⠉⠁⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢁⠀⠀⣴⠾⠀⠀⠀⠀⠈⠃⠿
⠀⠀⠀⠀⢰⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠭⢀⠾⠇⢀⡸⠎⠁⠀⠉⠉⠉⠁⠀⠄
⠀⠀⠀⠀⣎⣿⡀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⡀⠀⣀⣤⠆⠀⠀⠀⠀⡠⠰⠆⠀⠘⢷⣄
⠀⠀⠀⠈⠇⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠨⣟⠞⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⣠⡞⠁⠀⠀⢀⡐⠦⠁⠀⡀⢀⡀⡀⠀⠀⠀⢠⡀⠀⠰⠀⠀⠈⠂⠀⡀
⢠⠞⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠛⠉⠀⠀⡰⣴⠜⠛⠙⠑⠀⠀⠈⡁⠀⠀⠀⠀⠈⠂⠀⠀⣇
⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⢈⠀⠀⠀⢠⡻⠮⠃⣤⡴⠶⠶⢦⠀⠁⠀⠀⠇⠀⠀⠀⠀⢤⣼⡧
⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⣪⡁⠀⠀⠀⣸⡏⠀⠀⠀⠋⠁⢐⠀⠈⢀⠘⠃⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠺⠙⠄
⡸⠃⠀⠀⠀⠈⢆⠀⠀⠀⠀⠋⠀⠀⠀⢀⠏⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⠙⠲⠿⡟⠛⠆⠀⠀⠀⠀⠀⠀⢰⣟
⠄⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⢶⣶⡀⠀⠚⡴⠋⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠃
⠀⠀⢠⢶⡿⠋⠙⣷⣤⠀⠀⠀⣻⡅⣰⠆⠰⠀⠀⢠⣞⡿⠀⠀⢰⡷⠈⢀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⠃⠀⠀⠺⠀⠀⠀⣰⡆
⠀⠀⠀⣼⣃⣠⣴⢋⣖⣠⡶⣶⣾⡒⣿⣓⣼⣻⣄⣾⣏⣴⣶⣖⣾⣡⡶⣻⢶⣦⣄⣷⢶⣤⣆⣸⣏⣵⣻⣦⣶⣻⣆⣴⢒⣿
⢧⠀⠀⠉⠉⠁⠀⠀⠉⣨⢽⣿⠋⢁⠈⠁⢉⣭⡽⠋⠉⠈⣿⡏⠉⠉⠉⠁⠀⠉⠈⠁⠈⠀⠁⠈⠉⠉⠁⠀⠉⠀⠁⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠐⠋⣹⠀⠀⠘⢧⡄⠀⠀⠀⢸⠇⢀⡠⠆⡠⣦⡀⢀⡴⣦
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⡀⢨⡷⣴⣦⣄⣻⣴⠋⠃⣼⣷⢛⡁⣾⠗⣥⣤
⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⣷⣿⠚⠛⣻⣿⡇⠀⣿⠉⠙⠷⠿⠚⠿⠃⠀⠀⠀⠀⠹⢧⣤⣄⠀⠁⠀⠃
⡘⣄⠀⠃⠀⠐⠀⠀⠀⠔⠀⠀⠀⠀⠀⢴⣭⠻⣿⣇⠐⣾⠽⠋⠀⠀⠛⢈⡉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⠠⠆
⢸⠗⡄⠀⢣⡀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠙⠶⣤⠄⢒⠀⠀⠁⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠃⠁⠀⠀⠱⣄⠀⠐⠂⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠆⠀⠀⠀⢂⠠⠀⠀⢠⠄⠐⠉⠀⠀⠀⠀⠀⠀⠀⡠⠈⠉⠀⠂⠐⠉⠉⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⠀⠢⣤⡞⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠁⠐⠂⠒⠀⠈
⠀⠁⠀⠀⠀⠁⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⡄⠀⠼⢢⡄⡹⣆⣠⠀⠄⠀⣆⡔⠀⠀⣤⠀⡄⢰⠛⠁⠀⡄⣠⠀⠀⠄⠀⢀⡀⠀⠀⡠⠀⠀⡠⠀⠄⢠⠀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣆⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣶⠲⠂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⣸⡏⠀⠈⠻⣧⠄⠂⠀⠀⠀⠀⠰⠀⠺⡶⣶⣿⡿⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣦⣠⣦⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣉⡓⣦⠀⠀⠀⣿⡃⠀⢤⡀⠹⣦⡚⣾⡆⠀⠀⠀⠂⣁⣶⣿⡿⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⣣⠟⠀⠀⠀⢌⠛⢣⣜⡻⣄⠘⠶⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣽⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣁⣨⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣶⡎⠈⢹⣿⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠄⠀⠀⠀⠀⠀⠀⠻⡶⢹⠷⠚⢿⣶⣿⠃
⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⢺⣿⣧⠀⠀⢀⣼⣏⠀⠀⠀⠀⠀⢀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠞⠛⠘⠀⣤⡠⡅⣠⠀⠀⠀⠙⠾⠶⠶⠼⠟⠉
⠀⠀⠀⣿⣿⣿⣷⣦⣤⣤⣤⣤⣽⣿⣿⠀⠀⢸⣿⣿⣦⣤⣀⣤⣶⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⠀⠀⢰⡒⢝⠶⣰⣿
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢙⣭⣉⣇⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠁⠀⡀⢠⣤⢨⡍⠉⢉⠋⡙⠲⢶⣤⡀⠀⠀⠀⣠⣶⣿⣟⣿⣿⣺⣿⢿⣯⡏⣿⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⢲⣬⠻⣿⣿⡿⣧⣠⡟⣴⣿⢇⣾⢟⣿⣆⣰⣾⣿⣿⡿⣿⣿⣽⣷⣿⣿⣷⣮⣧⣿⠟⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠘⠿⣯⣿⣿⡟⠃⠈⠻⠿⠿⢿⣿⣷⣾⣟⣻⣿⣻⣿⣿⣿⣿⡿⠛⠛⠉⠛⠛⣿⣿⣲⣺⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠒⠒⢺⣿⣏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣰⣿⣿⣞⠲⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⢸⡾⠟⣻⣿⣶⣤⠀⠀⢀⣠⣿⣿⣿⣿⣾⣿⣟⣻⣿⣿⣿⣿⣷⣠⣶⣿⣿⣿⣿⣭⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣥⡟⣹⣿⣿⣿⣿⣾⣿⣿⣿⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣶⣯⣡⣸⣿⠟⣿⣨⣿⣶⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠋⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢀⠀⠀⠀⡿⠁⣾⠛⣁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣾⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿