Buttery Emojis & Symbols

⠀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⣿⡑⢌⣠⢡⣝⣓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⣫⡌⣄⡡⢊⡿
⠀⠘⣦⢻⡪⢙⣋⣙⡻⢯⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣿⡼⢋⣋⣙⡋⢕⡗⣴⠃
⠀⠀⠘⣎⢧⣏⢲⡆⠀⠭⠟⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⢿⠫⠩⠀⢰⡔⣹⡼⣱⠃
⠀⠀⠀⠸⡌⣎⠒⠬⢒⠤⡀⡀⠙⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡿⠏⠊⢀⠀⢤⣒⠥⠒⣱⢡⠇
⠀⠀⠀⠀⣿⢸⡗⠦⠔⢆⡈⠑⡓⠦⣌⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠞⣡⠴⢚⠈⢅⡐⠢⠴⢺⡇⡿
⠀⠀⠀⠀⢸⠨⡿⣓⣈⣀⢈⡁⠐⠤⠀⠙⠺⣿⡻⣦⠀⢀⡀⠀⣴⢟⣷⠗⠋⠀⠴⠃⢈⡁⣀⢁⡚⢿⠡⡇
⠀⠀⠀⠀⠘⣯⢇⣧⣤⣦⣀⣬⣨⣆⣠⠈⡂⠨⠻⣽⣇⣾⣷⣸⣯⠟⠁⢖⠁⣄⣰⣁⣥⣀⣤⣤⣼⡼⡽⠃
⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⡀⠀⠀⠄⠀⠉⠛⠲⢤⡈⣿⣿⣿⣿⣁⡤⠖⠋⠉⠀⠠⠀⠀⢀⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡻⢣⠟⡟⣞⠗⠶⣾⣟⣽⣿⣿⣏⣻⣷⠶⠻⣳⢿⠻⡝⠛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⢸⠀⡇⣜⠤⠈⠹⢿⡿⢹⡏⣿⡿⠏⠁⠄⣣⢸⠀⡇⠀⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠠⠃⠨⡇⠸⡀⢇⡐⠀⣀⠇⣿⡇⠸⢀⠀⢂⡼⢀⠇⢸⠅⠘⠄⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠹⣄⠙⢦⣈⢦⡞⠀⢹⡇⠀⢳⡔⣁⠴⠃⡰⠏⠀⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡌⢀⣀⡉⠓⠤⣤⠏⠀⠀⠘⠃⠀⠀⠹⣤⠤⠚⢉⣀⡀⢡⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⢦⢊⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⡑⡴⠒⠾

⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⢽⡞⠛⢻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡟⠛⢑⡮⢭⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⠏⣻⡍⠿⡽⠓⠞⠛⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠻⠚⢫⡾⢩⣟⠹⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢶⠯⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⡽⡶⢺⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⡷⠊⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠙⠶⣓⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⣗⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⡄⢰⡦⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡒⣥⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡷⢤⣀⣠⠤⠤⠄⠀⠀⠀⠀⢿⣼⣷⡿⠂⠀⠀⠀⠠⠤⠤⣄⣀⡤⢾⣥⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡭⠋⣡⠃⠀⢀⠠⠀⠀⠀⢀⡜⣿⣿⠣⡀⠀⠀⠀⠄⡀⠀⠈⢌⠙⢭⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠂⠀⠀⠈⠁⡄⠀⢀⡠⠴⠁⠀⢻⡟⠀⠈⠢⢄⡀⠀⠀⡀⠉⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣥⠀⠀⠀⠀⠀⠐⠀⠋⠐⠀⠀⠀⠈⠃⠐⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⣤⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⣇⣠⠀⠀⡀⠀⠠⠁⠀⠀⠀⠌⠀⢀⡆⠀⠡⠀⠀⠀⠈⢂⠀⠀⠀⠀⢄⣸⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣩⣇⣠⠂⢀⡔⠀⣠⣀⣴⡟⠀⠀⠘⠃⠀⠀⠹⣦⣀⣄⠀⠢⡀⠑⣤⣈⣏⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣾⣶⣞⣶⣪⡷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣕⣶⣟⣶⣿⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⣹⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⣯⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⣦⣤⣤⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣤⣤⣴
⠀⠀⠸⣿⣶⣩⡟⠋⠻⢾⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢾⠽⠛⠚⣯⣹⣽⡏
⠀⠀⠀⢫⡽⣤⢟⠋⢀⣙⡿⠄⣹⣫⣵⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣭⣿⡁⢾⣏⣉⣉⢻⢧⡼⣿⠃
⠀⠀⠀⠈⢯⣏⣹⣟⠁⠉⡻⢶⣉⣁⣞⣷⣭⣳⣤⡀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⣠⣶⣫⣴⣿⣟⣉⣵⢻⡋⠉⢹⡿⢉⣿⠏
⠀⠀⠀⠀⠈⢻⣿⣽⡟⠻⣽⡏⠁⠈⠑⠀⠀⠈⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠈⠁⠀⢉⡿⡤⠛⣟⣶⣼⠋
⠀⠀⠀⠀⠀⠀⠹⣯⣧⢾⣽⣦⣦⡀⠀⠴⣄⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣴⡄⠀⣠⣛⣿⣷⢴⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣟⣽⡏⢿⡏⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠈⣧⠽⣛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⡾⣧⣄⠀⠤⠤⠴⠖⠛⠓⠀⠀⠀⠀⠈⠳⡄⢠⣤⠀⡴⠋⠀⠀⡀⠀⠐⠛⠒⠶⠤⠄⠄⢀⣴⠟⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⢤⣤⣤⣤⣼⣿⣿⣿⣤⣤⣤⠀⢀⣴⣶⣶⣶⣶⣦⣤⣀⣤⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠅⠀⠉⠉⠉⠉⠓⠈⠀⠀⠂⠀⢀⠿⣿⣿⡿⣇⠁⠀⠀⠈⠉⠛⠉⠉⠉⠁⠀⠈⢭⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡤⠄⠀⠀⠀⠆⠀⠀⠀⠀⣠⠔⠉⠀⢹⣿⠑⡈⠓⢤⡀⠀⠀⠀⠀⠆⠀⠀⠠⠤⣼⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢳⣾⠁⠀⠀⠀⣠⠄⠀⣀⡤⠖⠋⠀⠀⡔⠀⢿⣿⠀⠐⡀⠀⠈⠳⣦⣄⣀⡀⣄⡀⠀⠀⠈⢻⣾⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢯⠿⣶⠦⠀⠈⣉⠔⠉⠁⠀⠀⠀⠀⠈⢁⡄⢸⣿⠘⣆⠉⠀⠀⠀⢀⡀⠉⠀⢍⡉⠓⠶⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣄⣠⡞⠁⠀⠀⠀⠀⠀⢠⠂⢰⡞⠀⠘⠟⠀⠘⣧⠀⢢⠀⠀⠠⠀⠀⠀⠹⣦⣀⣾⣧⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡿⣛⣿⣦⣀⣀⣴⠃⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⢳⡀⠀⢳⣄⣀⣠⣿⣋⡻⣽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣽⣿⣭⣿⣻⣶⢾⣇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣿⢶⣟⣹⣯⣿⣽⡽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠛⠋⠁

⠀⢠⣤⣤⣤⣀⡀
⠀⣮⣾⣾⣿⣴⣦⡉⠛⢶⡤⠀⡀
⠀⠻⣷⣿⣾⣿⣿⣟⣷⣶⣾⣿⣷⣦⣄⢀
⠀⠀⢸⣯⣇⣻⣿⣟⢛⠛⣯⣽⣿⣿⣿⣿⣧⣆⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢹⣿⡻⡟⢿⣍⣉⣹⡏⠀⠀⣠⣿⣿⣟⣷⡀⢄⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠈⢻⣿⠟⢻⣷⠤⠬⢿⡀⠰⣿⣿⠛⠉⠛⣝⢦⡁
⠀⠀⠀⠀⠘⢿⣿⢿⣿⣦⠴⠐⠚⠳⢬⡁⠀⣤⣿⣿⣷⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠘⡿⠶⠾⢿⡷⠒⠒⠒⠒⢿⣷⣮⣙⠻⡟⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠐⢦⢿⡿⠿⢻⠦⠀⠀⠠⠶⣿⣿⣿⡟⠲⢄⡈⢻⣿⡄⠀⠀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⢙⣿⠻⢻⣴⠂⠀⠒⠒⠚⠻⠿⠷⢤⣀⣹⣿⣿⣷⣤⣞⣻⣿⡿⠃⠀⠀⠀⣀⣀⣤⣴⣦⣦⣤⣆⣴⣶⣒⡲⠶⠤⣤⣤⣀
⠀⠀⠀⠀⠀⣠⣼⠿⣿⠋⣉⣩⡷⠒⠚⠉⠉⠉⠙⠃⠐⠢⢭⣝⣻⣿⣿⣿⣿⣿⣧⡶⠾⠟⠛⠛⠛⠛⢛⣻⣶⡾⠒⢶⣷⣭⡍⣙⡛⠶⢦⣌⣹⣶⣤⣀
⠀⠀⠀⠀⠀⣼⣹⣷⢿⡋⠁⣞⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⢙⣿⣿⣛⣿⣟⠿⢿⣿⡟⠿⠻⠶⠀⢤⣰⣿⠿⠃⢀⡽⣷⠇⠀⠈⢿⡗⠲⢶⣿⣿⣞⣛⢷⡆⡀
⠀⠀⠀⠀⢀⣼⣿⣤⣿⡟⢁⡼⠶⣤⣤⣤⣤⣶⠛⠁⠀⢀⡴⢪⣟⠦⣽⣿⡿⠋⠐⠈⡙⠢⣄⣀⣰⣾⣿⣿⣿⣲⢬⣿⣇⣀⣠⡤⡞⠑⢦⣴⣿⣽⣿⡟⣯⣅⣿
⠀⠀⠀⠀⠀⣿⣿⣱⣼⣿⡏⢀⣴⠁⠉⣡⠝⠁⠀⢀⣴⠟⣰⣿⣮⣿⡟⡀⠀⢰⡀⠀⠈⠲⣄⠙⠿⣿⡽⢏⡀⠁⠀⠉⠀⡈⠹⣦⣉⣷⣿⡛⢣⣭⢻⣧⡾⠟⠛
⠀⠀⠀⠀⠰⣿⣛⣫⣼⣿⣿⣿⣿⣤⣤⣧⣄⠀⣠⣾⠋⣰⣿⣿⣿⠏⣰⠇⠀⢰⣧⠀⠀⠀⠘⣿⠢⣬⣿⣶⣽⣆⣀⣶⣴⣼⣿⡟⣻⣞⣽⡷⡮⠟⠉⠉
⠀⠀⠀⠀⠀⣼⣿⡟⢫⣙⣿⡿⣻⣿⣿⣛⣿⡖⣷⠃⢰⣿⣿⠟⢁⡼⠋⠀⠀⢸⠟⣧⡀⠀⢀⡿⣦⣘⣷⣿⡿⣿⣿⣯⣽⣷⣾⣿⠟⠛⠋
⠀⠀⠀⠀⣸⢋⡔⠂⠀⣟⠿⠛⢿⡟⠘⠛⡟⣭⠏⠀⠘⠋⠁⡀⣺⠶⣶⣄⠀⣾⠀⢸⠉⠛⠈⣇⣸⡿⣶⣿⠇⠀⠉⠀⠉⠁⠀⠈
⠀⠀⠀⣴⡷⠋⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠉⠁⠀⠀⠀⠀⣠⠌⢿⡿⣸⣿⣀⡏⠀⣾⡀⣰⣶⡟⠻⣦⣿⣇
⠀⠀⠸⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⣠⣴⣿⣿⣿⣷⣴⣿⣿⣿⡋⢻⣤⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⢙⣿⢿⣿⢣⣿⣀⣿⣷⣾⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⡿⢷⣤⣿⣿⣿⣿⣿⡿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠳⣿⣿⡿⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⢡⡀⡍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡩⠥⠎⠄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣫⠤⣌⠍⠲⣄⠀⠀⠸⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⣝⣁⡼⢸⠀⢹⠀⠄⣢⢹⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠛⠷⢄⠀⠐⠁⠀⠀⠆⢉⠁⡘⡇⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣏⣖⡒⢦⠢⠁⠀⠀⠀⠀⠐⡀⠒⠁⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠈⠫⠥⠞⡠⠁⠀⠀⠀⢄⠀⠀⠀⢚⠃⠄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠦⣄⠀⠀⢸⡧⣿⢀⠀⢄⢈⠀⠀⠀⠀⠀⠀⣑⣤⣷⣾⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣛⣤⣼⣧⡀⠈⣷⢻⠘⡡⠜⠘⠀⠀⣀⠬⣴⣿⠟⠛⠛⠁⠀⠀⢀⣴⠾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⡘⢿⠻⡻⣆⣷⡀⠘⢿⣧⣀⣠⠴⠒⠉⠀⠾⠛⠁⠀⠀⠀⠀⠀⢠⣿⡜⣅⠔⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠖⣋⣉⣾⣷⣽⡟⢿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⠟⣳⡤⠚⣫⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣻⡄⢿⣟⠿⣧⠈⣇⣘⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡾⡟⣩⢷⡂⢁⠷⣻⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣽⠓⢢⣿⣗⠘⢧⣹⣿⣷⢹⠀⠹⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣓⢿⣿⡡⠞⣯⡠⠞⣹⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣧⣰⣿⡿⠯⠁⠀⠻⣿⠟⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⢴⠀⠀⠀⠸⠻⠳⠤⣧⣛⡤⠂⢉⣧⠔⠁⠾⡇
⠀⠀⠀⣀⣤⣤⣶⣤⣬⣝⣿⣇⠀⠀⠀⠈⠙⠆⢻⡇⢠⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡷⠋⡷⣳⣯⡴⠚⠉⣹⡖⠁⠘⠓⢲⡀
⠀⢀⣞⣻⡟⢽⣿⡄⢟⣆⣹⣟⣿⢾⣵⢶⡄⢸⣼⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⡠⢠⠿⣿⡾⠛⠉⣉⠴⣮⡤⠀⠉⢙⣦
⠀⢸⡭⣝⠰⠶⠦⠼⣏⡁⠐⠬⠝⣺⣿⣓⣽⣶⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⠇⢃⠂⠀⢠⣿⢾⠋⢁⡈⠩⢷⡶⠒⠚⠛⣦
⠀⠘⢗⣻⣇⡚⢃⣬⣉⡝⣻⣿⣯⣽⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣄⣠⠀⠀⠹⢾⣝⣇⣀⠀⢘⣷⣂⠀⠈⠙⢂⣤⣄⣀⡀
⠀⠀⠈⠓⠾⠧⠾⠷⠚⠋⠉⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⠶⠦⠤⣟⣼⣧⡤⠤⣼⣇⡀⢾⣙⣯⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⠉⠓⠶⣾⣁⢾⣍⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣄
⠀⠀⠀⣸⠋⣀⣉⣐⡒⠨⢕⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⠭⠒⣂⣈⣀⡈⢳
⠀⠀⠀⢸⡍⡡⠤⠤⠭⣍⣒⡟⠚⠓⢄⠀⠂⠀⠀⠀⠀⠀⠀⠠⠂⣠⠔⠛⠺⣖⣫⡭⠥⠤⢄⡉⣿
⠀⠀⠀⠀⢷⡀⠂⠒⠒⢒⣲⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⢗⣒⠒⠒⠂⠀⣼⠃
⠀⠀⠀⠀⠈⢷⡈⣉⣉⠀⠈⠩⣍⣳⣦⣀⡀⠑⣄⠀⡀⢀⠞⠁⣀⣤⣖⣉⡭⠉⠀⢈⣉⡁⣰⠃
⠀⠀⠀⠀⠀⠀⠻⢦⣀⣤⠄⠠⠤⠤⠤⠤⣭⠷⢮⡶⢺⣧⠶⢯⡥⠤⠤⠤⠀⠒⢤⣄⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠝⠛⠉⢙⣛⣛⣉⡩⢽⣷⣼⡿⢭⣉⢛⣛⣋⠉⠛⠛⢍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥⠒⣉⠡⢤⠞⠉⠀⣠⠃⡿⢸⡏⢦⠀⠉⠑⢤⠤⢉⡑⠦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠁⡀⠔⣧⣀⣤⠞⠙⢰⠃⠆⢧⢠⠙⣦⣀⣨⡇⠄⡈⠑⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡠⠋⡠⠊⢀⠃⠘⠀⢠⡞⠐⠆⠸⡜⠀⠸⠀⢇⠈⠢⡈⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠁⢀⠂⠀⠀⠀⣸⠁⠀⠀⠀⢳⡀⢀⠀⠈⢆⠀⢳⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀⠙⠾⣤⣤⡼⠖⠋

⠀⠀⢀⣾⣟⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣟⣿⣆
⠀⠀⠀⢻⣯⣿⣿⣿⠿⠿⢶⣼⣿⣿⣦⣄⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⢀⣠⣶⣿⣿⣿⡶⠾⠯⣿⣿⣯⣿⠋
⠀⠀⠀⠈⣿⣷⣿⣿⣶⠛⣿⣿⡇⠀⢈⣽⣿⣶⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣶⣿⡋⠁⠈⣻⣿⡿⠿⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠙⣿⣼⣿⣿⡟⠋⣙⣻⣦⣿⣿⠏⠁⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⢿⣿⣧⣴⡛⠙⠛⣿⣿⣿⣽⡟
⠀⠀⠀⠀⠀⠹⣷⣽⣿⣿⣿⠉⣉⣡⡽⠿⣆⣀⣠⣾⣿⣿⣦⡐⠀⠀⠀⢀⣴⣿⣿⣄⠀⢀⣼⣿⣉⠉⠙⢛⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣯⣹⣿⣿⣿⡉⣀⡤⠶⠚⠛⢿⣿⣿⣿⣿⣷⣾⣿⣦⣿⣿⣿⣿⣿⠿⠿⠷⣤⣀⠉⣳⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⣀⠀⢀⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢄⠀⠀⣨⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⣻⣿⣿⣿⢃⠠⠔⠚⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣍⠛⠛⠲⢤⣈⣸⣿⣿⡿⢛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⢿⣿⡆⠀⠤⠐⡘⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⡌⠒⠠⢀⣼⣿⣿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣷⡠⠐⢸⡇⢸⣿⣿⡿⣿⣿⢿⣿⣿⡇⠀⣿⠐⢄⢠⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣹⣿⣿⣧⣔⠀⠛⢹⡿⣿⡇⣿⣿⡇⣿⣿⡟⢚⠣⠑⢤⣿⣿⣿⢋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣟⢻⣿⣿⣿⣷⣦⣼⣧⣼⣇⠸⡿⠁⣿⣧⣇⣤⣴⣿⣿⣿⣿⠿⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣹⣿⣟⣿⣿⣿⣿⣿⡻⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⣻⣿⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣽⣿⣯⣽⣿⣽⣷⡴⠁⠀⠀⠀⠑⣴⣿⣽⣿⣛⣻⣿⡉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⢻⣦⡀⠀⣴⣿⠀⠀⢠⣤⣀⠀⠀⣀⣤⡄⠀⢰⣦⡀⠀⠀⢀⣄⡆⠀⢰⣦⣀⠀⠀⢀⣤⡆
⠀⠀⠀⢈⡏⢻⣿⠉⡇⠀⠀⠀⢃⣤⣵⣾⣥⣜⠃⠀⠈⠻⣾⢶⣶⢷⡞⠃⠀⠈⢿⡿⣦⣴⢿⣿⠃
⠀⠀⠀⢸⣮⠁⠁⢡⣟⠀⠀⠀⠺⠽⠋⠉⠯⠿⠀⠀⠀⠸⣿⠊⠁⢿⠟⠀⠀⠀⠻⣿⠎⠉⢾⡟

⠀⠀⢀⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⢠⡄
⠀⠀⠀⢿⣿⣦⣴⣿⡿⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⢇⡀⣠⣦⣀⡸⠇⠀⢠⠀⠒⣢⣆⠒⠀⡀
⠀⠀⠀⢸⣿⠏⠋⣿⡷⠀⠀⠀⠐⠀⠈⠇⠀⠂⠀⠀⠀⢿⣰⡟⠻⣆⣽⠀⠀⠀⠙⢟⠻⢟⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⣗⠲⣤⣤⠖⢲⠆⠀⠰⡒⠐⢦⡴⠒⢒⠶⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣄⠂
⠀⠀⠀⠸⣲⠚⠛⣖⠏⠀⠀⠀⠀⢳⠞⠳⡾⠁⠀⠀⠀⠀⢠⡄⢡⡄⠀⠀⠀⠀⠸⣯⣻⢟⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⢠⠆⠀⠀⠀⠀⠠⡄⠀⠀⠰⢢⡖⠀⠀⠀⠀⠀⠀⢶⡴⠆⢰⡇⠂⠀⡀⠀⠀⡀⠐⠲⡷
⠀⠀⠀⠈⢦⣀⠀⣰⠀⢀⡠⠏⠀⠀⠀⣿⣰⢩⢄⡰⡍⣆⣻⠀⠀⠀⠈⠇⠀⠀⢠⡄⠀⠀⢾⠀⠀⠀⢳⠀⠀⠨⣶⡌⠀⠀⣺⠁
⠀⠀⠀⠀⣴⠀⠀⢼⠀⠀⢰⠄⠀⠀⠀⢩⣾⠘⣾⣷⠃⣷⣍⠀⠀⠀⠀⣠⡀⠀⠸⠇⠀⢠⡄⠀⠀⠀⠈⣳⢂⣴⢻⢲⣔⢲⠋
⠀⠀⠀⠀⠘⣷⠶⠖⠶⢶⡟⠀⠀⠀⠀⠈⢿⣇⠈⠁⣸⡿⠁⠀⠀⠀⠀⠙⢷⣤⡄⢠⣴⠿⠃⠀⠀⠀⠀⠹⣜⣱⠀⢸⣋⡼
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⣀⠀⠘⠁⠀⠈⠙⠀⣀
⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢰⡂⠖⣤⡀⠀⠀⣠⠰⠂⡆⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠘⣆⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⣇⠀⠀⠀⣴⠀⠀⠀⣠⠃⠀⠀⢻⠙⠚⡘⣶⢚⠙⠚⣼⠁⠀⠘⡇⠀⠀⠀⣤⠀⠀⠀⣾⠁⠀⠀⠸⠟⠂⢰⠀⠚⠿
⠀⠀⠀⠈⣷⡀⠀⠹⠀⠀⣸⠏⠀⠀⠀⠨⣗⢆⡙⠻⠊⣠⢆⡏⠀⠀⠀⠻⡄⠀⠀⡟⠀⠀⣰⠋⠀⠀⠀⣆⠀⠀⠘⠀⠀⢀⠆
⠀⠀⠀⠀⠙⠿⠶⠀⠶⠾⠛⠀⠀⠀⠀⠀⠈⠣⠭⠀⠨⠵⠋⠀⠀⠀⠀⠀⠱⠤⠄⠀⠠⠴⠋⠀⠀⠀⠀⠘⢶⡤⠀⠠⣴⠟
⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⣀⠀⡤
⠀⠀⠈⢷⡈⠊⠀⣀⠀⠙⠈⡼⠃⠀⠀⡀⠀⠀⠰⣿⡆⠀⠀⢀⡀⠀⠀⠐⢰⡆⠂⢀⠀⠂⣶⠐⠀⠀⠀⠀⠀⠠⣿⡆
⠀⠀⠀⠀⣙⠀⠀⢿⠀⠀⢚⠁⠀⠀⠈⠓⠀⠀⠀⢹⠀⠀⠀⠘⠃⠀⠀⠀⢨⠃⠀⢻⠃⠀⢫⠀⠀⠀⠀⢀⣌⡓⣛⠒⣋⡄
⠀⠀⠀⠀⠘⠦⠦⠈⠰⠴⠛⠀⢤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢳⡀⠀⠀⣰⠃⠀⠀⠀⢠⣶⠯⢍⣩⣏⠭⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠈⠁
⠀⠀⣶⠖⣠⡄⠀⠀⠀⢠⣤⠲⣶⠄⠀⣶⣶⣤⡀⠀⠀⢀⣤⢶⣶⠀⠀⣶⣶⢄⠀⠀⠀⢠⣶⣶⠀⠠⣤⣄⠀⠀⠀⠀⠀⢀⣤⡤
⠀⠀⠹⠀⢿⠀⠀⣤⠀⠀⣿⠀⠘⠀⠀⢹⡀⢁⣞⢳⡞⢻⡈⢀⡏⠀⠀⢻⠀⠀⠡⣀⠊⠀⢨⡇⠀⠀⠸⣧⠀⠀⣤⠀⠀⢰⡟
⠀⠀⠀⠀⠘⢧⣀⣿⣀⣴⠋⠀⠀⠀⠀⠈⢓⠘⠏⠈⠁⠹⠃⣚⠁⠀⠀⠘⠦⠀⠀⡿⠀⠠⢴⠁⠀⠀⠀⢙⡗⠀⢹⠀⢰⡏
⠀⠀⠀⠀⢷⣦⣉⠀⢉⣥⡾⠀⠀⠀⠀⠀⠘⣦⡤⠀⠀⢤⣴⠃⠀⠀⠀⠀⢧⣤⠂⠁⠰⣤⡼⠀⠀⠀⠀⠈⢷⣴⠏⣧⡴⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉

⡾⣿⣿⣓⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⢺⣿⣿⡟
⠹⣟⣿⣿⣅⣼⣿⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠉⣿⣇⣴⣿⣿⣿
⠀⠹⣽⣿⣯⣈⠿⠀⢼⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣿⣧⡠⠙⠓⣿⣿⣽⠃
⠀⠀⠹⡽⣿⣍⣁⠀⠸⣿⠀⣾⣿⣷⣄⠀⠀⠀⡄⠀⠀⠀⠀⢀⡄⠀⠀⣠⠾⣿⡏⠀⣻⠏⠀⠶⣿⣿⢷⡏
⠀⠀⠀⢳⠻⣿⣦⣠⣀⠛⠢⣿⡇⠀⢹⣷⣄⠀⠑⢄⠀⠀⠀⠌⡠⣠⣾⣇⠀⠘⣿⠄⠁⠀⢬⣶⣿⣟⡿
⠀⠀⠀⠈⢷⠻⣿⣧⣤⣠⠀⠾⠃⠀⣿⣿⠙⣷⣌⠄⣿⣿⣄⣪⡾⠛⣿⣿⠀⢀⡛⠀⠀⢠⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠈⢷⣛⣿⣦⣤⡄⠀⠀⢀⣿⠋⠈⢾⣿⣷⣾⣿⣿⣿⠃⣀⣸⣿⣆⠀⠀⠠⢤⣴⣿⣿⡜⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⢦⠄⠙⠁⢰⣆⠀⢹⣿⣿⣿⣿⡇⠈⢿⡇⢈⠩⣯⣜⠒⠛⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠚⠀⢹⡀⠀⠐⣽⣿⢿⠁⠀⢸⠀⠈⡑⢿⣽⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⠀⢦⡀⠀⡧⠀⢧⢿⣿⡼⣇⠀⡟⠀⢠⡏⣿⡟⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⣿⣷⣤⠀⠅⠀⣷⢠⢸⠘⡟⢰⣄⢠⠃⠰⠋⣤⣼⢷⡟⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠿⣿⣿⣰⡆⠀⢻⠈⣐⠀⠀⣸⠁⣸⠀⠰⣀⣬⡏⡾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⡿⣿⣵⣦⣾⣦⠶⠀⠀⠰⢆⣿⣷⣤⣾⣹⣿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⣾⣋⣾⣥⣿⠋⠀⠀⠉⣟⣹⣟⣙⣏⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⣹⣯⡞⠀⠀⠀⠀⠻⣽⣏⡙⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⢒⣿⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣗⣒⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⣤⡼⠿⢟⣬⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣞⠿⠿⢧⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡦⠤⠤⠬⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠤⠤⠤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠱⢤⡀⠉⢷⡄⠀⣀⠀⣰⠟⠁⣠⠴⠁⠤⠤⠤⢤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣀⠀⠀⠀⠀⠀⠈⠑⠠⠙⣾⣿⣞⠡⠐⠉⠀⠀⠀⠀⣀⣀⣀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣛⣿⣿⣿⠿⠿⠶⠶⢲⣿⢸⣿⠖⠶⠿⠿⢿⠿⢻⣟⣛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⠀⢰⠊⠁⢀⠔⠨⢿⣿⠿⠀⠀⠀⠈⠱⠀⠀⠀⢽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣈⣁⠠⠖⠁⡀⠀⢸⣿⡀⠀⠄⠈⠢⠄⣈⣀⠀⠠⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠀⢀⠌⢠⡞⠀⠌⠀⠠⢹⣿⠑⡀⠈⢆⠀⢦⠈⢂⠀⢢⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣎⣀⡌⢀⠌⢀⡔⠀⠀⠛⠀⠀⢆⠀⢂⠀⣅⣀⣷⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣾⣦⠞⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⠾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣴⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠰⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠴⠞⠁⢀⣤⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠼⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⢀⣶⣴⣿⣿⡇⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡇
⠀⠀⠀⠀⢀⣤⡤⠴⢖⣲⠟⠛⠋⠉⠀⠀⠀⠀⠈⠉⠉⠉⡉⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⢠⣾⢟⠅⠂⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢉⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡇
⠀⠀⠸⣿⣍⣰⠇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⣿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⠀⠀⠀⠙⠻⣿⣶⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠰⠋⠀⡿⢿⣿⣿⣏⠛⠦⣄⠀⠀⠀⠀⠀⠀⠠⣄⣨⡟
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣴⣶⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢿⣦⠀⠀⠁⠀⠀⠀⠤⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠟⠀⢀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡆⠀⣰⠀⠀⢀⠀⠀⠀⠀⡀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⣿⣆⣠⣾⡂⢠⣄⣠⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢳⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡞⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠤⠽⢿⣛⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣛⡿⠯⠤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡖⠒⠲⢿⡟⠁⢉⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡉⠈⢻⡿⠒⠒⢲⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣷⡒⠒⣚⣧⣰⣿⡿⢉⣿⣄⠀⠰⠀⠀⠆⠀⣠⣾⡉⢿⣿⣆⣼⣛⡚⢒⣾⢷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⢉⣉⣉⢻⣿⡀⢸⣿⡿⣦⠘⡀⣠⠃⣼⢿⣿⡇⢀⣿⡯⣍⣁⡉⣹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣇⣀⢠⠤⠿⠟⣿⡿⢥⣹⣇⣿⣿⣸⣏⡬⢿⣿⠻⠿⠤⠤⢀⣸⣟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡤⠔⠒⠒⠒⢿⡟⠒⠦⣽⡇⢸⣯⠖⠒⢻⡿⠐⠒⠒⠂⢤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⡟⠛⢋⣉⣉⣽⠿⠛⣿⣇⣸⣿⠛⠿⣯⣍⣉⡉⠛⢻⣿⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⡟⠋⡹⠋⢠⡿⢀⡼⣹⣿⣿⣏⢧⡀⢿⡄⠘⢏⠉⢻⢿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⡷⠚⡇⠀⢘⣷⡾⢠⡇⢻⡟⠸⡄⢷⣾⡃⠀⢸⠓⢺⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣷⠞⣹⠒⡟⢻⣷⡿⠀⠀⠀⠀⢿⢺⡟⢻⠒⣏⠳⣿⣴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⣍⣧⣧⣰⣧⣼⣽⡇⠀⠀⠀⠀⢸⣯⣧⣼⣦⣼⣼⣭⣿⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⣿⣿⣶⣿⣷⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣾⣿⣶⣿⣿⢫⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣽⡿⠾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣯⡾⢿⠿⠁

⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢹⡿⣋⡟⢿⣤⢶⣆⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣼⠟⣿⣻⡟
⠀⠀⠀⢻⢻⠗⢿⣤⡀⠨⢿⣿⠛⢷⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠟⢻⣿⠯⢤⣤⣼⠛⣿⣿⠃
⠀⠀⠀⠘⣿⣹⢯⣦⣤⠴⠞⣯⣁⡾⡞⢻⡟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣻⣿⡿⣆⣩⣷⠶⢦⣤⣮⢽⣽⡟
⠀⠀⠀⠀⠙⣷⣴⣿⣦⣀⡠⣏⣹⠶⠶⣏⠛⠳⠾⢿⣦⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⣠⣾⠷⠶⠿⢿⡷⠶⠾⣭⡧⣀⣠⣟⡃⣼⡟
⠀⠀⠀⠀⠀⠘⢿⣳⣾⠉⢱⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣞⣷⠈⢹⣾⣷⠏
⠀⠀⠀⠀⠀⠀⠈⣻⣾⡟⣳⣾⢾⡧⠄⠀⠞⠦⢄⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢀⡤⠿⠆⠀⠴⢭⣿⢿⡳⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣵⣿⠝⢿⠁⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⣿⠞⢯⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⣛⣧⣤⠤⠤⠤⠒⠒⠛⠙⠓⠀⠀⠀⠀⠈⠳⡄⢰⣶⠀⡴⠋⠀⠀⢀⠠⠐⠊⠉⠓⠒⠒⠠⠤⢤⣤⡟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢁⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠯⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⠤⣤⣤⣤⣤⣽⣿⣿⣿⣤⣤⣤⡀⠀⣤⣶⣶⣶⣶⣶⣤⣤⣀⣠⣾⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⠍⠉⠉⠉⠉⠉⠻⠆⠁⠀⠤⠐⠀⢉⡿⣿⣿⣿⣏⠉⠐⠠⠤⠉⠛⠛⠉⠉⠉⠉⠀⠫⣍⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢯⣀⡀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⠴⠋⠘⢹⣿⠹⡈⠳⢄⡀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣀⣸⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣷⠊⠁⠀⠀⠀⡀⠀⠀⢀⣠⡴⠊⠁⠀⡰⠀⣾⣿⠆⠁⡀⠀⠉⠲⣤⣀⠀⠀⠠⡀⠀⠀⠀⠈⢻⣯⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣛⣷⣄⣀⠀⠐⠚⢁⠴⠛⠉⠁⠀⠀⠀⠸⠃⡀⢸⣿⠐⡄⠙⠄⠀⠀⠀⠉⠙⠳⢀⠛⠒⠤⢀⣀⣼⣿⢾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣬⣿⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠀⢠⡼⠁⢸⡿⠀⠹⣴⠀⢀⠀⠀⠀⡀⠀⠀⠑⢦⡀⠀⢹⣞⢻⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⣿⣷⣾⡇⠀⠀⠀⡔⠀⠀⣠⠃⢀⡿⠁⠀⠀⠁⠀⠀⠹⡆⠀⢣⡀⠀⠐⡀⠀⠀⠀⣿⡶⣿⠿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣭⣶⢿⣿⡶⣶⣾⣇⣀⣴⠃⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢳⣄⣀⣿⣶⡶⣾⢿⢶⣮⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣷⣿⣲⣻⣭⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣾⣯⣿⣷⣺⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠘⣿⣧⡈⠻⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠟⢁⣾⣿⠃
⠀⠀⠈⢻⣿⡤⢿⠀⢀⣑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣊⡀⠀⡾⢤⣿⡟⠁
⠀⠀⠀⠀⣿⡇⢸⣰⣿⣿⣷⢌⡢⡀⠀⠀⡴⠊⡑⠢⡀⠀⠀⠀⠀⢀⠔⢊⠑⢦⠀⠀⢀⢔⡡⣾⣿⣿⣆⡇⣸⣿
⠀⠀⠀⠀⣿⣿⠉⢣⠹⠋⣗⡦⠙⡌⠢⡀⠙⠒⠁⠀⠹⡄⠀⠀⢠⠏⠀⠈⠒⠋⢀⠔⢡⠋⢴⣺⠙⠏⡜⠉⣿⣿
⠀⠀⠀⠀⢸⣿⣀⡸⠘⠤⣈⣀⠜⠦⡀⠙⢆⠀⠀⠀⠀⢹⠀⠀⡏⠀⠀⠀⠀⡰⠋⢀⠴⠣⣀⣁⠴⠃⢇⣀⣿⡇
⠀⠀⠀⠀⣾⡟⠀⢇⠀⠀⢀⣤⣤⣤⣈⠳⣄⠳⡀⠀⠀⠈⡇⢸⠁⠀⠀⢀⠞⣠⠞⣁⣤⣤⣤⡀⠀⠀⡸⠀⢿⣷
⠀⠀⠀⠀⠻⣷⡤⠤⣵⠀⣿⣿⡋⢑⠄⠙⢮⣢⡙⡄⠀⠀⣇⣸⠀⠀⣠⢋⣔⡵⠋⠠⡏⢙⣿⣿⠀⣮⠤⢤⣼⠟
⠀⠀⠀⠀⠀⣿⡇⠀⡇⠀⠙⠿⣉⣉⠀⠀⠀⠑⣕⣜⣆⠀⣿⣿⠀⡰⣣⣫⠊⠀⠀⠀⣈⣉⠿⠋⠀⢸⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣗⠉⠱⢄⡀⠀⠀⣴⣿⣿⣿⣶⣮⣿⣾⣎⣿⣿⣰⣷⣿⣵⣶⣿⣿⣿⣦⠀⠀⢀⡠⠎⠙⣺⣿
⠀⠀⠀⠀⠀⠈⠻⠷⢴⣮⣭⣓⣶⣽⣿⣿⠭⠭⠭⣶⣶⣿⣿⣿⣿⣶⣶⠭⠭⠭⣿⢿⣯⣶⣞⣭⣵⣦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢫⠟⠉⣩⢟⡩⠔⠚⣩⣋⡟⠀⣿⣿⠀⢻⣙⣍⠓⠢⢍⡻⣍⠉⠛⡝⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠘⠢⠚⣵⣿⠀⠀⣰⡷⣿⡄⠀⣿⣿⠀⢠⣿⢾⣆⠀⠀⣿⣮⠓⠔⠃⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠀⠀⢿⣿⣷⡴⢻⠁⠸⣿⠀⢻⡏⠀⣿⠇⠈⡟⢦⣾⣿⣿⣀⠀⠀⢴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡖⢰⡋⢱⠌⠁⠀⠘⠢⠖⢹⡇⠀⠀⢸⡏⠣⠔⠁⠀⠀⠁⢏⣈⡇⢲⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⠉⠁⠀⠀⠀⢀⣄⠀⣸⡇⠀⠀⢸⣇⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⣾⣷⣄⣼⣿⣶⣾⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣷⣶⣿⣧⣤⣾⣷⣾⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⠙⢿⡿⠋⠙⠿⠋⠉⠛⠋⠀⠀⠀⠀⠙⠛⠉⠙⠿⠋⠙⢿⡿⠋⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄
⠀⠀⠀⠀⠀⠰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡷⠀⢀⡿⠹⢷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⣿⠷⠒⢀⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⠿⠥⠧⠤⣴⠿⣷⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⣧⣶⠿⢎⣹⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⢤⠀⠀⠀⠨⢧⡀⠉⠛⣦⡀⠀⠀⠀⠀⠀⢀⡔⠋⠀⣠⡯⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⣟⡄⠠⠄⠀⠠⠷⢄⡀⠈⠻⣦⢠⣀⣔⡴⠋⠀⣠⠞⠁⠀⠀⠀⠀⣼⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣤⣤⣴⣶⣶⣶⣿⣷⢦⣬⣿⣿⡟⣡⣴⡬⠤⢤⣤⣤⣤⣤⣴⣟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣉⡅⠞⠛⠃⢠⠄⠉⠲⢺⢿⣿⢏⡷⡯⢤⡄⠂⠉⠛⢿⣿⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣅⡠⠀⢀⡚⠉⡠⠊⢀⠂⢸⣿⠙⡇⡀⢄⠈⠫⠁⠀⠀⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠈⠔⠑⠒⠁⢀⠂⠐⢨⣿⠀⠰⡈⠄⠑⡆⢬⠀⠀⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡄⠀⠀⠀⠂⢀⠀⢀⠠⢻⣿⠀⠀⢡⠈⣄⠈⠄⠣⡈⣲⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣫⣶⣠⡴⢀⢴⣠⡆⠀⠘⠏⠀⠈⢢⣆⣈⣄⡸⣤⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠛⠋⠁

⠀⠀⠀⣤⣴⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤
⠀⠀⢸⣿⣷⣿⣿⣿⣿⠿⣖⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣲⠿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠈⢻⣿⣿⣟⢉⣿⣶⡿⢏⣻⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣟⡹⢿⣶⣿⡉⣻⣿⣿⡟⠁
⠀⠀⠀⠀⠙⣿⣿⣿⡉⠉⠙⠻⡋⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠛⠉⢙⠟⠋⠉⢉⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠘⣿⣿⡟⠉⠉⠀⠓⢤⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⡤⠚⠀⠉⠉⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⡷⠒⠒⠒⠒⠒⠚⠓⠢⣄⠈⠻⣄⢰⡆⣠⠟⠁⣠⠔⠚⠓⠒⠒⠒⠒⠒⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠒⢬⣿⣿⡥⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⡿⠿⠿⠿⢿⣛⣻⡿⠿⢿⣿⣿⡿⠿⢿⣟⣛⡿⠿⠿⠿⢿⣿⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡯⠤⠒⢒⡲⠋⠀⠀⡠⠖⣡⣿⣿⣎⠲⢄⠀⠀⠙⢖⡒⠒⠤⢽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠤⠒⢉⡝⢀⣀⡤⠊⢀⠜⡱⣿⣿⢏⠣⡀⠑⢤⣀⡀⢻⡉⠒⠤⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⡤⠚⢁⠏⠁⡔⠁⢠⠊⡰⠁⣿⡿⠈⢆⠑⡄⠈⢣⠈⠹⡈⠓⢤⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣤⠎⠀⡸⠁⡠⠁⢰⠃⠀⢸⡇⠀⠘⡆⠈⢆⠀⢆⠀⠑⣤⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣯⣷⣾⣧⣴⡁⣠⠏⠀⠀⠘⠃⠀⠀⠹⣄⢈⣦⣼⣷⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⡽⢩⣟⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡟⠻⠛⠉⣿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣠⣴⢁⠔⠋⣀⠽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡏⠀⡟⢁⡠⠚⠁⣀⣼⡿
⠀⠀⠀⣴⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡿⠀⢠⠓⠉⠀⣠⣾⠟⠁⣀⣀
⠀⠀⠀⠻⣿⣟⢲⡟⠫⣿⣷⣶⣤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡎⠀⣠⣾⣿⡿⠛⢉⡻⠿⣿⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣯⣽⠿⠅⣨⡟⠻⢿⣶⣥⣀⠀⠀⠀⠀⠀⢸⠀⣸⣠⣾⢟⣟⡡⠔⢊⠡⠄⠒⠊⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡤⠤⠝⠲⢤⣀⡉⠛⠻⢦⣄⣰⣶⣾⡶⠟⣫⠔⠉⠉⠁⠉⣳⢶⣒⠉⠉⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡒⠂⠉⠁⠀⠉⢉⣉⣽⣿⢿⣿⣷⣿⣒⠒⠒⠒⠛⠣⠤⣀⠀⠉⡳⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠾⣿⣿⣿⣛⡫⠔⢋⠻⣿⣿⡪⢍⠒⠢⠤⣀⡀⠀⢉⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣀⠜⢫⠀⢀⠆⠘⡘⡝⣿⡁⠛⠦⣄⡀⢈⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠋⣤⡼⡄⠀⢇⠸⣸⢿⣄⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣥⡑⡘⢄⠘⠀⢹⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠷⣷⡾⠁

⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⣶⣶⡶⡶⡶⣶

⣲⣿⡟⠉⠉⠉⠙⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠚⠉⠉⠉⠙⣿⣷
⣿⠅⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⢼
⠸⣆⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⢀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡾
⠀⠈⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⣦⣠⣿⣧⣠⡞⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉
⠀⠀⠀⠈⢢⡤⠄⠒⠂⠁⠀⠀⠀⢀⣠⠤⠿⠟⠿⢿⣿⣿⠿⠿⠿⠧⢤⣀⠀⠀⠀⠀⠁⠒⠂⠤⣤⠊
⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⣀⣤⠞⠉⠀⠀⠄⠀⠀⡼⣿⡿⡄⠀⠀⠄⠀⠈⠙⠶⣄⡀⠀⠀⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠋⠀⠠⠀⠀⠀⠀⠀⣿⡄⢹⠁⣸⡇⠀⠀⠀⠀⠠⠀⠈⢳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡟⠀⠀⠀⠀⠀⡀⠐⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡔⠀⠠⠀⠀⠀⠀⠀⠀⢡⠀⢠⠃⠀⠀⠀⠀⠀⠰⠀⠐⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠃⢀⠀⢠⠀⠀⠀⣼⠀⢸⡄⡀⠀⢠⠀⢠⠀⢁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⡆⠀⢸⠀⢀⡟⠁⠀⠀⠙⣇⠀⢠⠀⠀⣆⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡶⣾⠶⠿⠃⠀⠀⠀⠀⠻⠷⢾⡶⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠛⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⡽⢿⣿⣴⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣷⠛⣿⣵⢋⣭⣿⡾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣼⣹⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢾⣿⡶⢻⣿⣯⣀⣿⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⣯⣽⣻⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⢀⣾⣯⡶⠋⠁⠀⠈⣻⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⣷⡇⠀⢹⡟⣷⡄⠀⠀⠀⠀⢰⡿⠛⠋⢻⠏⠀⠀⠀⣠⣶⣿⣿⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠙⢇⠀⢸⠉⢹⣿⡄⠀⠀⢠⣿⠀⠀⠀⣿⠀⢀⡴⠞⠋⠁⠈⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣆⢸⠀⢸⠛⢿⣤⣤⣼⠇⠀⠀⢰⣿⠞⠉⠀⠀⠀⢀⣤⣾⣿⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡜⣆⠀⢸⣿⠀⣸⠀⢸⠇⣸⡟⠀⠀⢀⣿⠁⠀⠀⢀⣤⡾⠋⠁⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⡆⠀⣿⠀⡿⠀⡌⢀⣿⠁⠀⢀⣾⣃⣠⣴⠾⠛⠁⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠹⡄⢸⣦⡇⢰⡗⣿⠇⠀⢀⣾⠟⠋⠁⠀⠀⠀⠀⣀⣴⣿⣯⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣆⢿⡇⢸⣱⠏⠀⢠⠞⠁⠀⠀⠀⠀⣀⣴⡾⠟⠛⢉⣙⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣬⣧⡑⣸⡟⠀⠔⠁⠀⠀⣀⣤⣶⠿⠿⠭⠴⢖⡉⠉⠁⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⣯⣀⣤⣤⡴⠶⠛⠋⢉⣀⣀⡀⠠⢤⣤⣟⡉⠉⠉⠙⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⣿⠭⢍⣉⡀⠉⠙⠓⠶⣤⣀⠀⠀⠉⠉⠲⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣍⣙⠒⠲⠤⣄⣀⣉⣷⣶⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⢀⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠹⠄⠀⠈⠙⠀⠉⢻⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠴⠉⠑⡆⠀⣤⠀⠀⠠⠛⠉⢳⡄⠀⠀⠀⠀⠀⢸⣄⠀⡀⠉⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⣌⠑⠆⠠⠴⠃⠀⠈⢷⣄⡀⠀⠀⠈⡧⠀⠀⣾⣦⣴⣦⠈⠉⠈⢦⣀⡤⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⡰⡁⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢸⡏⡼⠏⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣠⡄⠰⠚⠲⢤⡀⠀⠀⠈⣴⠀⢀⡴⠋⠛⣦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢰⠃⠀⠀⡀⠀⠀⠙⠲⣄⠀⠘⠶⠉⠀⠀⢀⡟⠀⣰⠟⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⢄⡠⠂⠀⢸⡇⠀⡼⠀⠀⠀⠷⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠉⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣷⠀⠐⠛⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡽⢆⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⢠⡀⣠⠇⠀⠀⢀⡄⠀⣤⠀⠀⠀⠀⣼⠃⠸⣿⣇⠀⠀⠀⢹⡀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠀⠀⠉⠁⠂⢀⣀⡞⠀⠙⠀⠀⠀⠀⠘⣷⡐⠢⠿⠿⣿⠖⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⠀⠀⠈⠁⠁⠀⠀⢀⡀⠀⢠⣊⣀⣤⣬⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⠹⡄⠈⠉⠋⠁⠀⠀⠀⠀⢠⣄⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣭⣿⢻⡆⠀⠈⠓⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⡺⠈⣿⣤⠀⠀⠀⠀⠀⣠⡶⠀⠀⠈⠳⡄⠀⢠⡷⠤⠀⠀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠈⢻⣆⠀⠀⠀⠀⠈⠉⠲⠦⡀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠐⠒⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠏⠀⠀⠀⠀⠒⠚⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⠿⢻⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⠀⠀⢸⠟⠻⡟⠙⢿⠻⣏⣵⣼⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠻⡉⢻⠙⣿⣦⣿⡇⠀⡇⠀⠎⢀⢿⣧⢽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡋⠓⢄⠀⣈⡃⠡⢸⣿⠁⠀⠁⢀⠶⠚⣻⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠉⠲⢦⣝⡇⠙⠦⣼⣿⠀⠀⡴⠃⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣉⠓⠦⣌⠻⣄⠀⢿⡇⠀⠘⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠑⢈⣳⣼⣇⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠒⠶⢿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠂⣠⠔⣨⠞⢿⡏⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠤⠒⢋⣥⡞⠁⢀⣿⡇⠀⢠⡀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠴⠚⢋⢴⣀⡴⠋⢿⣇⠀⠀⠳⡀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⠚⢁⠌⢰⠀⡆⣼⣿⠀⠀⠀⠘⠲⣤⡝⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣮⣤⣯⣼⠿⠋⣿⠀⢸⠀⠀⡆⢰⣾⣛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢿⣦⣾⣦⣴⣷⣾⡉⡏⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣷⣧⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠇

⢼⣶⠆⡀⠀⠀⠀⠀⣀⠰⣾⡧⠀⢸⡿⢖⣀⠀⠀⠀⠀⠀⢀⡴⢶⣶⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣿⣷⣦⡀⠀⠀⢀⢴⣾⣿
⢸⠿⣛⣛⣥⡀⢀⣬⣉⣛⠻⡇⠀⠈⣿⠛⠻⢷⡄⠀⢀⡴⠿⠟⢾⡏⠀⠘⣭⠚⣱⣿⣶⣄⣴⣤⣴⣾⣌⠓⡽⠀⠀⢹⣿⡇⠈⣦⣠⠀⠀⣿⡟
⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠡⢀⠄⠀⠙⣶⠞⠀⠀⠀⠨⠁⠀⠀⠀⢨⠛⠿⠛⣻⣿⣿⠛⠿⢛⠄⠀⠀⠀⠀⣸⠿⠋⠹⠛⠉⠻⣧
⠀⠉⢿⣿⠏⠸⠇⠹⣿⣿⠁⠀⠀⠀⢰⠁⠀⠀⠀⢻⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⠟⠀⠠⠁⠀⠀⠀⠀⠀⠻⣦⣀⡄⠀⣄⣠⡿
⠀⠀⠀⠛⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠘⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠈⠉⡇
⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡿⠛⠉⠀⣀⠀⠀⣀⠀⠉⠉⠻⡄⠀⠸⣿⡗⣦⡀⠀⠀⠀⠀⣠⢾⠛⡟⠁⠀⠀⠀⠈⢢⠀⠀⢀⠀⠀⠀⠀⠀⣸⠿⠛⠀⠀⠀⠀⠀⠀⠈⠛⠿
⠁⢠⣾⣏⠁⢠⡀⠀⣹⣿⡦⠀⠀⠀⠀⢳⣷⣻⣿⣦⠀⢀⣼⡿⠁⣷⠃⠀⠀⠀⠀⠀⣤⣗⣄⣦⡄⠀⠀⠀⠀⠉⢀⣤⣶⠊⠀⡀⠈⢳⣶⣆
⢠⢾⣿⣟⢀⣼⣧⡀⢹⣿⡇⡆⠀⠀⠀⢈⡝⠋⠈⢿⢿⢿⠎⠉⠜⣌⠀⠀⠀⠀⢠⡟⢿⠟⠟⣿⠻⣦⠀⠀⠀⠀⣼⣿⣿⠂⣨⣇⡀⢺⣿⣷⢀
⠈⠀⠙⠻⠿⠉⠋⢻⡿⠋⠀⠁⠀⠀⠀⠀⢢⢈⣱⡦⠈⠠⣴⡍⢁⠊⠀⠀⠀⠀⠘⢷⡆⠀⠀⢰⣶⠏⠀⠀⠀⠀⠂⠙⢿⣿⠏⠏⢿⡾⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡾⣻⣴⠦⠀⠀⠀⠀⠀⠠⠶⣮⣝⠇⠀⠉⠰⣄⠀⠀⠀⠀⠀⢀⡤⠒⠀⠀⢶⡴⣤⡀⠀⠀⠀⠀⢀⣠⣴⡶⠀⣟⠒⢀⠀⠀⠀⠀⠀⠀⠀⠐⢚
⣿⠋⢀⣠⣤⣠⣠⣠⣠⣤⣀⡀⢙⡇⠀⢀⣀⣿⣷⡀⠀⠀⣠⣾⣗⣀⡀⠀⠸⣿⡙⢯⣆⠀⢀⣴⡽⢫⣿⠃⠀⠹⣮⢿⣷⣄⠀⠀⢀⣴⣿⢦⡾
⠘⢓⢛⡿⡝⣯⣿⣏⡿⣽⣿⢛⡛⠁⠀⠸⣿⣁⣹⣿⣤⣴⣿⣁⣹⡿⠁⠀⠀⠙⣣⠘⢻⣿⣾⠛⢠⡛⠁⠀⠀⠀⠻⡇⢙⣿⣦⣤⣾⡟⠡⡿⠃
⠀⢾⣼⣿⣿⣿⢸⠹⣷⣿⡿⣼⠇⠀⠀⠀⣴⣿⣿⡿⣿⡿⣿⣿⢷⡄⠀⠀⠀⠐⣿⡄⠞⠸⠘⣇⣬⡗⠀⠀⠀⠀⠀⣶⣿⠛⠛⡏⠙⡟⣶
⠀⠈⠛⠾⠟⠁⠈⠀⠈⠒⠛⠋⠀⠀⠀⠀⢿⣦⠿⠀⢩⠁⠸⢷⡾⠇⠀⠀⠀⠠⠙⠇⠀⠀⠀⠈⠟⢢⠀⠀⠀⠀⠀⠈⠻⠃⠀⠃⠘⠿⠉
⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠁⠈⠱⠗⣄⠀⠀⣠⠐⠆⠃⠂⠀⠀⠘⣿⠿⠶⡄⠀⠀⠠⠾⠿⡿⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠀⠀⢿⣿⢟⣥⠄⠀⠀⠀⢠⣔⢻⣿
⠀⠀⠀⣀⠀⣿⣿⡄⣀⠀⠀⠀⠀⠀⠀⣯⡦⠀⣀⣰⣆⣄⠀⠀⡱⠀⠀⠀⠄⠀⠀⠀⢰⡖⠀⠀⠀⠀⠃⠀⠀⠈⢿⣸⣁⣀⡠⣿⢀⣀⣹⢣⡟
⠀⠀⠔⠈⠀⢹⡏⠁⠛⠦⠂⠀⠀⠀⠀⢠⣼⠛⢙⢻⡟⡏⠛⣷⡄⠀⠀⠀⢀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠁⠀⡏⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⠞⠉⠉⢳⡤⠛⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠳⢤⡄⠀⠁⠠⣤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⡿⠷⢦⣄⠀⣠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡇⠀⠂⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠈⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⢷⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠿⠻⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⡈⣿⣶⣀⣾⠃⢦⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⡾⣟⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⢀⣾⣿⣿⣿⡟⡗⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡿⠟⠛⠻⢿⣿⣿⣿⡏
⠀⠀⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣼⣿⣿⣿⣿⣿⣆⠙⢿⣿⣆⡙⠦⣄⠀⢈⣿⣿⣿⣷⡄
⠀⢸⣿⢿⡿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣿⣿⡄⠀⠙⠫⣑⠦⣌⠙⣿⣿⣿⣿⣿⣿⡀
⠀⢸⡏⠀⢱⡟⠉⠙⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡇⠀⠀⠀⠁⠀⠀⠀⠈⠓⠯⢻⣿⣿⣿⣿⣿⣿⠇
⠀⢸⡇⠀⢸⠇⠀⠀⡇⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⣿⣀⣠⣤⣼⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠁
⠀⠘⣷⣦⣾⣶⣤⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠛⠛⠛⠛⠿⠛⠛⠛⠋⠉⠁⠈⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋

⣴⠉⡟⢓⣶⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣖⠛⡏⢱
⣿⣿⡻⣿⣿⢿⣍⣻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣋⣽⢿⣿⡿⣻⣿
⠹⣿⣬⣿⣿⡿⣏⠉⠉⠁⣈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡀⠉⠉⣉⣿⣿⣿⣯⣼⡿
⠀⠸⣿⣿⠿⣃⠐⢫⣿⣿⠛⣿⣏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣿⡟⢻⣿⣯⠓⢀⣻⢿⣿⡿
⠀⠀⠹⣿⡤⠾⣿⣿⣿⠟⠛⢿⠋⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⢻⠟⠛⢿⣿⣿⡿⠦⣼⡿⠁
⠀⠀⠀⢻⣿⣼⡟⠉⠀⠀⠀⠀⠑⢄⠀⠙⢿⣷⣄⠀⠀⠀⢀⣴⣿⠟⠁⢀⠐⠁⠀⠀⠀⠈⠙⣿⣼⣿⠃
⠀⠀⠀⠘⣟⢻⡽⠒⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⣿⣦⣶⣦⣾⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠐⠺⣽⢛⡟
⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣈⣿⣿⣿⣏⣀⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠈⠛⠿⢿⣿⢿⡿⠿⠿⠿⢿⠿⠛⠉⠁⠀⣿⡇⠀⠉⠙⠻⢿⠿⠿⠿⠿⣿⢿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠠⢿⠇⠊⠈⠀⠀⠶⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠱⠆⠀⠈⠈⠒⢿⠧
⠀⠀⠀⠀⠀⠀⣾⠙⡧⠀⠀⠀⠠⠟⠒⠂⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠒⠚⠧⠀⠀⠀⠠⡝⢹⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣙⡇⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠉⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣹⣇⣀⡀⣂⣀⡤⠂⠀⠀⠀⠀⠀⠀⠢⣄⣀⡂⣀⣀⣿⡩⠋⠁

⠀⠀⡶⣤⢄⠀⠀⣀⣤⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⡘⠉⠳⣴⣦⠞⠉⢓⡲⠆⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⣿⣟⣷⣶⣻⣿⠛⠀⠈⢷⣿⣶⣤⣴⡾⣷⠏⠀⠀⠉⢶⣀⣼⢣⣀⣶⠉⠀⠀⠙⢃⢼⡿⢾⡾⣿⢆⠑
⠀⠀⠀⢿⣿⠕⠃⢟⣿⠂⠀⠀⠀⢌⣙⡛⣛⣁⠄⠀⠀⠀⠀⠨⠛⠁⠈⠛⠇⠀⠀⠀⠀⠈⠻⠯⠁⠩⠿⠋
⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠠⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⣠⣴⣄⠀⠀⢀⣤⣤⣄⣤⣤⣄⣤⣤⢤⣤⣤⠀⠸⣿⣿⠓⢠⡄⠚⣿⣿⠇
⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⣀⣴⣺⣿⣿⣿⣟⣢⣄⠉⠛⠻⣿⢿⠿⡿⣿⠛⠋⠉⠀⠀⠈⢻⣆⡘⢃⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠿⣯⠿⢯⠿⠛⠋⠁⠀⠀⠑⠚⠀⠓⠈⠀⠀⠀⠀⠀⠀⢨⠛⠋⠙⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀
⠀⠀⢄⠒⢠⣤⠐⠀⡔⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⣿⠿⡿⠃⡀
⠀⠀⠀⠠⠤⠃⠤⠀⠀⢠⡄⠀⣠⠀⠀⠀⠄⠡⠄⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠙⠺⠻⠚⠁⠀⠀⠀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⡔⠒⣶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢶⡶⠒⣤
⠀⠀⠀⢸⣿⣹⣿⡓⠒⠿⠛⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⠛⠗⠒⣻⣿⣹⣿
⠀⠀⠀⠀⢿⡤⣇⣿⡀⠁⢠⣿⡇⠑⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⠁⢿⣷⠀⠁⢸⡇⡧⣼⡇
⠀⠀⠀⠀⢸⡇⢧⠸⡆⠀⠪⠅⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⡄⠩⠂⠀⣼⢣⠇⢿
⠀⠀⠀⠀⢸⡇⢺⠈⣷⠀⠀⠀⠈⠉⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠈⠉⠀⠀⠀⢰⡏⢸⠃⣿
⠀⠀⠀⠀⠀⢿⠘⡆⢻⡆⠀⠀⠀⠀⠀⠈⠛⠁⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣾⡇⡾⢸⡏
⠀⠀⠀⠀⠀⠘⣎⢣⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣄⢲⣷⣆⣼⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⢹⡟⢡⢋⡾
⠀⠀⠀⠀⠀⠀⠈⠂⠑⠙⠂⠀⢀⣤⣤⣀⣀⣀⣹⣿⣿⣿⣯⠈⣿⣿⣿⣿⣁⣀⣀⣠⣤⣤⠀⠀⠸⠁⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢸⡗⠀⠉⠉⠉⠉⠉⠉⣿⣿⣷⣶⣿⣿⡏⠉⠉⠉⠉⠉⠁⠀⣿⠑⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠹⡶⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⢛⠳⠵⢛⡻⠃⠀⠀⠀⠀⠀⠀⠀⣿⠐⣾⠡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣟⢹⡅⠀⠀⠀⠀⣀⠀⠀⠀⢨⡙⠚⣋⠇⠀⠀⢀⡀⠀⠀⠀⠀⢸⠙⣧⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣧⢸⣇⠀⠀⠀⠀⠉⠀⠀⠀⠸⡆⠔⡺⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⢀⡇⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠻⣆⠹⣦⣤⠀⠘⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠙⠀⢀⣤⡾⠃⡾⠃⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠐⠛⣶⣄⠸⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢁⣴⡞⠓⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠗⠛⠻⣄⠙⠛⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⠛⢁⡼⠛⠓⢿⣆
⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠙⢧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡃⠴⠐⡌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠷⢄⡊⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠺⠎⣣⢀⠘⡆⠀⢀⢳⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⢧⡈⠚⠡⠂⠀⢀⠠⠞⠘⡆⠀⠉⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢏⡶⢄⠨⠁⠀⠀⠀⠀⠄⠡⠃⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡏⠘⣉⠼⠣⠁⠀⠀⠀⠀⠀⠀⠒⠁⠃⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡶⢤⡀⠀⢸⡧⡇⣄⠠⡈⠀⠀⠀⠀⠀⣈⣦⣴⣶⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢩⣵⣼⡷⡄⠈⣏⣣⠉⠔⠁⠀⣀⠤⣶⣾⠟⠉⠉⠁⠀⠀⣠⣞⠻⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢘⣏⢫⢳⣽⡄⠈⠻⠧⠴⠒⠋⠀⠀⠛⠁⠀⠀⠀⠀⠀⣸⠳⣵⠖⢉⣽⣆
⠀⠀⠀⠀⠀⠀⣰⣿⢩⣴⣶⣿⠛⡇⢹⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⡡⢿⣁⠴⣟⣦
⠀⠀⠀⠀⠀⠀⣿⣿⠇⣙⣧⠙⣧⢹⣾⣧⣇⠀⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣽⣿⡵⢋⣧⠔⣩⢾⣇
⠀⠀⠀⠀⠀⠀⢿⡏⢠⣾⣿⡒⠈⢻⣿⣿⣼⠀⠈⠀⠀⠛⠀⠀⠀⣀⠀⠀⢠⢶⢞⣑⡍⣟⡁⠘⣧⡠⠊⣿
⠀⠀⠀⣀⣠⣤⣤⣉⣻⣿⡃⠀⠀⠀⠻⠄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⢸⠒⡎⣷⣯⡴⠒⢙⡤⠀⠸⠶⣄
⠀⢀⡾⣿⠻⣧⡍⢛⣏⣻⣻⣶⣗⡦⡄⢰⣼⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠡⢿⣿⡖⠛⢉⡥⣎⡄⠀⠉⣷
⠀⢸⠭⡇⠶⡶⠴⣯⣁⠀⠬⣓⣿⣿⣾⣶⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⣼⡷⣏⣁⡈⠭⢷⠖⠚⠛⣢
⠀⠘⢏⠽⣌⢫⣴⢤⣏⣹⠿⠿⠛⠛⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⠀⠈⠻⣯⢳⡄⠀⠨⣯⡁⠈⣉⣁⡦⣤⣤⡀
⠀⠀⠀⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠛⠓⠊⠶⣵⣖⠒⢿⠦⣜⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠈⠙⠳⠬⠗⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢱⣇⣀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣥⡀⠀⠐⠟⢛⣿⢾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠙⠳⢤⣤⣽⣿⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣤⠄⠀⠀⠀⠈⣙⣛⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠷⢣⠀⠀⢠⠞⠋⠀⠙⢛⠟⠃⠲⣷⠀⠀⠿⠇⢹⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⢁⡴⠋⠀⠀⢦⣴⣻⡄⠀⠀⠀⠀⠨⣦⠉⣟⡉
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⡆⠀⠀⢠⠾⠀⠀⠀⣀⡿⢟⣏⠁⠀⢰⣄⣰⣦⣍⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢠⣿⡀⠀⠀⣶⠈⠀⠀⠉⠒⠚⠻⣿⣿⣭⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⣿⡿⢃⠞⠃⠰⢦⣤⠄⣀⣀⠀⠀⠈⢛⣻⣃⣙⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣈⢁⣿⣧⠞⠁⠀⠀⠤⠶⠾⡶⠄⠀⠀⢠⣬⣭⣋⡀⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡆⠒⠒⠀⠀⠀⠒⠒⠀⠀⠐⢸⣯⣟⣡⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠻⣦⠀⠂⢄⡀⠀⠀⠀⠀⣷⣾⣝⠋⣹⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠒⢤⣀⣴⣿⣟⣻⣷⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠻⠟⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠖⠀⠀⠄⠴⠶⣾⣿⣿⣿⣷⠶

⢠⣶⣶⢠⡀⠀⠀⠀⢀⡀⣶⣶⡄⠀⢠⣶⢠⢀⠀⠀⠀⠀⠀⢀⣠⠀⣶⠀⢰⣶⡦⢄⡀⠀⠀⠀⠀⠀⣀⠴⣶
⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⢻⡘⠾⣅⣆⢠⠀⣐⡸⠟⣱⠏⠀⠀⢷⠛⠉⠀⠲⡀⠀⡴⠂⠋⠛⢲
⠀⠘⠻⠤⠐⠒⣿⠒⠀⠠⠟⠃⠀⠀⠀⠈⣹⣾⠉⢉⣿⣏⠉⠙⣾⡋⠀⠀⠀⠘⢠⠤⠤⠤⢼⣯⠤⠤⠤⢤⠋
⠀⢰⡇⠀⠀⡈⠿⢁⠀⠀⢸⡆⠀⠀⠀⠀⢻⣿⣈⣙⠙⢘⣈⣰⣿⡃⠀⠀⠀⠀⡇⠀⠀⠀⡼⡧⡄⠀⠀⢸⠇
⠀⠀⠙⠶⠚⠁⠀⠈⠓⠶⠋⠁⠀⠀⠀⠀⠀⡟⠟⠋⠀⠈⠙⠛⢇⠀⠀⠀⠀⠀⠙⠲⠦⠆⠀⠁⠀⠦⠶⠋
⠀⡀⠀⠃⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣶⣶⣤⣀⠀⠀⠀⠀⢀⣤⣶⣶
⠘⣿⡿⠆⣄⠀⠀⠀⣠⠰⢿⣿⠃⠀⠘⢦⣒⠝⠑⠦⣀⣀⠔⠙⠇⣂⡜⠁⠀⢹⣿⡑⢮⣱⣄⣀⣶⣹⢞⣽⡿
⠀⢸⡧⠀⠄⠱⣤⠜⠠⠀⢼⡇⠀⠀⠀⠈⢿⣧⠤⠔⢻⡗⠤⢤⣾⠟⠀⠀⠀⠀⠙⢿⡆⠛⢻⣿⠛⠃⣾⠟⠁
⠀⠀⡿⠉⢉⠉⣿⠉⡉⠉⢻⠀⠀⠀⠀⠀⠘⡧⠀⠀⠙⠑⠁⠀⡽⠀⠀⠀⠀⠀⠀⢾⣷⣤⠿⠿⣦⣼⣿
⠀⠀⠻⣦⣤⡀⠉⠁⣤⣴⠟⠀⠀⠀⠀⠀⠀⣸⠒⠊⠀⠈⠓⠺⡀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠃⠀⠛⠻⡁

⠀⠀⢀⠌⠀⠀⠀⠹⡀⠀⣀⣬⠆⠀⠀⠀⠀⢻⡄⠀⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣄⠋⠀⢀⣠⢤⠘⠇⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡥⠞⣂⠀⠀⠀⠈⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠴⠀⠀⢴⠂⠐⢟⡽⢿⠟⢷⣂⡄⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠣⠀⠀⠀⠀⠐⠀⠻⡀⠀⠀⠀⠀⠐⠀⠘⢠⡀⠀⡴⠃⠀⠈⠉⢠⡇⡼⣄⠉⠳⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠒⠆⠀⠀⠠⠁⠀⠀⢤⡄⠄⠀⠀⠛⢠⡾⠁⠀⠀⠀⠀⣼⠀⣧⢹⡇⠀⠀⠀⠀⠚⠒
⠀⠀⠀⠈⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠢⠊⠱⠛⠀⡟⠰⠇⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠄⠀⢀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠠⠄⠒⠊
⡀⠄⠀⠀⠤⠨⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣀⡀⡀⠤
⠀⠀⠀⠀⠠⡄⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⣁⠀⠀⠐⠂
⠀⠀⠀⢀⡀⠉⠘
⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢗⣂⣀⡀⠀⠒⢂
⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠄⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡸⡄⠀⠀⠀⠀⠀⠈⠀⠈⠀⡴⠀⠀⠀⠀⢼⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⢀⠀⠀⠀⡀
⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠘⠀⢀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠁⠘⣿⠀⢀⠤⠁⠤
⠐⠀⠀⠀⠀⠉⠃⠁⠀⠀⠀⠀⠐⠛⠋⠀⢰⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⢀⠇⢤⣀⢀⠀⠀⠠⡖⠁⢀⠀⠀⠀⠀⠠⠁⡠⠴⠶⣯⡵⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠂⠄⡀⢘⠛⠻⠷⠂⠀⠀⠀⠀⠙⠀⠀⠘⠀⣣⣀⠀⠀⣱

⠀⠀⠀⠀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⢿⣿⣿⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣤⠀⠌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣍⠙⢿⣿⣆
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣀⡀⠽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠉⢹⣟⡲⣿⢿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣉⠻⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢶⣤⣴⠆⣰⠖⣯⣿⡷⡏
⠀⠀⠀⠀⣀⣠⣿⣿⠿⡗⢲⣤⡄⢸⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢊⡛⠻⢋⠉⠿⢤⡾⢫⡅
⠀⠀⣤⣾⣽⣿⣿⣿⢢⣽⣿⣿⣿⣾⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⣦⢀⠈⣥⣤⡈⠐⠖⠀⣦⡭⣷
⠀⣲⣭⣿⣿⣿⡏⠀⠀⠁⠈⠻⣿⢟⣄⣾⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⡅⠁⠈⣃⠀⠨⢁⡀⠖⠀⣼⠒⣾
⠀⢩⡘⢿⣿⣿⣿⡟⣠⣴⣶⣶⣾⣿⣿⣿⠟⢤⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠀⠉⡀⠀⢄⡢⠤⣤⡸⠆⢀⡿⣩⠃
⠀⠀⠀⠈⠉⠀⠛⠁⠛⠛⠛⠛⠉⠞⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠰⢶⡿⣼⠧⢡⡤⠭⠭⠭⠁⣒⡻⠄⣾⡓⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠘⠛⠺⠏⠄⠀⠀⠒⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠻⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠖⣶
⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡁⠀⠀⠀⢹⣧⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣽⡯⣿
⠀⠀⠀⠀⠀⠀⢰⣿⡻⠄⠀⠀⠀⠀⠸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⡿⢭⣿⣓⡏
⠀⠀⢀⣤⣴⠦⠿⡟⠉⠀⠀⠀⠀⠀⠀⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣭⡿⢖⣾⣿⣭⡇
⠀⣴⠉⠙⠃⠀⠀⠀⠑⢄⠀⠀⠀⠀⢠⡏⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢻⣤⣿⣄⣽⡎⢹⣧⣀
⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣤⡌⢻⣟⡿⣿⣿⣿⣤⡽⢷⡶⠞⠛
⠀⠹⢈⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣴⡇⢡⣿⣿⣿⣷⢾⡃
⠀⠀⠳⣬⢀⡀⠀⠀⠠⠀⣀⣰⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣌⣹⣿⣿⠟⠛⠃
⠀⠀⠀⠀⠈⠙⠒⠀⠀⠈⢹⠛⠋⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⢨⠽⣿⣿⣿⢿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠂⡄⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣄⣀⣠⠴⠒⣒⣒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⣀⣤⠤⣤⡴⠋⠛⠋⠉⠁⡴⠋⠀⠈⠉⠉⠉⠙⠓⠦⣌⠳⣄
⠀⠀⠀⠀⣼⠱⠂⠀⢸⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣈⣧
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠙⠯⢽⡲⣄
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⢠⠪⠀⠀⠀⠀⠀⢀⣠⣤⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠀⠀⠀⡠⠚⠁⠀⠀⠈⠻⠝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂⠀⠀⡠⠴⠖⠒⠶⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠠⠤⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠙⠛⠋⠓⠒⠛⠲⢤⣤⣀⣠⡾⠵⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡤⣤⡀⠀⠀⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⣤⡄
⠺⡄⠀⠀⢰⣦⣄⠀⠀⣠⣴⡶⠀⠀⢀⡗⠘⠇⠀⠀⠀⢠⡄⠀⠀⠀⠸⠃⠀⠀⠹⣦⠀⢳⣄⠀⣴⠇⢀⣼⠃⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠈⠓⢤⡀⢈⣩⣽⣟⣍⡁⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠈⠻⣿⠋⢠⣾⠁⠀⠀⠀⠀⠀⠀⠰⣟⢹⣄
⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠘⢦⣀⠈⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⢿⡷⠆⠇⠰⣿⠟⠀⠀⠀⠀⠀⠈⠳⠞⣣⣮⡿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⣄⡁⠀⠀⠀⠀⠀⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⢠⣤⡄⠀⠀⢀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠹⣟⣷⣄⠀⠀⣠⣾⣻⠏⠀⠀⠀⠀⢻⣯⣷⣄⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠉⠳⡤⣠⡼⡧⣤⡠⡞⠉⠀⠀⠀⠀⠀⠻⠿⠿⢷⡾⠿⠿⠟⠀⠀⠀⠀⠀⠀⢹⣾⡏⡟⢽⣿⠃⠀⠀⠀⠀⠀⠠⠀⡀⠈⡃
⠀⠀⠀⠀⠀⠷⡶⠂⠑⢶⡾⠃⠀⠀⠀⠀⠀⠀⠰⠀⠠⢚⡗⠄⠀⠆⠀⠀⠀⠀⠀⢀⣨⠟⠃⠃⠙⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡷
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⠛⠉
⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⣰⠖⠀⠀⠀⠻⣟⢷⣦⣀⠀⠀⣀⣴⡾⣿⠟⠀⣶⡲⣦⣄⡀⠀⠀⠀⢀⣤⡶⣲⡆⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠘⣧⠀⢀⡄⠀⣴⠏⠀⠀⠀⠀⠀⠘⢷⡝⠻⢷⡶⠟⢫⡾⠃⠀⠀⠈⢿⠊⠻⣷⠄⡀⢴⡿⠋⢚⡟⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠸⣇⠀⠹⠏⠀⣠⡇⠀⠀⠀⠀⠀⠀⠸⣿⣄⠸⠇⣠⣿⠇⠀⠀⠀⠀⠈⢳⣤⣘⢶⣷⢞⣡⣴⡏⠀⠀⠀⠀⠀⢰⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠘⣟⡾⠀⠀⠸⢗⡿⠁⠀⠀⠀⠀⠀⠀⠳⠞⠁⠐
⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠈⠹⣿⣿⣷⡄⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣴⣶⣶⠂⠀⠀⠀⠀⣀⠂⡀
⠀⠀⠀⠀⠙⡟⢻⣿⡿⣟⢻⠛⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠃⠀⠀⢰⠀⠀⠀⠀⠀⠀⣤⠈⠀⠇⠈⢠⡄⠀⠀⠀⠀⠀⠙⠳⣦⣶⣟⢇
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠘

⢀⣴⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣦
⣿⣿⡿⠋⠉⠛⠛⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠿⠛⠛⠉⠙⢿⣿
⠻⣿⣿⣄⠙⢿⣿⣶⣶⣬⣝⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣫⣥⣶⣶⣿⡿⠋⣠⣿⣿
⠀⠈⠙⢿⣷⡌⢿⣿⣿⠿⠛⠻⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠟⠛⠿⣿⣿⡿⢁⣾⡿⠋⠁
⠀⠀⠀⢈⣿⡇⠘⣿⣿⣿⣶⣶⣤⣄⡉⠻⢿⣿⣷⣄⠀⠘⢶⣄⠀⠀⠀⠀⠀⠀⣠⡶⠃⠀⣠⣾⣿⡿⠟⢉⣠⣤⣶⣶⣿⣿⣿⠇⢸⣿⡇
⠀⠀⠀⢸⣿⣇⠀⣿⣿⣿⡟⠋⠛⠛⠻⠷⣦⣝⢿⣿⣦⡀⠀⠙⢆⠀⠀⠀⠀⡰⠋⠀⢀⣴⣿⡿⣫⣴⠾⠟⠛⠛⠛⢛⣿⣿⣿⠀⣸⣿⡇
⠀⠀⠀⠀⢿⣿⣆⠹⣿⣿⣿⣷⠶⠶⠤⠀⠀⠙⠻⣿⣿⣷⡄⠀⠀⠂⠀⠀⠀⠁⠀⢠⣾⣿⣿⠟⠋⠀⠀⠤⠶⠶⢾⣿⣿⣿⠏⣠⣿⡿
⠀⠀⠀⠀⠀⠙⣿⡇⢹⣿⣿⣤⣀⣀⣀⡀⠀⠀⠀⠈⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠁⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿⡏⢸⣿⠋
⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⣿⣧⠘⢿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⣿⣿⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⠃⣼⣿⡆
⠀⠀⠀⠀⠀⠀⢿⣿⣷⣌⡙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⣡⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣶⣶⣾⠿⠟⠛⠛⠛⠛⠛⠒⠀⣼⣿⣿⣷⠀⠒⠛⠛⠛⠛⠛⠻⠿⣷⣶⣶⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋⠀⠀⠀⠀⣠⣤⠶⠒⠀⠀⢸⣿⣿⡏⠀⠀⠒⠶⣦⣄⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣱⡿⠁⠀⠀⠀⠀⣰⣿⠏⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠈⢿⣯⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢱⣿⡷⠖⠀⠀⠀⠀⠹⣿⣀⣀⠔⠀⠀⠀⡆⣿⣿⢰⠀⠀⠀⢢⣄⣀⣿⠟⠀⠀⠀⠀⠲⢶⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣸⠃⣿⣿⠘⣧⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡜⢿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣿⣿⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢣⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣇⣀⣤⠖⠀⠀⣴⠀⠀⠀⠀⢠⣿⠁⠀⣿⣿⠀⠈⣿⣆⠀⠀⠀⠈⣦⠀⠀⠲⣤⣀⣸⣿⢸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣛⠻⣿⣀⣀⠀⢿⣶⡴⠊⣰⣿⠇⠀⠀⠘⠃⠀⠀⠸⣿⣆⠑⢶⣶⡿⠀⣀⣀⣿⡟⣛⣥⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣧⣍⡛⢿⣧⣀⣀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⣀⣀⣴⡿⢛⣩⣼⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣮⣙⣛⣛⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⣛⣛⣵⡿⠋⠁

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢿⡟⠈⠳⣄⠀⠀⠀⠀⡤⠊⠁⣻⠗⠀⠀⠀⣿⡇⣶⣤⡀⠀⠀⠀⠀⠀⣠⣴⡆⣿⡇⠀⠀⠘⢻⡷⡦⣄⠀⠀⠀⠀⠀⣠⣴⡾⣿⠓
⠀⠀⠀⡉⠁⠀⠈⠁⣴⡄⠊⠀⠀⠈⣩⠀⠀⠀⠀⠸⣷⡙⠻⣤⣇⢀⣄⢀⣧⡼⠛⣱⡿⠀⠀⠀⠀⠫⢿⡹⡟⠀⣀⣸⣀⡠⠘⡟⣽⠯⠃
⠀⠀⠀⠛⣳⠖⠶⠖⣿⡗⠲⠖⠲⡛⠋⠀⠀⠀⠀⠀⠙⣷⡾⠉⠉⣹⣿⡉⠉⢹⣾⡟⠁⠀⠀⠀⠀⠀⠻⣿⣛⡈⣹⣿⣏⠁⣘⣿⡟⠁
⠀⠀⠀⠘⡀⢠⠔⠀⣿⡇⠑⢤⠀⣈⠀⠀⠀⠀⠀⠀⠸⣿⣷⠘⠻⠏⠏⠿⠛⢸⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡤⠁⢸⠈⢠⣟⣿⣿⣆
⠀⠀⠀⠀⢳⣀⣀⠂⠀⠀⠂⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡞⠂⠀⠛⣾⣿⡟⠃⠀⠀⠀⠀⠀⠸⣨⣻⣴⠇⠀⠀⠀⠘⣧⣝⣉⡇
⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠉⠉⠆⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠱
⠀⢿⣿⣶⣦⢀⠀⠀⠀⠀⢀⠀⡠⣴⣾⣿⡇⠀⠰⣄⣀⣶⣶⢤⡀⠀⠀⠀⣠⢴⣶⣆⣀⡶
⠀⠈⣿⡯⠨⠈⠳⣄⠀⠀⡠⠋⠩⠁⣿⡏⠀⠀⠀⠘⢷⣮⡁⠀⠈⣶⣷⡎⠀⠀⣩⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢸⣿⣀⣈⣀⣈⣶⣞⣁⣊⣀⣰⣿⠃⠀⠀⠀⠀⠈⢿⡿⠛⣋⣹⣿⣉⡛⠻⣿⠏⠀⠀⠀⠀⠳⣦⠀⠀⠀⠀⢺⣿⡗⠂⠀⠀⠀⡰⡾
⠀⠀⠀⣿⠁⠈⣉⠉⣿⣏⢉⡉⠀⠹⣯⠀⠀⠀⠀⠀⠀⠸⣇⠀⢉⡉⠃⣉⠁⢠⡿⠀⠀⠀⠀⠀⠀⠈⠀⡤⡖⠉⠘⣿⡇⠈⢐⣤⡄⠋
⠀⠀⠀⢿⣥⣀⡀⠘⠙⠙⡀⣁⣡⣼⡟⠀⠀⠀⠀⠀⠀⠀⣸⠲⠚⠁⠀⠙⠲⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠿⠄⠀⠀⠄
⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⣾⣷⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣿
⠀⠴⠀⠶⣤⢀⠀⠠⢴⡤⠀⢀⡀⡴⠖⠰⣄⠀⠀⡏⠁⠂⠀⠉⠢⣠⣦⡠⠚⠁⠀⠂⠉⡇⠀⠀⠹⡶⠻⠹⠊⠶⡄⠀⢀⡶⠂⠏⠝⠳⡏
⠀⠻⣷⡀⠀⢀⣠⠔⢻⡃⢤⣄⡀⠀⡐⡾⠋⠀⠀⠑⠒⣶⠶⠦⠤⣾⣿⡦⠤⠴⢶⠒⠒⠁⠀⠀⠀⠷⣀⣀⣀⣀⣸⣶⣏⣀⣀⣀⣀⠸⠃
⠀⠀⠈⢃⠈⠉⠀⠀⣼⡄⠀⠈⠉⠀⠛⠁⠀⠀⠀⠀⠘⠁⢀⠄⢀⡿⡿⣇⠀⢤⠀⠙⠀⠀⠀⠀⠀⢰⡏⠀⠈⡀⠘⣿⡧⠀⡉⠀⢘⣦
⠀⠀⠀⠈⠢⢀⠠⠜⠁⠈⠢⢀⠀⠘⠀⠀⠀⠀⠀⠀⣀⡦⠀⠠⠃⠀⠀⠈⠣⠀⠠⣆⡀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠋⠹⠙⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠈⠛⠛⠁
⢀⣤⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⣄⠀⠀⢰⣿⣿⠳⢄⠀⠀⠀⠀⢀⠴⢻⣿⣷⠀⠀⠀⢾⣷⣶⣤⣀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣷
⠀⢿⠂⠀⠙⢦⡀⠀⠀⠀⠀⢠⠞⠁⠀⢘⠟⠀⠀⠘⣿⡏⠂⠀⠐⠀⠀⠀⠀⠀⠊⣿⡟⠀⠀⠀⠘⣿⣿⠷⣟⣳⣄⠀⢠⣖⣻⡾⣻⣿⡏
⠀⠀⡛⢐⠢⠀⠈⠀⢰⡄⠔⠁⠠⠐⠘⠋⠀⠀⠀⠀⠹⢿⡥⠄⠐⢶⣷⠖⠀⠤⣽⠟⠁⠀⠀⠀⠀⠘⣿⣷⡉⣿⣿⣿⣿⣿⣉⣴⣿⠏
⠀⠀⠈⠂⢠⡤⠀⢠⣾⣧⡄⠠⣤⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠾⡟⠆⠀⠂⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣧⡀⢸⣿⡅
⠀⠀⠀⢰⠏⠀⠀⠀⢿⡇⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡾⠀⠁⠸⣦⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠉⢹⣿⣿⡿⠃
⠀⠀⠀⠈⠃⠼⠄⠀⠀⠀⠀⠤⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠤⠾⠳⡥⠋⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⢬⡞⠷⠤⣶
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢶⠂⠤⠛⣄⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⣠⠛⠤⠄⠶⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡆⣀⡸⠀⢦⣠⣿⣧⠼⠀⠀⠀⣀⠄⠄⠄⠀⠀⠀⠧⣼⣿⣄⡴⠀⢇⣀⢰⡇
⠀⠀⠀⠀⠀⠀⢠⠚⠀⣹⠆⢠⣼⣧⡊⣛⣷⡀⠀⠀⠐⡀⢐⠀⠀⠀⠀⣾⣛⢑⣵⣧⡄⠠⣏⠀⠓⡄
⠀⠀⠀⠀⠀⠀⠈⡧⠮⡁⢦⡞⡿⠷⣬⡿⠹⠳⠄⣀⣸⢆⡘⣄⣀⡠⠞⠏⢿⣭⠾⢿⢲⡴⢈⠽⢼⠁
⠀⠀⠀⠀⠀⠀⠰⣇⠀⡳⠀⣿⣾⣛⣹⣴⣾⡄⣶⡿⠛⠸⠖⠝⢿⣶⢠⣷⣶⣟⣙⣳⣞⠀⢟⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⣸⠄⡼⣠⣾⠍⢑⣡⡴⡿⢏⣾⠇⠀⣴⢦⡄⠸⣷⡽⢿⢦⣍⡊⠩⣷⣄⢣⠀⣇
⠀⠀⠀⠀⠀⠀⠐⠯⣜⠓⠯⡉⢹⣿⠏⣠⠓⢸⣿⠀⠀⢹⣵⠀⠀⣿⠇⠸⣄⠹⣿⡏⢉⠽⠚⣣⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠀⠙⠼⡇⢤⠓⠀⣰⡏⠀⠀⢸⣭⡇⠀⠹⣆⠀⠚⡤⢸⠧⠋⠂⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⡜⣿⡄⠀⠀⢘⣛⡃⠀⢠⣿⢃⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢀⣿⡇⠀⠀⢈⢈⡃⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡆⢀⣴⡏⡏⠀⠀⠀⠘⣯⡇⠀⠀⢹⢹⣦⡀⢠⠲⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣳⡌⠘⣿⡇⠀⠀⠀⠀⠐⠀⠀⠀⢸⣿⠃⢡⣞⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⡶⢢⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣰⣓⣾⢹⣦⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡼⣏⣿⣾⠿⠿⠤⠤⢤⣴⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠀⠀⠀⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⢠⡴⠒⠋⠁⠀⠀⢀⡅⠈⠋⢿⡿⣷⣿⣀⡀⠀⠀⠀⠈⢣⠀⠛⠛⠀⠀⢠⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣦⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠸⣿⣶⠀⠀⠉⠉⠙⠻⠟⠶⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣤⡀⠀⠂⠀⡀⠀⠀⠀⢸⠀⠀⠐⠀⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠉⠙⠦⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣀⠀⠀⠙⣤⠔⠁⠀⠀⠀⠀⠀⠘⠿⣦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠘⠀⠐⣿⣿⣿⣿⣿⣿⣷⡀⡴⠃⢀⣀⣀⣀⣀⣄⣀⠀⠀⠀⠉⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⠿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣯⠠⠤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠘⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡄⣍⠢⠀⢴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⡄⠉⢻⣄⠀⠀⢹⡿⢱⣦⡀⠈⠛⠻⠛⠉⠀⠀⠀⠀⠘⠿⠟⠀⠛⢷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡧⠀⠀⠙⣷⡴⠋⠀⠀⠉⠉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⢀⣤⡾⠋⠀⠀⠀⠀⠀⠰⠾⠿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡆
⠀⠀⠀⠐⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠳⠶⣤⡀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⣃⠀⠀⠀⠀⣠⡴⡏⣿⡙⣿⣿⡇
⠀⠀⠀⢸⣴⣿⣤⣦⣤⣤⣀⠀⠀⠀⠛⠛⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠙⢶⣿⣤⣤⣴⣶⣶⣤⣤⣾⣿⣷⣴⣦⣾⣯⣴⡾⣿⢃⣿⣽
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣵⣶⡞⠛⠋
⠀⠀⠀⠀⠘⢿⣿⡿⢿⠿⠛⠁⠀⣠⡦⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⢤⣤⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⣠⣾⣿⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠆⠀⠙⠀⠸⡃⠙⢿⣿⣿⣿⣿⣿⣿⡿⠉⢀⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢿⣿⣿⣿⡿⠃⠀⠀⠹⢿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⢰⣶⣄⠀⢀⣴⡶⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⢠⢤⡀⠀⠀⠀⢀⡠⡄⠀⢠⣤⡀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⢿⠹⣶⡾⢹⠃⠀⠀⠀⠿⣈⣱⣴⣞⣁⠽⠃⠀⠈⠿⣼⣦⣤⣴⣧⡿⠃⠀⠘⣿⣿⣦⣀⣴⣿⡿⠁
⠀⠀⠀⠰⣏⡖⠙⠑⣚⡇⠀⠀⠀⢸⣟⣿⠛⢿⣛⡧⠀⠀⠀⢰⣿⡮⠿⢵⣿⡆⠀⠀⠀⢾⣿⣜⠛⣣⣿⡇
⠀⠀⠀⠘⠙⠁⠀⠀⠙⠑⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⣶⣶⢄⠀⢀⢴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠠⠀⠀⠀⠆⢻⡇⠀⠀⠀⣀⡀⠀⢀⣀
⠀⠀⠀⢈⣿⣿⣿⣟⣿⡏⠀⠀⠀⠀⣈⠀⣿⠀⢀⠁⠀⠀⠀⣉⠤⢸⣿⡧⠠⣌⠀⠀⠰⣤⣀⣭⣿⣍⣁⣠⠆
⠀⠀⠀⠘⢿⠗⠈⠸⢿⠏⠀⠀⠀⠀⠁⠀⠙⠀⠀⠁⠀⠀⠀⠹⣦⠟⠙⠻⣴⠏⠀⠀⠀⠀⠋⠝⠙⠭⠙


⠀⠀⠀⢾⠒⢦⣤⣤⠖⢺⠆⠀⠰⣖⠋⠲⣴⠶⠊⢒⠖⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠐⢡⣶⣦⣤⣴⣶⡌
⠀⠀⠀⠈⣷⡦⠿⢧⢴⠏⠀⠀⠀⠀⠹⣶⠟⣦⡞⠀⠀⠀⠀⠀⠀⣤⠈⣠⡄⠀⠀⠀⠀⠘⣿⣛⣿⣛⣿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⣤⡀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠸⠈⢰⠊⠱⠃⠀⠷⠁⢀⡀⠈⠪⠃⠀⣿⣦⣀⣾⡿⠀⠀⣿⢟⣦⣴⡟⣿⠁⠀⢿⣷⣄⣠⣶⡿⠁
⠀⠀⠀⠧⠀⠠⡞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢨⣿⠻⣿⠁⠀⠀⠸⣿⡿⢿⣿⡇⠀⠀⠈⣿⠟⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⣀⡈⠃⠀⠙⢀⣀⠀⣄⡈⠁⠀⠁⣠⡀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⢰⡶⣦⣴⣤⡴⣶⠆⠈⣵⣶⣴⣮⡅⠀⠁⠈⢢⣠⠞⠀⠀⠀⢹⣿⣆⣠⣾⡟⠀⠀⣿⢇⣀⣀⣸⢿⠁
⠀⠀⢹⣿⣿⣿⣿⠋⠀⠀⠠⠟⠛⠇⠀⠀⠀⡄⢀⢷⠀⡐⠀⠀⢠⣿⠟⠻⣿⡆⠀⠀⠀⢰⡟⠻⣆
⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⡈⠀⠀⠁⢁⡀⠀⠈⠋⠀⠀⠙⠃
⠀⠱⣀⣀⡀⢠⣊⣠⠃⣿⢶⣄⢀⣴⣿⠂⠸⠙⡤⣀⠄⠋⠇⠀⠋⠀⡀⡀⣄⠘⠃⠰⠂⠀⢀⡀⠀⠐⠆
⠀⠀⢈⣿⡿⣿⣯⡁⠀⠈⠘⠿⠿⠇⠌⠀⠀⡀⠀⠟⠈⣠⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠘⠃⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⣶⣢⡀⣠⡰⣶⠀⢹⡷⣄⢀⡴⡿⠀⢐⢄⠀⠀⠀⡄⠂⢻⣷⣄⠀⠀⣠⣾⡿⠁⠟⠳⡄⢠⠞⢻⠁
⠀⠀⢹⡋⠻⠋⢹⡇⠀⠠⡾⡿⢻⡿⡄⠀⠀⠘⡿⠿⢻⠁⠀⠀⠓⡹⢷⣺⢿⡛⠁⠀⠈⠶⡿⢿⠶⠁
⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠑⠀⠀⠂⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠞⠁⠀⠀⠀⠈

⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠰⢢⡶⠀⠀⠀⠀⠀⠀⠰⣆⠶⠀⣶⠒⠂⢀⠀⠀⠀⠀⡐⢰⡶
⠀⠀⠀⠈⢧⣀⡀⢰⡆⢀⣀⡼⠁⠀⠀⢰⡇⡶⢡⢀⢠⡱⡆⣷⠀⠀⠀⠈⡷⠀⠀⢀⡀⠀⠀⠸⡇⠀⠀⠘⡆⠀⠀⢡⣤⠄⠀⠀⣾⠁
⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⡆⠀⠀⠀⠈⣡⡇⢻⣼⡼⠃⣧⡉⠀⠀⠀⠀⢀⡄⠀⠘⡇⠀⠀⣄⠀⠀⠀⠀⠙⡶⢠⡴⡿⣦⡐⢶⠃
⠀⠀⠀⠀⠘⢷⣤⡤⢤⣤⡾⠃⠀⠀⠀⠀⠹⣿⡄⠸⠁⣴⡿⠁⠀⠀⠀⠀⠙⢷⣤⣄⢁⣤⣼⠟⠀⠀⠀⠀⠈⢇⡛⡧⠁⣟⢃⡼
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠉⠧⠀⠀⠀⠀⠀⡀⠈⠟⠁⠀⠙⠋⠀⢀
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⣠⠠⠄⡀⠀⠀⠀⣀⠤⠄⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⢧⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠘⣇⠀⠀⠀⢠⡀⠀⠀⠀⡼⠁⠀⠙⣆⠦⠏⠶⣤⠞⠻⠶⣴⠃⠀⠸⡇⠀⠀⠀⣀⠀⠀⠀⢠⡗⠀⠀⠈⣷⢦⠀⣤⠠⢶⡾
⠀⠀⠀⠙⣷⠀⠀⢸⠃⠀⠠⡾⠃⠀⠀⠀⢻⢤⡀⠦⡿⠞⢀⠔⡟⠀⠀⠀⢷⡄⠀⠀⢿⠀⠀⢀⡼⠃⠀⠀⢠⠀⠀⠀⠟⠀⠀⢠⡀
⠀⠀⠀⠀⠹⣷⣄⡈⢠⣰⣾⠇⠀⠀⠀⠀⠈⠳⣙⡆⠀⢒⣫⠞⠁⠀⠀⠀⠀⠳⣀⡀⠈⢀⣀⡼⠁⠀⠀⠀⠈⢧⣄⡀⠀⣀⣠⡞
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠉⠁⠀⠈⠉
⠀⠀⠘⣧⠐⡢⠀⠀⠀⠠⠔⢂⡾⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⡠⠀⠀⢄⢠⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠈⢧⡀⠀⢸⡆⠀⢠⠞⠁⠀⠀⢰⣆⠀⠀⠘⣿⠁⠀⠀⣰⠆⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠴⣌⢿⣵⠆
⠀⠀⠀⠀⢺⣄⣀⠸⢁⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠁⠀⣰⠃⠀⠀⠀⢠⣘⠷⠶⢢⠴⢾⣣
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠈⠛⠒⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠐⠒⠛⠀⠀⠈⠧⠀⠀⠼⠁⠀⠀⠀⠀⠿⠆⠽⠷⠿⠯⠍⠸⠗
⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢿⠃⣼⡗⠀⠀⠀⠀⢻⡆⠹⡟⠀⠸⡟⠳⠗⣦⣀⣠⣔⠻⠛⡿⠀⠀⢿⠛⠓⢄⠀⠀⠊⠛⣿⠃⠀⠙⣿⠢⠀⠀⠀⠀⠀⢺⡿⠋
⠀⠀⠈⠀⢸⣆⠀⢸⡇⠀⣸⠇⠀⠀⠀⠀⢻⡀⣰⡆⢸⠁⢼⡀⣰⠇⠀⠀⢸⡁⠀⠀⣶⠃⠀⠀⡿⠀⠀⠀⠹⣇⡀⠀⣿⠀⢀⡼⠃
⠀⠀⠀⠀⣄⠙⠶⠜⠷⠾⢋⡄⠀⠀⠀⠀⠀⣦⠈⠀⠈⠀⠈⢀⡆⠀⠀⠀⠀⡏⠉⠀⠹⠀⠈⢉⡇⠀⠀⠀⠀⢸⡁⢀⣧⡀⢸⡇
⠀⠀⠀⠀⠘⠿⠶⠀⠐⠶⠟⠁⠀⠀⠀⠀⠀⠸⠛⠃⠀⠀⠛⠻⠁⠀⠀⠀⠀⠹⢾⠃⠀⠀⢷⠞⠁⠀⠀⠀⠀⠈⠻⠞⠈⠷⠛

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣟⣛⣿⣻⣿⣿⣶⣶⡆⢀⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⡯⠡⠏⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⡟⠿⡧⠴⠶⠿⠛⠻⠟⠟⠋⠁⠀⠀⠘⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⠟⠿⣿⠀⢿⣾⣿⣿⠉⠀⠠⠤⠀⠠⠄⠀⠀⢀⣶⣿⣷⣤⣶⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣿⣶⡘⣦⣌⠛⢃⣀⢀⣠⣀⣄⣀⣀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢹⣿⡿⠟⠁⣨⣿⠁⠰⠿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡏⠀⠀⠀⣠⣶⣿⢠⡇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⣾⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣿⡗⣾⣿⢟⣀⣈⣠⣾⣿⣛⣟⡃⠿⣿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠆⠈⢻⣿⡟⠋⠉⠀⠍⠻⠉⠙⠻⢿⣷⣦⣄⡀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡁⢰⢃⣼⡟⠀⠐⠲⠦⠄⠀⠀⠀⢊⠄⣩⡙⠟⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡷⢸⠿⡃⠀⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣡⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⡖⠛⢀⠀⠀⠀⠄⡀⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣿⠀⢸⣿⡦⡀⠀⠀⡐⢦⣄⡀⠀⠀⢀⣠⣄⠀⠁⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⢸⣿⡅⣄⠀⠀⠀⠀⠉⠙⠛⠉⣈⣻⡏⠧⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⢸⣿⣗⡙⣺⣶⠶⠦⣀⡀⢀⣈⡿⢻⣿⣀⠀⠋⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⢿⣿⣿⣿⣿⣿⢇⡠⠟⠋⣿⣿⣿⣾⣿⢏⠠⡈⡇⡔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠾⢿⡧⠿⠟⢽⡿⣿⡿⠛⠙⠙⣷⣾⣿⣿⡷⣾⠀⠫⠐⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣦⠤⣤⠀⣌⠉⢮⡉⠁⠀⠈⠙⠛⠛⠻⠇⢿⡄⢆⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⠛⠉⡰⠛⠂⠛⠀⠀⠘⠛⢶⠀⠀⠀⠀⠀⢺⡏⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣇⣀⣄⣀⠀⠀⠀⠀⢠⡀⣷⣶⣤⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠉⠛⠻⠏⠙⡟⠣⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⣤⣾⣸⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠰⠟⠙⠾⣷⣶⣮⣾⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠶⠀⠀⠀⠈⢿⣿⡟⡘⠂⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣋⡭⠀⠀⠀⡀⠀⠀⢠⣠⣀⡄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣠⠚⣽⡁⣴⣿⠏⠁⠀⠀⣠
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠹⣿⣭⣽⠁⣠⠔⢩⡇
⠀⠀⠀⠲⣄⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⣿⠋⠀⢀⡨⠃
⠀⠀⠀⠀⠘⠷⠟⠛⢷⣤⡄⣢⡀⠀⣀⠀⢀⡜⢁⡔⠀⢀⠀⢰⣶⢬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⢇⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠿⠿⠿⠛⠚⠿⠿⠞⢧⣀⣏⣠⡦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⡉⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⢤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠁⠀⠀⠈⠓⢄⡀⠀⠀⠙⠀⠒⢦⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠈⠒⢤⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢡⡀⠉⡐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠉⠀⠠⢀⠀⠉⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⠸⣧⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢠⡀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣧⠀⡀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠠⠀⠈⣳⠀⢿⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⣷⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠸⡄⠀⠀⣹⡆⢀⡀⠀⠠⠀⠀⣸⠀⠀⡎⠀⢀⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⡟⣰⡇⠀⠐⣿⠁⠀⡇⠐⠁⠠⣰⠇⢠⣿⣧⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⠷⠷⠶⣿⣶⣾⣷⢂⣀⣴⣏⣠⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉

⠀⣾⣿⠿⣧⣴⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣦⣼⠿⣿⣷
⠀⣿⣿⠓⣯⣀⠠⠼⣯⡟⠹⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⠏⢻⣭⠧⠄⣀⣽⠚⣿⣿
⠀⠸⣯⡿⢿⣤⠴⠶⢿⣍⡰⠿⣿⣟⡳⢤⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⢀⡴⢞⣻⣿⠿⢆⣩⡿⠶⠦⣤⡿⢿⣽⠇
⠀⠀⠹⣷⢾⣟⣤⣠⣼⡿⠷⠶⠾⠛⠛⠒⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠖⠛⢛⠷⠶⠾⢿⣧⣄⣤⣻⡷⣾⠏
⠀⠀⠀⠘⢿⣯⣏⢈⣿⡁⠀⠀⠀⠐⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠂⠀⠀⠀⢈⣿⡁⣹⣽⡿⠃
⠀⠀⠀⠀⠘⣿⣿⣛⣿⣷⠦⠀⠐⠚⠓⠢⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⠔⠚⠓⠂⠀⠴⣾⣿⣛⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣟⣏⣙⣯⠀⠀⠀⠀⠀⠀⣈⣆⡀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢀⣰⣁⠀⠀⠀⠀⠀⠀⣽⣋⣹⣻⡏
⠀⠀⠀⠀⠀⠈⣿⣿⣯⣽⡶⠂⠐⠒⠉⠉⠁⠀⠈⠑⠀⢄⡀⠀⠙⣦⣾⣷⡴⠋⠀⢀⡠⠀⠊⠁⠀⠈⠉⠉⠐⠂⠐⢾⣯⣽⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡛⣿⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠒⠤⢈⣿⣿⡁⠤⠒⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣶⣾⡿⠿⢿⣿⣿⠿⠷⠶⠶⠶⠶⣿⣿⣿⣿⠷⠶⠶⠶⠾⠿⣿⣿⡿⠿⢿⣷⣶⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⣿⠋⠁⠀⠀⠀⢀⠔⠁⠀⠀⠉⠀⢀⠜⢹⢿⡿⡏⠣⡀⠀⠉⠁⠀⠈⠢⡀⠀⠀⠀⠈⠙⣿⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠾⣿⠗⠒⠒⠉⠉⡉⠀⠀⠀⢀⡠⠖⠁⠀⠃⣾⣷⠘⠀⠈⠲⢄⡀⠀⠀⠀⢉⠉⠉⠒⠒⠺⣿⡷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⢀⣠⠞⠀⡤⠴⠚⠉⠀⠀⣠⠂⡀⣿⣿⢀⠀⡄⠀⠀⠉⠓⠦⢤⠀⠳⣄⡀⠀⠀⢸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⣿⡟⠉⠀⣠⠔⠁⠀⠀⠀⠀⠀⠐⢀⣰⠁⢹⡏⠈⣆⡀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠉⢻⣿⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣤⡞⠁⠀⠀⢀⠀⠀⢀⠀⠀⣾⠃⠀⠘⠁⠀⠘⣷⠀⠀⠀⠀⠀⡀⠀⠀⠈⢳⣤⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣻⣿⣻⣦⣤⣴⡏⠀⣠⠆⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⣇⠀⠱⣄⠀⢸⣦⣤⣴⣟⣿⣟⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣿⣳⣾⢯⣽⣏⣿⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣿⣻⣯⡽⣷⣞⣿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁

⠀⠀⠀⣀⣤⣤⣤⡤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠄⣤⣤⡤⢤⣀
⠀⠀⣿⡟⢈⣿⠿⠀⠉⠁⠀⠈⣭⣝⣲⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⣋⣭⠁⠀⠈⠁⠀⠘⠿⣧⢈⣿⡇
⠀⠀⢿⣯⠘⣓⠒⠀⠀⡀⠀⠶⠟⠃⠈⠉⡐⣱⡦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣏⣁⠀⠀⢙⠿⠁⠀⠀⣀⡈⠭⣛⣲⣿⠃
⠀⠀⠀⠛⣽⣳⣈⡼⠗⣀⡠⠀⠀⣹⣶⠾⣟⡛⠏⠈⣷⣄⠀⣀⡀⢀⣞⣕⡩⢛⣉⡿⢷⣾⡅⠒⠀⢤⡔⢒⣦⣽⣛⠟⠁
⠀⠀⠀⠀⠈⠹⡞⣛⣡⠖⢂⡠⠤⢹⣿⣮⣉⣉⣙⠲⣦⣝⣧⡅⣧⣿⡽⠞⠋⠡⠤⢤⣿⣯⡀⠠⢄⡓⣂⢬⣛⠖⠁
⠀⠀⠀⠀⠀⠀⠈⠱⠾⣯⣠⠞⢃⠩⠟⠓⣂⡠⠤⠉⠩⠉⠿⣿⡻⠅⠀⠊⠉⠀⠀⣒⠚⠩⢅⣙⣦⣤⣛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣇⠎⢁⠀⠄⠀⠀⠀⠐⠁⢼⢘⢁⠀⠑⢄⠂⠀⠉⠂⢀⠀⢋⣿⠿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣫⣍⡀⡌⠀⢀⠠⠀⠀⠀⠎⠀⠨⠀⠄⠀⢂⠙⠦⢀⠀⢀⡧⢀⡮⣽⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣹⢋⡁⡠⠊⠸⠁⠀⢀⠂⡌⠀⠀⠐⠀⠘⡈⠀⢆⠐⠀⠘⡈⠱⡄⢈⢻⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⢯⠞⣰⢀⢃⠀⡇⡜⠰⢀⠀⠀⠀⠀⠀⠠⠀⠘⡄⢆⢠⢱⠰⡌⢲⡟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⣷⢧⣎⣼⣰⣡⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠡⣳⣸⣘⣆⢷⠻⣏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠰⠏⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠛⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠛⠛⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢾⡏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣾⢁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⡇⠈⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠀⣰⡟⡇
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠻⣿⣻⣧⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⣀⣼⡿⣷⣤⣴⣾⣿⣷⣾⣿⣠⠇
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⣾⣿⢿⣦⣶⣤⣶⣾⣿⠟⠛⠛⠛⠛⠉⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢸⣇⣀⣤⣶⣶⣤⡀⠀⠀⢸⣿⣿⣶⣶⣾⡿⠟⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠈⢻⣿⠋⠉⠙⠻⣷⣤⣾⡿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣄⡀⣀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠒⠒⠒⠒⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⣀⡀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠈⠉⠓⢦⡀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣸⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣀⣀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡿⠀⢀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⠉⠉⠙⠳⢦⡉⠳⡄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⡼⠃⢀⡼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠙⣦⠙⠆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣤⡤⠴⠛⠓⠛⠻⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣸⣧⣄⣠⣤⣤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡴⠶⠦⢭⡀⠀⠀⢀⡿⠦⠤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⢹⣦⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

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

⠀⠀⢀⣤⡤⣤⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣤⣤⡤⣤⡀
⠀⠀⠘⣿⡇⣿⣿⢸⣏⡅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠰⡍⡇⢹⣿⡧⣿⠇
⠀⠀⠀⠹⣯⣾⣷⣀⣹⠤⣃⣀⡾⠋⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠑⢷⣄⣈⢤⣇⣁⣾⣿⣼⡟
⠀⠀⠀⠀⠹⣧⣾⣿⡤⠔⠚⢻⣤⣤⣾⣿⡟⢦⡀⠀⠀⠀⠀⢀⣴⢟⣿⣷⣤⣠⡟⠛⠒⢤⣽⣟⣾⠏
⠀⠀⠀⠀⠀⠙⣿⢻⣷⠖⠉⢁⣀⠹⠿⣿⣿⣿⣿⣦⣴⣶⣠⣿⣷⣿⣿⠿⠯⣀⡈⠉⠓⢶⡿⣾⠟
⠀⠀⠀⠀⠀⠀⠹⣯⣿⠞⠉⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠓⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃⣠⣤⡤⠶⠒⡛⠛⠻⣿⣿⡿⢿⣿⣿⡟⠛⢛⠒⠶⢦⣤⣄⡐⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⢻⣯⠀⡀⠴⠁⢀⣴⡟⠙⡿⢺⠏⢹⣦⡀⠀⠦⢀⠀⣿⡟⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠈⡟⣷⠚⣿⡁⠐⠣⠔⡋⢸⠀⠀⡇⢸⠀⢀⡇⠉⠲⠔⠂⣌⣿⠓⣾⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠹⡶⢿⣅⡀⡆⠀⡇⡞⢀⠀⢧⢸⠀⠠⢧⢘⠀⠐⣀⣸⡿⢷⠏⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣧⣼⠛⢿⣷⣸⣄⣧⡈⠀⠈⠀⠀⢀⣼⣨⣆⣶⣿⠛⣧⣼⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣛⣿⣦⣄⣋⣻⣩⣧⠀⠀⠀⠀⣼⣏⣛⣉⣠⣼⢿⣻⡵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣝⣻⣝⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⢠⡾⠟⢁⡤⠒⠉⠁⠀⠀⠘⠉⠐⠢⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡶⠀⠀⠀⢀⠴⢂⡀⠀⢄⣀
⠀⠀⠈⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠔⠁⠐⠉⠀⠀⠀⠈
⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠂⠀⢰⡖⠀⠀⠀⠀⠀⠀⠁⠈⠐⢄
⠀⢰⠡⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⣄⣀⣤⣄⠀⣠⠶⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⡠⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠁⠀⠀⠄⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠄⠀⠱⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠃⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⣀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡄⠀⠘⡄⠀⠀⠰⠤⠀⣀⡄⠠⠀⠀⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⡀⠀⢄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣄⠀⠀⠀⠀⢸⡀⡀⠀⠃⠀⠀⠹⠋⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⣼⠃⠀⠀⠐⠀⠀⠳⠤⢀⣁⠀⠀⠀⠀⠀⠀⠀⠼⠓⠋
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⣿⠋⢻⣿⣿⣧⡀
⠀⠀⠀⠀⣼⡟⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⣽⠿⣿⣅⣼⣿⣷
⠀⠀⠀⢀⣿⡿⣿⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣾⣧⡞⣡⠞⢛⣻⣧⣼⣿⡇
⠀⠀⠀⢸⣿⢱⠏⣾⢷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⣼⣯⡀⣹⣿⣯⡴⠛⢻⣿⠉⣿⣿
⠀⠀⠀⢸⣏⡿⢾⣇⣾⣭⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⣿⣿⠟⢋⣿⡿⠷⣤⣼⣿⠾⣿⣿
⠀⠀⠀⠈⣟⣷⣾⢿⣧⣾⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣰⣿⣯⡶⠟⠁⠀⠀⠀⠙⣿⣤⣿⣿⡀
⠀⠀⠀⠀⣿⠛⢿⣼⠋⠀⢹⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⠻⣿⡟⠁⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⣧
⠀⠀⠀⠀⢹⣷⠾⣿⠀⠀⢸⡿⠾⣿⣷⡀⠀⠀⠀⠀⣸⡿⠁⠀⠀⢀⡿⠀⠀⠀⣀⣴⡿⠟⠛⠻⣿⣶⣿⣿⡄
⠀⠀⠀⠀⠈⣿⠀⠘⣆⠀⢸⡇⠀⢸⣯⣿⡀⠀⠀⢠⣿⠃⠀⠀⠀⣸⡇⢀⣤⠾⠋⠁⠀⠀⠀⠀⢸⣿⣾⣿⣧
⠀⠀⠀⠀⠀⢻⡀⠀⠘⣦⢸⠀⠀⢸⠉⢻⣧⣶⣶⣼⡟⠀⠀⠀⢀⣿⡿⠋⠁⠀⠀⠀⠀⢀⣤⣶⠿⣿⣼⣿⡇
⠀⠀⠀⠀⢶⡄⢧⠀⠀⢹⣿⠃⠀⣿⠀⢸⣿⠁⣹⣿⠁⠀⠀⠀⣼⡟⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠱⡘⣧⠀⠈⣿⡀⢀⡿⠀⢸⠹⢀⣿⡇⠀⠀⠀⣼⡿⠁⠀⣀⣤⣾⠿⠋⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⢣⠘⣆⠀⢸⣇⢸⠇⠀⡞⣠⣼⡟⠀⠀⠀⣰⣿⣷⠾⠟⠛⠉⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢧⠘⣆⠈⣿⣾⠀⢠⣧⢻⡿⠁⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢧⠸⣿⠀⢸⢡⣿⠁⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠛⠉⢉⣉⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣈⣳⡈⢧⢸⣿⠃⠀⡠⠋⠀⠀⠀⠀⢀⣠⣴⣾⣿⣛⣉⣤⡔⠒⠋⠉⠉⠁⠉⠉⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⡾⠃⠀⠈⠀⣀⣠⣤⣶⡿⠿⠛⠉⠀⠈⠉⠀⠀⠉⣳⠦⠶⠶⠶⠶⢶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣾⣿⣿⣶⣶⣿⣟⣛⣩⣭⡤⠤⠤⣤⣴⣶⠒⠂⠙⠛⠛⠷⠦⣤⣀⡀⠀⢨⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠻⢗⡒⠦⢤⣀⣀⠀⠀⠈⠙⠻⠶⣦⣄⡀⠀⠀⠀⠀⢉⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣉⡉⠓⠲⠦⢤⣄⣀⣀⢉⣿⢶⣶⣲⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠾⠯⠛⠛⠛⠉⠁

⠀⠀⠀⢰⣶⣄⠀⢀⣴⡶⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⢠⢤⡀⠀⠀⠀⢀⡠⡄⠀⢠⣤⡀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⢿⠹⣶⡾⢹⠃⠀⠀⠀⠿⣈⣱⣴⣞⣁⠽⠃⠀⠈⠿⣼⣦⣤⣴⣧⡿⠃⠀⠘⣿⣿⣦⣀⣴⣿⡿⠁
⠀⠀⠀⠰⣏⡖⠙⠑⣚⡇⠀⠀⠀⢸⣟⣿⠛⢿⣛⡧⠀⠀⠀⢰⣿⡮⠿⢵⣿⡆⠀⠀⠀⢾⣿⣜⠛⣣⣿⡇
⠀⠀⠀⠘⠙⠁⠀⠀⠙⠑⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⣶⣶⢄⠀⢀⢴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠠⠀⠀⠀⠆⢻⡇⠀⠀⠀⣀⡀⠀⢀⣀
⠀⠀⠀⢈⣿⣿⣿⣟⣿⡏⠀⠀⠀⠀⣈⠀⣿⠀⢀⠁⠀⠀⠀⣉⠤⢸⣿⡧⠠⣌⠀⠀⠰⣤⣀⣭⣿⣍⣁⣠⠆
⠀⠀⠀⠘⢿⠗⠈⠸⢿⠏⠀⠀⠀⠀⠁⠀⠙⠀⠀⠁⠀⠀⠀⠹⣦⠟⠙⠻⣴⠏⠀⠀⠀⠀⠋⠝⠙⠭⠙


⠀⠀⠀⢾⠒⢦⣤⣤⠖⢺⠆⠀⠰⣖⠋⠲⣴⠶⠊⢒⠖⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠐⢡⣶⣦⣤⣴⣶⡌
⠀⠀⠀⠈⣷⡦⠿⢧⢴⠏⠀⠀⠀⠀⠹⣶⠟⣦⡞⠀⠀⠀⠀⠀⠀⣤⠈⣠⡄⠀⠀⠀⠀⠘⣿⣛⣿⣛⣿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⣻⡟⠂⠀⠀⠀⠻⣼⠀⠀⠀⠈⡧⠶⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠔⣷⡀⠀⠀⠀⠈⢻⡉⠟⠢⣀⠔⠻⠈⣿⠁
⠀⠀⠙⠲⠄⢰⡇⠠⠴⠚⠀⠀⠀⠀⣿⠀⠀⣤⠀⣨⠃⠀⠀⠀⠀⠀⠘⠃⢹⣿⠀⠀⠀⠀⠘⠷⡴⠆⣿⠐⢦⠼⠏
⠀⠀⠀⢄⡁⠀⠁⢐⡁⠀⠀⠀⠀⠀⢿⡄⠸⣍⠾⠁⠀⠀⠀⠀⠀⠀⣤⠀⠁⡌⢣⠀⠀⠀⠀⠀⠷⠴⠛⢦⠾
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢠⣼⠩⣧⠀⠀⠀⢸⡝⢗⡄⠀⢠⡺⢫⡇⠀⠈⣉⠀⠄⠀⠀⠂⢉⠁⠀⠀⠀⠂⡈⠇⠀⢤⠀⠀⠀⠀⠉⠉⡅
⠀⠀⠀⢰⡇⠐⡸⠃⠀⠀⠈⢲⠖⠙⣿⠉⠲⡞⠁⠀⠀⠸⣄⡀⣴⢀⣠⠟⠀⠀⠀⠀⠉⢊⡷⠀⠀⠂⣀⣹⡤⠖⡶⡀
⠀⠀⠀⠘⢯⣉⢲⡕⠀⠀⠀⠹⣤⠴⠀⢦⣴⠇⠀⠀⠀⠀⣆⡀⠙⢀⣠⠄⠀⠀⠈⠳⠀⠰⠊⠀⠀⠀⠈⣤⡌⢦⠶⠆
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠆⠀⠀⠀⠱⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⣶⠠⠀⠀⠀⠠⢐⡆⠀⠀⠀⡿⣿⢦⠀⠀⣀⡀⠀⠀⠘⣿⣦
⠀⠀⠐⢂⢀⠀⠀⠣⠐⠇⠀⠀⠀⢸⣏⠉⠀⠀⠀⠀⠿⣄⠁⢰⡀⢀⡸⠇⠀⠀⠀⡻⠥⢵⣷⡞⡿⠀⠀⠀⡠⢴⣿⡀
⠀⠀⠀⠈⠰⠴⢿⠐⠎⡅⠀⠀⠀⡂⢙⠤⢰⡀⠀⠀⠀⣐⡱⠜⠴⢛⣀⠀⠀⠀⠰⣇⣀⠎⡉⡝⠁⠀⠀⢾⡀⠀⢿⠇
⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⣀⠐⠋⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈
⠀⠀⠀⣤⠄⠄⠀⠠⠠⡄⠀⠀⠀⢸⠋⠑⡀⠀⠀⠀⢀⡀⠀⠈⣷⡙⠀⢠⣤⠀⠙⣱⡏⠀⠀⠀⡀⠀⠀⠀⢠⣎⢹⡀
⠀⠀⠀⠘⠤⠤⣶⠤⠴⠃⠀⠀⠀⠘⠀⠄⢀⡄⠀⢀⠎⠀⠀⠀⠘⡳⠚⠐⠗⠘⠲⡛⠀⠀⠀⠀⠱⠷⠆⢀⡀⠚⢛⡁
⠀⠀⠀⠀⣦⡄⠁⢤⡴⠀⠀⠀⠀⠀⡀⡀⢾⡁⠐⠁⠀⠀⠀⠀⠀⠑⠬⠄⠁⠬⠔⠀⠀⠀⠀⠀⠀⠀⢺⡍⡧⢀⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄
⠀⠀⢻⣧⣏⡗⠚⠷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠟⠲⣏⣯⣿⠁
⠀⠀⠈⣽⢤⣿⣋⣈⣽⡇⢨⣿⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣽⣯⠰⣿⣉⣉⣹⣥⣿⡇
⠀⠀⠀⠹⣯⣼⣯⣀⣨⣛⡧⠤⡿⠷⠮⢷⣄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⣠⣴⠯⠶⠿⡯⠴⣟⡯⣀⣨⣟⣼⡟
⠀⠀⠀⠀⠘⢿⣾⡉⡱⡗⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⠀⠀⢀⣼⣿⡉⣳⣿⠏
⠀⠀⠀⠀⠀⠠⡿⣫⢽⣿⠛⠂⠀⠉⠒⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠔⠋⠁⠀⠛⢾⣻⡽⣧⡟
⠀⠀⠀⠀⠀⠀⢹⣿⣤⢷⣀⠀⣀⣀⠤⠴⠦⠄⠀⠀⠈⠳⡀⢀⣀⢀⡴⠋⠀⠀⡀⠠⠶⠤⠄⢀⡀⢀⣸⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠘⣾⣿⠎⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣤⣶⣶⣶⣶⠒⠒⠤⣤⢤⣼⣿⣿⣷⣤⣤⠀⢀⣶⣶⣶⣶⣶⣤⣤⣴⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⠞⢿⣿⡟⢄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡽⠓⠂⠀⠀⠉⠀⠀⣀⡤⠊⠁⠄⢸⣿⠀⡀⠙⠢⣀⠀⠀⠈⠀⠀⠀⠒⠻⣜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣻⣄⣀⠀⠰⢊⠠⠒⠋⠁⠀⠀⠜⠀⢹⣿⢠⠘⠄⠀⠀⠉⠒⠦⠘⠲⠀⣀⣀⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡅⢀⡔⠁⠀⠀⠀⠀⠀⠀⣤⠃⠸⡟⠈⢷⡀⢀⠀⠀⠀⠀⠀⠱⣄⠀⣵⣹⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡿⣟⣿⣄⣀⣠⡆⠀⡰⠁⣰⠃⠀⠀⠀⠀⠈⢧⠀⢣⡀⠈⣦⣀⣀⣼⣛⡟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣻⣽⣿⣷⣺⣇⡴⠃⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⣲⣯⣿⣽⣿⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉

⠀⠀⠐⠁⠀⠀⠩⡀⣀⢴⠂⠀⠀⠀⠹⡄⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠏⡀⣀⣤⡄⠳⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠉⠑⣋⡅⠀⠀⠀⢀⠙⡄⠀⠀⠀⠀⠀⢸⠇⠘⠀⢀⠏⠀⡯⠛⡟⡙⢧⣆⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠐⠀⢀⡀⠀⠀⠙⠄⠀⠀⠀⠈⠀⢰⠇⣰⠃⠀⠀⠀⣸⢸⡹⣄⠈⠃⠀⢀⣄
⠀⠀⠀⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠸⠃⠀⠀⠄⢢⠿⢸⠇⡿⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄

⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠈⠁
⠀⠀⠀⠈⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⢈⡀
⠀⠀⠀⠀⠓⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣒⠒⠐⠂⢀
⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⢤⡀⣀
⠀⠀⠀⢀⠰⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠐⠂⠀⡀⠀⢈⠛⠁⠈⢛⠛
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠁⡔⠀⠀⠀⠸⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⢈⣀⠀⠀⠀⠁⢠⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⡇⠀⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⢀⡀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⡄⢀⣠⣴⣢⡄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠄⠀⢈⡟⠳⠷⠈⠀⠀⠀⠒⠀⠀⠀⢣⣀⠀⢙⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠉⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱⡄⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠁⣀⠴⠉⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡆⠘⠀⡀⡂⠀⠀⣠⡳⣸⠞⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀
⠀⠀⠀⢀⠎⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⣰⢣⡟⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆
⠀⠀⢀⠞⠊⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⡸⢁⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠒⠋⠉⠑⠲⢌⣇
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⢃⠎⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢢⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡜⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢣⠀⠀⠀⠀⢿⠀⡀⠀⢸⠃⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠄⠄⡀⠒⠈⢯⣆⠀⠀⠀⢸⠘⡡⠀⢸⠀⣠⠀⣰⠃⠀⠀⠀⠀⠀⠈⠠⠠⠄⠀⣀⣀⠀⠀⠀⠉⠣⠀⠀⠘⣆
⢧⠁⠤⣔⡒⡛⠛⣡⣠⠤⠖⠛⠚⠚⠛⠛⠶⠤⣬⣦⣘⣇⣼⠀⠁⢀⠃⠀⠀⠀⠀⠀⢀⣤⠶⠒⠋⡩⠩⠍⠉⠭⠝⠛⠻⣄⡀⠀⠸
⠈⠓⠤⠤⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⠇⠂⠀⠀⠀⢠⠖⣩⠤⠒⠚⠉⠉⠉⠐⠓⠒⠢⠤⣀⡀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠄⡀⡄⣴⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⢺⣹⠋⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣾⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠴⠖⠒⠒⠲⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠒⠦⣄⠙⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⢘⢧⠀⠀⠈⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡀⡇⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⠐⠀⠂⠔⠠⠈⠐⠠⢀⠀⠀⠀⠀⢠⠇⢠⠇⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣊⣠⠾⠖⠋
⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣤⡀
⢰⡆⠀⠀⠀⣤⣄⡀⠀⠀⠀⢀⣠⣤⠀⠀⠀⢰⡆⠺⡁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡿⠀⠀⠈⢻⣆⠉⠰⣄⠀⠀⣠⡖⠈⢁⡾⠃⠀⠀⠀⠀⠀⠀⣼⣿⣷⡗
⠀⠙⠦⣄⠐⢉⠛⠻⠶⣶⠾⠟⠛⠡⠀⣠⠴⠋⠀⠀⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻⣦⠀⠻⣷⣴⠿⠁⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡇
⠀⠀⠀⠈⠑⢦⣶⣾⣷⣿⣿⣷⣦⡔⠊⠁⠀⠀⠀⠀⠀⠰⡀⠀⠀⢻⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠹⡟⢀⣴⣿⠄⠀⠀⠀⠀⠀⠀⢤⣀⣬⡗⣸⣳
⠀⠀⠀⠀⠀⠀⠙⠛⠟⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⠀⠀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⡸⠯⠛⠀⠃⠙⠭⢏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠶⠷⢯⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⣤⣶⡆⠀⠀⠀⠠⣦⣄⣀⠀⠀⠀⠀⢀⣠⣴⡆
⠀⠀⠠⢴⣶⠄⠀⠀⠀⣀⠀⠀⠀⠠⣶⡦⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠹⣿⡽⣷⣄⢀⣴⡿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠙⢳⢄⣀⣤⣿⣤⣀⣠⡞⠋⠁⠀⠀⠀⠀⠀⢻⣿⠿⠿⣦⡾⠿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠈⣿⡻⡹⡟⡽⣿⡏⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠈⠃
⠀⠀⠀⠀⠀⠸⣷⣠⡤⠋⢮⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡴⢻⠳⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠂⠃⠻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣸⣿⣦⡄
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⣄⣼⠿⠛⠁
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⣤⢦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣦⡶⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠙⢷⣝⢿⣷⣄⢀⢠⣴⣿⢟⣽⠟⠀⠘⢿⣮⡻⣿⣦⡀⠀⠀⠀⣴⣾⡿⣩⣾⠃⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⢘⡿⠀⣀⣶⣀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⢙⣇⣉⠋⣿⡏⢋⣠⡟⠁⠀⠀⠀⠀⢻⡑⢈⠻⣿⢀⡄⢺⡟⠉⢈⡽⠃⠀⠀⠀⠀⠒⠀⠁⠈⠂
⠀⠀⠀⠀⠀⠸⣇⡀⠈⠿⠁⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠸⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⢹⣶⣦⣙⢿⡿⢟⣤⣶⣾⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⡀⠢
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠘⢿⣲⠏⠀⠀⠨⣗⣻⠋⠀⠀⠀⠀⠀⠀⠀⠘⠶⠿⠅⠐
⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠻⣿⣿⣿⣦⡀⠀⢀⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣤⣠⣄⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⢠⠀⠀⠂⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣤⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣾⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠙⠟⠻⡟⠻⠋⠛⠁⠀⠀⠀⠀⠀⢰⣦⣄⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⣧⠰⠟⠛⠻⠆⣼⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠈⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠸⣧⣤⠀⠃⢤⣤⡟⠀⠀⠀⠀⠀⠀⠀⣡⣹⣷⣿⣷⢱⡆
⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉

⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⢀⡞⠋⠀⠀⢀⠀⠀⢰⠉⠘⢦⣣⠀⠀⢀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠠⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠙⢦⡀⣈⠅⠀⠰⠀⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠤⢤⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⢰⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠳⠀⠠⠠⡀⠈⠁⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠘⠃⠀⠀⠀⠀⠀⡠⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⢿⡗⠀⠀⠀⠀⠀⡠⢊⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠆⠀⠀⠀⡛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠀⠐⠀⠂⠀⠀⡀⠤⠀⠠⢀⢄⡀⠀⠀⠀⠀⠠⠘⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠉⠀⣀
⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠋⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠓⠀⡀⠀⢠⡿⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⢴⠀⠀⡀⠀⠀⣠⡀⠀⠀⠀⠄⠀⠀⠀⠠⣀⣀⠃⠀⢠⠇⠀⠚⠀⠀⠄⠀⠑⢄⠀⠀⠀⠄⠀⠀⡀
⠀⠈⠉⠉⠉⠃⠀⠀⠀⠀⢀⠈⠀⠀⢀⠀⠊⠉⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡇⠀⢀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢸⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠈⠓⠶⡆⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠈⠒
⠀⠀⠀⡀⠀⠂⠀⠄⠀⠀⠀⠀⢀⣼⠋⠀⢀⡐⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠈⠛⠭⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠘⠂⢄⣀⠋⠀⠀⠚⠈⠑⠦⠀⠀⠀⠀⠁⢀⣶⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣿⣟⣻⣿⣟⣛⣛⣻

⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⡄⠀⠀⡀⠀⢀⠟⠁⠀⡞⡠⠀⠀⢄⢳⠀⠀⠉⣟⠀⠀⠀⠀⠀⡷⠉⠘⣇⠀⠀⣀⡀⠀⢀⡏
⠀⠀⠀⢨⠀⢸⡇⠀⣍⠀⠀⠀⣃⡇⣿⣿⢈⣘⠀⠀⠀⢈⡀⠀⡿⠀⢀⠁⠀⠀⠹⡤⣀⣽⣅⢠⡼
⠀⠀⠀⠘⡦⠤⠤⢴⠏⠀⠀⠀⠹⣷⠈⠁⣾⠏⠀⠀⠀⠘⢷⣤⠀⣤⠾⠃⠀⠀⠀⢧⣻⠈⢜⣣⠇
⠀⠀⠀⠸⠁⠀⠀⠀⠓⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⢤⠀⠁⠀⠈⠁⢠⠄
⠀⠘⣏⠀⠀⠀⠀⠀⠀⣹⠃⠸⡌⣵⢦⣀⡴⣮⢡⠇⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠈⣦⡄⢀⢀⣤⡎
⠀⠀⠘⣦⠀⠸⠇⠀⣴⠃⠀⠀⢻⢄⠰⠿⠆⡠⡟⠀⠀⠻⡄⠀⢸⠀⠀⡰⠃⠀⠀⡉⠀⠸⠀⠈⡀
⠀⠀⠀⠙⠷⠆⠰⠾⠋⠀⠀⠀⠈⠻⠽⠀⠯⠟⠁⠀⠀⠀⠱⠤⠀⠠⠴⠃⠀⠀⠀⠳⠤⠀⠠⠴⠁
⠀⠀⣆⠠⡀⠀⠀⢀⠄⣰⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠘⢦⠀⢰⡆⠀⡴⠃⠀⠠⡆⠀⠈⣿⠁⠀⢰⠄⠀⠀⠸⠍⢰⡆⠁⡇⠀⠀⠀⠀⢤⣻⣣⠄
⠀⠀⠀⠸⣤⡌⢡⣤⠏⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⣄⠈⠁⣀⠃⠀⠀⢠⣾⣳⣾⣶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠂⠀⠀⠀⠈⠀⠛⠛⠛⠃⠋
⠀⢰⡟⣴⠆⠀⠀⠰⣦⢻⡇⠀⡿⠶⢤⡀⣠⡴⠾⡷⠀⢺⠗⠀⠀⠀⠐⢻⠆⠐⢶⡄⠀⠀⠀⠀⣶⠖
⠀⠀⠀⢹⡄⢸⡇⢠⡏⠀⠀⠀⠹⡀⡶⠸⠁⡧⠰⠃⠀⠸⣀⡀⢰⠂⢀⡸⠀⠀⠘⢧⡀⢸⠀⣠⠏
⠀⠀⠀⢶⣝⡋⢙⣫⡶⠀⠀⠀⠀⢧⣄⠀⢀⣠⠖⠀⠀⠀⢇⣠⠘⠠⣄⡇⠀⠀⠀⠸⣄⡞⣄⡼
⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢐⣾⣻⣻⣿⠖⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⣿⣟⣟⣶⡂
⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⢰⣟⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⣻⡆⠀⠙⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣶⣛⣻⣍⠙⠛⢷⡄⠀⠀⠀⠀⢠⡾⠛⠋⣩⣟⣛⣶⣀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣉⣠⡤⠬⠷⠦⣄⡹⣆⢀⡀⣰⢏⣠⠴⠾⠥⢤⣄⣉⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⣁⣀⣠⣤⣤⣤⣤⡭⢻⣿⣿⡟⢭⣤⣤⣤⣤⣤⣀⣈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣍⠻⡿⠛⢋⡝⢿⡿⢫⡙⠛⢿⠟⣩⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣏⠽⢗⡚⢀⣴⠋⠀⢨⡅⠀⠙⣦⡀⢓⡚⠯⣹⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⠴⢫⠏⡽⠁⠈⠀⢨⠅⠀⠠⠈⢯⠹⡝⠦⣌⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣴⠋⣼⠁⢌⠄⠀⠈⠁⠀⢠⡡⠈⣧⠙⣦⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣷⣾⡞⠀⠀⠀⠀⠀⠀⢳⣷⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⠩⡅⠀⠀⠀⠀⠠⠤⠤⠀⠘⠈⠂
⠀⠀⠀⠀⠘⠛⠙⠓⠁⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⣛⢁⡄⠀⠀⠀⠐⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠃⠃⠀⠐⠲⠖⠀⠀⠸⠰⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⢠⠀⠀⠀⠀⡉⣾⠁⠃⠀⢈⠁
⠀⠀⠀⣀⡀⠀⡀⣀⣀⡀⠀⠀⠀⠘⠋⠉⠉⠉⣙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠁⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠅⠈⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠡⠀⠀⠀⠖⡆⣷⠀⠀⠀⠘⢚⣎⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠃⠇⠟⠀⠀⠀⠀⠀⠇⠇
⠀⠀⠈⠉⠉⠀⠈⠀⠀⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠈⠩⠭⠭⠭⠭⠭⠭⠭⠭⠿⠉⠁⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⡀
⠀⠀⠀⣀⣒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠘⠗⠇⠀⠀⠀⠀⠘⠇⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠒⠒⠀⡀⠀⠀⠠⠄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢁⠀⠀⠁⠰⠆⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠿⠅⠀⠸⠿⠀⠀⠿⠧⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡑⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠛⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢤⣄⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⢤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠈⠀⠀⢀⡀⠀⠀⠉⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠤⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢷⠀⠴⠙⠀⠀⠀⠀⠀⠀⠁⠁⠀⣃⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⢿⣗⠲⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣨⣴⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠊⠔⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠠⢤⠘⠛⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⡀
⠀⠃⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⢘⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⣷⡇
⠀⡤⠜⡀⠽⣘⢆⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⠃
⠀⠀⠀⠂⠀⠠⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⠁
⠀⡆⠈⠂⠀⠀⠊⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢸⣿
⠀⠋⠂⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡟
⠀⠀⢶⣤⣀⠀⣸⣧⡹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠉⠛⠻⠿⣿⣿⡿⢉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠼⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠙⣼⠀⢀⣼⡞⠀⠀⠀⣀⡤⠤⠶⠶⠦⣤⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⢸⣽⣦⡀⢹⣷⣌⣽⣇⢀⣢⡾⠉⠀⠒⠈⠙⠒⢦⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠶⣌⢻⣿⣧⣠⣿⣿⣿⣿⣿⣿⣷⣶⣞⣭⠄⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠠⢾⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣫⣴⡖⠀⠀⠈⣒⢌⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⣁⠀⠲⣿⣿⡟⠚⠋⠉⠁⠀⠈⠙⠛⢿⣿⣿⡟⠀⠀⠀⢀⣸⣷⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⠤⠀⡸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠻⠀⠀⠒⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠐⣄⠀⠀⢀⣠⡄⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⣦⢠⢟⣳⠿⠛⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠀⠀⠜⠛⠉






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

⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠠⢐⣀⣰⠆⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠄⠀⠀⠁⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠈⠉⠠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⢀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⡀⡀⠈
⠈⠀⢈⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠁⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠠⠤⠀⠠⠀⠰⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡲⠀⠀⠀⢆⡀⣠⠄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⢠⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠠⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠐⠄⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣉⣀⣈⡉⠤⢴⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⢀⠀⠀⠀⠇⠀⠠⠄⠀⠀⠤⢀
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⢂⢀⡄⢲⠐⠀⢀⡇⠀⠀⠀⠀⠆⡐⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⡈⢀⢀⠈
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⡠
⠀⠀⠀⠁⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠉⠒⠒⠓⠒⠉⣀

⢤⣤⣄⠀⠀⠀⠀⣠⣴⡆⣀⠀⠀⠀⠀⠀⢀⣀⢶⣶⢄⠀⢀⢴⣶⠂⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⢀⡄
⠀⠱⣽⠻⣦⣴⡿⣻⠋⠀⠻⡯⢦⣄⣤⣖⡽⠃⠀⠇⠘⢷⠛⠀⠃⠀⢳⠦⣄⣠⡴⢶⠃⠀⠙⠚⠛⠚
⢀⣀⠈⠻⡬⠣⠟⣁⣤⠄⠀⢸⡏⠛⠙⢹⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⣠⢧⠀⠁⠀⠀⢀⣄⡀⠀⠂
⠈⠲⡟⠶⣤⣴⠞⣫⠊⠀⠀⠀⠓⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⢀⣤⡖⠀⠀⠈⠁⠃
⠀⣀⠈⠾⠝⠫⠟⢁⠀⠀⢴⣖⠀⡤⠐⣤⡄⠰⡖⣶⣤⣶⢟⠗⠀⠀⠨⣶⢣⡾⠀⠈⠻⣶⢤⣤⣶⠟⠃
⠀⢻⡿⣦⠀⢠⡾⡯⠁⠀⠀⠈⠛⠑⠛⠁⠀⠀⠈⢮⣟⣵⠃⠀⠀⣀⡀⠉⠈⠁⠀⠀⠀⠀⠐⠃
⠀⠀⠁⡘⢿⠟⣀⠁⠀⠀⠈⠀⠀⠀⠀⡁⢠⣤⠄⠃⠀⢘⠠⢤⡄⠹⣫⠂⢠⡐⡎⣿⠁⣀⠀⢰⠀⢀⠄
⠀⠀⠘⠿⠋⠛⡋⠀⠀⠀⠀⣄⡀⢀⣰⠀⠀⢣⠀⠁⣤⠀⠀⡾⠀⠀⠀⣄⡐⣀⡬⠀⠀⠀⡀⠀⠀⢀
⠀⠰⠊⠀⠀⠀⠀⠲⠀⠀⣀⠈⠁⠀⠁⠀⡀⠈⡅⠀⣿⡄⢀⠆⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢐⢢⣼⠂
⠀⠀⢀⡀⣀⠀⣀⠀⠀⠀⠈⠳⠖⣶⠲⠟⠁⠀⣨⡌⠀⠉⠉⠀⣤⡜⢿⡷⢦⠀⡰⢚⣿⠃⠘⠁⠙
⠀⠀⠀⠰⠉⢇⠀⠀⢶⣶⣦⣄⠀⠈⢀⣠⡤⣶⠝⡀⠀⢠⠀⠀⡘⠁⠘⢿⠄⠿⠠⡼⠏⣀⣤⣤⣤⡀
⠀⠀⢠⠀⢠⠀⠠⠀⠀⠈⠛⠛⠷⣤⠿⠿⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠶⠐⠶⠇⠘⠛⢿⠋⣿⠿⠧
⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠣⠤⠑⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣏⣀⠘⣛⣴⣾⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣦⣛⠿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢿⣫⣵⠿⢟⣋⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣟⡛⠿⢾⣽⣿
⠀⠀⠀⠀⠀⠀⠐⢻⡏⠀⠀⢸⡏⣿⡌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⡧⠀⠀⢨⣿⠃
⠀⠀⠀⠀⢠⡀⠀⢸⣷⡀⢀⣾⣵⣿⣿⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣻⡄⠀⣸⣿⠀⠀⡀
⠀⠀⠀⠀⠈⣷⣄⠘⣿⠛⠾⢻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⠻⠞⢷⡛⢀⣼⡇
⠀⠀⠀⠀⠀⣽⣿⣶⣅⡀⠀⠘⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠞⠀⠀⣈⣵⣿⣿⡀
⠀⠀⠀⣠⠔⢻⡄⡙⠻⢷⣦⣀⡀⠀⠁⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠁⠀⣀⣤⡶⠟⠋⠁⣿⠣⢄⡀
⠀⠀⠀⠇⠀⢸⣇⠻⣷⣦⣌⡙⠻⣶⡄⣤⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⠀⣴⡟⠉⠁⠀⠀⠀⣸⣇⠀⢨⠁
⠀⠀⠀⢸⠀⢾⡛⢦⡀⠙⠻⣿⣷⢈⡟⠉⠳⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⡰⠉⠙⣿⡇⠀⠀⠀⠀⣼⠟⣿⠀⡸
⠀⠀⠀⠀⡆⠘⣧⠰⣄⡀⠳⣦⢁⣾⠀⠀⠀⠑⣄⡈⢷⡀⠀⠀⠀⠀⡴⠋⣀⠜⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⣸⡏⠀⠇
⠀⠀⠀⠀⢱⠀⡿⢧⠘⢿⣆⣤⢾⡇⠀⠀⠀⠀⡼⠟⢀⡷⠀⠀⠀⠸⣅⠛⢧⡀⠀⠀⠀⠘⣿⣿⣆⠀⠀⣸⢟⠃⡸
⠀⠀⠀⠀⠈⡄⠀⣸⠆⠀⠠⢶⣧⣥⡀⠀⣠⠎⢀⠔⠉⠀⠀⠀⠀⠀⠈⠳⢄⠙⢦⠀⠀⣰⡏⠈⠉⠁⠸⣧⡘⠀⡇
⠀⠀⠀⠀⠀⠁⢸⡏⣿⣷⢠⣤⣀⠬⣁⠘⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠑⢀⡥⠀⠀⠀⠀⠀⠸⣇⢸
⠀⠀⠀⠀⠀⣤⣿⠃⣿⡏⣼⣿⡟⣠⡜⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⡏⣿⠀⣿⡇⣿⡿⢡⣿⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆
⠀⠀⠀⠀⢠⠀⣿⠀⣿⢰⣿⢃⣾⢃⡜⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⢸⠀⣿⠀⡿⣼⠇⡼⠁⣼⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⣡
⠀⠀⠀⠀⢸⠀⣿⡀⢠⡟⠸⡁⢚⣥⣾⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣦⣀⢰⡄⠀⠀⠀⢸⡇⡿
⠀⠀⠀⠀⠈⢸⣿⣇⠈⠁⣵⣶⠟⠉⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⠛⢿⣿⡄⠀⠀⢸⡇⠇
⠀⠀⠀⠀⠀⠀⢿⣿⡀⣼⠏⣿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡏⣿⣆⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⣿⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡇⠸⣿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⡋⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢸⠃⠀⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⣷⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡃⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣧⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⡟⣽⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠹⡆⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⣼⠁⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⠀⢻⡀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠇⢰⠇⠀⣿⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠈⣧⠀⣷
⠀⠀⠀⠀⠀⠀⣾⢀⡿⠀⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⢹⡆⢹⡀
⠀⠀⠀⠀⠀⢀⠃⣸⠃⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡆⠀⠀⢷⠈⡇
⠀⠀⠀⠀⠀⢈⠀⡟⠀⠀⢀⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠸⡆⢀
⠀⠀⠀⠀⠀⠌⢸⡇⠀⠀⠘⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠏⠀⠀⠀⡇⠈
⠀⠀⠀⠀⡀⠀⠸⠀⠀⠀⡐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡀⠀⠀⢻⠀⠠
⠀⠀⠀⠀⣧⣀⡇⠀⠀⢰⣥⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣧⠀⠀⠸⣄⣴⡆
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⡗⠞⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣀⠀⠀⠀⠀⠀⠈⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠉⠀⠀⠀⢉⣠⡄⠀⠀⠀⣴⡟⢋⠉⠙⣟⣿⡆⠀⠀⣀⣤⣿⡛⣦⡀
⠀⠀⠀⠀⠀⠀⢀⢴⣾⣏⣿⣿⣷⣶⢾⡿⣿⡿⢦⡀⣼⣿⣿⣿⣦⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠿⢹⣿⣿⣾⠃⢿⣿⠀⢠⣿⣿⡼⣿⣿⣿⣿⣟⣿⡄⢸⣧⡹⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢀⣨⣿⣿⡇⠀⡴⠉⠀⢠⣾⣿⣴⢿⣿⣿⣿⣶⣿⣿⣾⣿⡇⣿⣷⡻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⡆⠀⠀⠀⠙⠁⣩⠿⣬⣷⣹⣿⣿⣆⠉⠈⣿⣧⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢛⣿⣿⢿⠀⠀⠀⠀⠀⠉⠈⢻⣿⣟⣿⣿⠇⠀⠀⣿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⡇⣿⠀⠀⠀⠀⠀⠀⡀⠀⢹⡧⣿⣿⡄⠀⠀⢸⣿⠾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣈⣱⡇⠀⠀⠀⠀⠀⠀⢳⡀⠈⣧⣿⣿⡇⠀⠀⣨⣡⢦⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢷⡄⢸⣿⣿⠁⠀⢸⣧⣴⣿⣙⢾⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⡿⠀⠀⠘⠏⣿⣉⣜⣪⡏⠿⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⡿⣿⡇⠀⠀⠛⠻⣿⣿⣿⣷⣶⣿⡿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠩⣿⢻⡟⣿⡧⠑⡀⠀⠀⠀⠀⢸⡀⠁⢻⠀⠀⠀⠀⣾⡆⣾⣟⣿⣿⣿⡿⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⣰⠉⡈⠀⡇⠀⠀⢈⠳⠦⢤⣀⣸⣧⣄⠘⣇⠀⠀⠀⣹⣠⢷⢹⡇⣿⠁⠇⠃⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠀⠁⢠⡏⠀⡇⠀⢡⠀⠀⠈⢳⡌⢺⡷⣌⣿⣿⠀⠈⠀⠀⢀⡟⣹⢸⢸⠁⢻⠀⠀⠐⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⡾⠀⠀⠇⠀⢸⡄⠀⠀⢤⡿⣄⢷⡘⢿⣿⣇⠀⠀⠀⠸⠀⡇⠈⠈⠀⢸⡆⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡠⠊⣠
⠀⠀⠀⠀⠀⠈⠍⠀⠀⣸⢁⠇⠀⠀⠀⢸⣧⠀⠀⠘⢻⣽⣿⣄⡀⣿⢻⣆⣸⠀⢀⡀⠃⠀⠀⠀⠀⠁⠀⠀⡇⠸⡇⠀⠀⠀⣠⠖⢀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣸⠀⠀⣶⡀⠈⣿⡄⠀⠀⠠⠻⠙⠏⠀⣿⠈⣿⣿⠀⠘⠇⠀⠀⠀⠀⢰⠀⠀⠀⠁⠀⠇⠀⣠⡐⠁
⠀⠀⠀⠀⠑⠴⢆⢠⡜⠀⡇⡆⠀⢿⢻⡀⢹⡅⠀⠀⠀⠁⠀⠀⠀⠏⠀⢿⡟⠇⠀⠀⠀⠀⠀⠀⠈⠰⣶⠀⠀⠂⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠁⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣀⣈⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⣷⡄⠠⠄⠀⡀⠀⣄⠀⠀⢆⡀⠀⠀⢆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠏⢿⡁⠀⠀⠀⠙⠀⠈⠀⠀⠀⠳⠀⠀⠈⢠⡄⠀⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠄⠳⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢇⠀⠀⠘⠇⢰⠇⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠸⣆⠀⠸⠀⣿⠁⠀⠀⠀⢸⡀⠀⠀⢸⡇⠀⢀⡏⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠻⠀⠀⠈⡄⠀⠃⢾⣀⡀⠈⡁⠈⢳⣄⢰⡾⠀⠀⢘⠃⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠂⠀⢀⡤⠀⠀⠲⢶⡆⠀⠀⢫⡼⡀⠀⠀⠉⢿⣿⠃⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠹⢦⡀⠘⣇⠈⢆⠀⠀⠈⣿⠀⠀⠀⢿⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠟⠀⠀⠀⠀⠀⢷⡀⠙⢷⣄⡇⠰⠆⣿⠀⠀⠈⣿⠁⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⣧⠐⠀⠀⠀⠀⠀⠀⢹⣦⣦⡿⣷⣶⡴⢿⣷⣶⣶⣿⣶⡶⣶⣶⣶⠶⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⡿⠛⣿⠃⣼⣿⢻⣿⠋⡟⢱⣿⠿⠿⡷⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢰⡟⢺⡇⠘⣷⡀⣻⣧⣸⣿⢸⡏⠀⣿⡟⣿⠀⡀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⡆⠀⠀⠀⠀⣼⣃⣚⣓⣻⣟⣻⣿⣿⣿⣿⣸⣿⣐⣛⣛⣛⣈⣋⣁⣘⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣘⣛⣃⣀⣀⣀⠀⣿⡉⠉⠉⠉⠉⠉⠉⢻⣿⡏⣹⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠀⢀⢀⡀⠀⠀⠀⢿⠉⢉⠍⠉⠉⠉⢹⡿⠀⣿⠀⠀⠀⣀⣀⠀⠐⢿⣿⣿⣿⠃⠂⢠⣄⠠⡄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠖⢤⠘⢷⡀⠀⠀⠸⣷⣼⣿⠛⠓⢰⠟⠇⠀⡿⠀⠀⠂⣹⡏⠓⠀⢾⣿⣿⡿⠤⠀⠨⡿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠐⠀⠘⠳⡤⠃⠀⠀⠄⠙⣻⣷⣦⣐⠚⠂⢀⠀⠁⠤⠀⠀⢸⡇⠀⣠⣼⣿⣿⣗⣲⣾⣶⣿⣿⣷⣦⣦⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢀⣤⡀⠀⠀⠠⠘⢿⣄⠆⠀⣻⣿⠋⠉⠉⠙⢷⢏⡀⠀⡀⠀⠠⡈⠡⠀⠠⣿⣿⣿⣿⣤⣿⣭⣽⣿⣯⣽⣿⣧⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⢀⠀⠙⢢⡀⠁⠀⣙⣿⣿⠀⠀⠀⠀⢨⡾⢁⣾⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⣿⠛⡙⠛⠙⠛⢙⠛⠛⢉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⢻⣶⣿⣿⣿⠾⠂⠲⣶⢻⣿⣿⡟⠉⠀⠀⣶⣶⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠸⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠄⢠⡀⢈⡉⢳⣦⡀⢻⣿⣟⢻⣉⣎⣷⣿⣯⣿⣋⣽⣿⠐⠂⠀⣿⣇⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⢿⡿⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⠀⢰⡄⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡟⠓⠀⠀⠂⠀⠋⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠻⢿⠗⠀⠀⠉⠈⠉⢻⣿⣿⡿⠏⠙⠀⠉⠀⣙⠿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠛⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⢨⡄⣠⣤⣤⣼⣿⡟⢧⣄⡰⠀⠰⣶⣜⠀⢹⣿⠺⠻⠃⠀⢿⣷⡆⠀⢿⣿⣿⣿⠆⠀⠀⠀⠀⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⠉⠙⠋⢹⣿⣶⣿⣿⣿⣄⢰⣿⣿⣷⣿⣿⡀⠀⠀⠀⢸⣿⡇⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠘⠋⠀⠀⠀⠜⠛⠉⠁⠉⠉⠉⠁⠈⢩⡍⠙⠛⠄⠀⠀⠀⢸⣿⡅⠀⣿⣿⣿⣿⠽⠄⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⠐⠒⠂⠀⠠⠤⠤⠤⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠏⠁⠀⣿⣿⣿⣷⠀⠀⠀⠲⠒⠤⠔⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠀⠤⠀⠶⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⠘⠉⠀⠉⠛⠷⠄⠀⠘⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠁⠘⠛⠚⠶⠦⠤⢤⡤⠤⠤⢤⣤⣤⣤⣤⣶⣶⣶⣶⡶⠾⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠂⠀⠂⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠠⠀⠨⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄






⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣉⣿⣋⣙⣋⣉⣉⣀⣩⣉⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣤⣥⣤⣤⣤⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠦⢄⡤⠖⠚⣛⣉⣉⡉⣉⣉⣉⠉⠙⠛⠒⠲⢤⡀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⡴⣋⠤⠒⠀⠀⠀⠀⠀⡞⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡠⠖⠊⠉⠁⠐⠊⠭⢝⡒⠤⣀
⠀⠀⠀⠀⠀⡞⠘⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⠙⠢⣄
⠀⠀⠀⣠⠖⡇⢸⠀⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⢀⡞⠁⠀⢻⠈⡆⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢀⡎⠀⠀⠀⠸⡄⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⢎⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⡠⠤⢔⣒⣉⣭⠤⢤⣷
⣼⠀⢀⠀⣀⡀⢧⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⢠⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⢔⣪⠵⠒⠋⠉⠀⠀⠀⠀⠀⠀⠙⣄
⡇⠀⠔⢋⣠⠴⠚⢦⣀⣠⡤⣤⣀⣧⠀⠀⠀⠀⢰⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡭⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠳⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣄⠀⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠹⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢕⣦⣔⡀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠫⢭⣓⣂⣀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠤⠤⠤⠄⣒⣒⡒⠠⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⠔⣡⠤⠖⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠙⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠓⢤⡀⠀⠀⠀⠀⢀⡴⢃⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⣉⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⡠⣠⠞⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠠⣤⣦⣶⠿⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢠⠞⢻⣭⠭⢽⡓⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣚⡯⠭⣭⡟⠳⡄
⠀⠀⠀⠀⣿⠀⠻⠿⠁⣀⣈⠑⢄⠙⠻⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠿⠋⡠⠊⣁⣀⠀⠿⠟⠀⣿
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠻⠟⠁⠀⠑⣄⠈⠢⡑⢄⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⡠⢊⠔⠁⣠⠊⠀⠈⠻⠟⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠹⡄⠀⣤⣤⠀⠀⠔⠋⠀⢱⣄⠈⢆⡑⣄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣠⢊⡴⠁⣠⡎⠁⠉⠢⡀⠀⣤⣤⠀⢀⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠛⠛⠀⡌⠀⣀⣠⠃⠈⠳⣜⠛⢌⠳⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⠜⡡⠛⣣⠞⢁⠘⣄⣀⠀⢡⠀⠙⠛⠀⢸
⠀⠀⠀⠀⠀⠀⢧⠀⠀⣴⣤⡅⠘⠿⠟⠀⠋⠀⠈⢳⣄⠱⣝⢄⠀⠀⠱⡀⠀⠀⠀⠀⢀⠎⠀⠀⡠⣋⠎⢠⡞⠁⠀⠙⠀⠹⠿⠃⢈⣤⣦⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠙⠋⠁⢀⣤⣤⠀⠀⠀⡰⢅⣈⠳⣌⠁⢧⡀⠀⠱⠀⢀⡀⠀⠎⠀⢀⡼⠛⣩⠞⣁⡈⠆⠀⠀⠀⣠⣤⡀⠸⠙⠋⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⡘⡈⠛⠛⡀⠀⠀⡇⠀⠋⠙⠪⣑⠦⣙⢦⡀⣨⣿⣿⣅⢀⡴⣋⠴⣊⠔⠊⠙⠁⢸⠀⠀⢀⠛⠛⢃⢂⣀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠇⠀⡀⠀⠡⣾⣿⠧⣀⣉⠉⣁⡲⣵⣬⣓⢿⣿⢻⡟⣿⡿⣞⣥⣮⣴⣊⡉⣉⣀⠸⣿⣷⡌⠀⢀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⡈⠄⠀⢣⣠⠤⠷⢒⠒⡉⠩⣿⣭⣍⣛⣿⣿⣿⣿⣛⣩⣭⡿⠍⢉⠐⡒⠾⠤⣤⡜⠀⠠⢃⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠟⠋⠁⣀⣠⣤⣈⡑⠾⢦⠶⢾⣿⣻⣿⣿⣿⣿⣿⣿⡷⢶⡴⠷⠊⣁⣤⣄⣀⠈⠙⠻⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠊⠍⣙⡽⢃⠠⢀⣶⢶⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⡶⢦⡀⠄⡘⢯⣋⠩⠙⢦⡀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⣺⢟⣪⠴⠛⠉⢀⣠⣶⣫⣽⠿⣻⡿⠃⣸⣿⣿⣇⠈⢿⣯⠻⣼⣝⡶⣄⡀⠉⠛⠦⣕⡻⣗⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⢉⠁⠀⠀⡀⠘⠋⢉⠔⠁⡼⢻⠁⣠⢿⣿⣿⡿⣆⠈⡛⢷⠈⠢⡉⠙⠓⢄⠀⠁⠈⡉⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠔⠁⠀⢀⢸⣿⠀⣐⠁⢠⠟⠄⡄⢠⠇⢸⣽⣯⡇⠸⡄⢡⠠⠻⡄⠈⣂⠀⣿⡇⠀⠀⠈⠢⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⠁⢸⡏⣸⡿⠀⣟⡜⡐⢀⡎⠀⢸⢾⡷⡇⠀⠱⡀⢂⢳⣳⠀⢿⣧⢹⡇⠈⠄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣄⠂⠀⠈⢰⡿⠁⠀⠟⡰⠁⡸⠀⠀⠘⣿⣿⠇⠀⠀⢧⠈⢆⠻⠀⠈⢿⡆⠁⠀⠘⣀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢦⡀⠀⠆⠀⠀⠀⡰⢁⣶⠇⠀⠀⠀⠛⠛⠀⠀⠀⠘⣶⡈⢆⠀⠀⠀⠐⠀⢀⡴⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠳⠴⡀⠀⣀⣠⡷⢋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⢾⣄⣀⠀⢀⡦⠞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠙⠊⠉⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠉⠉⠑⠋⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣉⣹⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⢲⣤⣶⣶⣶⣠⣶⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠆⡆⠀⠀⢴⡾⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡩⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⢿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢄⡟⠀⠀⣔⣀⠉⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⢀⡿⠁⠈⠀⠁⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠠⣤⣼⠄⠤⠴⠤⢄⡀⠀⠀⠀⠀⣴⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⢛⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠓⠛⠚⠛⠛⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇
⡖⠈⠭⠭⠭⠭⠭⠭⠥⠤⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⢀⣀⣀⣀⡀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⢀⡠⠄⠂⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡔⠀⠉⢀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠀⠀⠀⠁⠀⠀⡄⠰⠀⠀⢃⠀⠀⢠⠀⢰⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⠸⠀⢸⠀⠀⠀⠸⠀⠀⡸⠃
⠀⢦⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠘⠘⣾⣾⠾⠬⠽⠴⠄⠚⢊⣉⣀⣐⡀⢲
⠀⠸⣄⣀⣀⠀⢤⠏⠀⠀⠀⠀⠀⠸⡀⠀⠊⠀⠀⠀⠀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠠⡈⢉⣩⡋⢻⣽⣇⣳
⠀⠀⠀⠈⠉⠉⠍⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡷⠀⠀⠀⢀⡓⠠⡟⢙⣿⣀⣻⡭⠇
⠀⠀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠙⠂⠛⢯⢉⡤⠛
⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⡀⠀⠀⠈⢇⠀⣀⠤⠒⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣐⣒⣒⣂⣮⣁⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠒⠠⠤⣀⡀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠳⠶⠂⠚⠚⠀⠀⠀⣨⡍⢐⢢⣤⠈⠓⠁⡔⠒⠒⠒⠒⠒⡄⠀⠰⡉⣁⠀⠀⢀⠸⠥⠤⠼⢇⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠊⠻⠜⠂⢦⠭⢛⡀⠀⣴⠂⡰⠂⠈⠀⠀⢸⠀⠀⣠⠋⡜⠻⣆⠀⣠⠛⡀⠀⠈⠁⣠⠔⠁⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⣀⢔⡎⢡⡤⠤⠐⢒⠶⠫⣁⣤⡀⠀⠀⠉⠀⠀⠺⠀⠀⢘⠀⢰⠧⠤⠼⠾⠧⢴⠧⠤⠶⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⢘⠉⠙⠶⠚⠙⡄⠀⠘⠤⠔⣇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠢⡀⠇
⠀⠀⠘⠘⡀⠘⠒⠊⠀⠀⠀⠀⠀⢥⡠⠇⡠⣠⢤⣄⣀⠤⠔⠒⠊⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠔⠓⠉⠈⠁⠀⡔⠒⠒⠢⡀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠸⣼⣀⠠⠄⠒⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡴⠁⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣤⣄⠀⠒⠒⠒⠀⠀⠀⠐⠒⠒⠀⢀⣤⡀⠈⠉⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀⡠⠃⡄
⠀⠀⠀⠀⠀⢸⠀⠈⢉⢍⣑⣒⣒⣒⠒⠀⠈⠉⠉⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠸⢿⣃⣠⣮⢿⠀⠀⠀⠀⠀⠀⠀⡏⠲⢄⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⡇⢰⣦⣶⢰⢴⠀⣤⡴⠀⢽⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠈⠱⣄⠀⠀⠀⠀⠀⠀⣇⡰⠋⠉⡆⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢇⠈⠁⠉⠈⠙⠓⠉⠙⠀⣸⠀⡇
⠀⠀⠀⠀⢀⠎⠁⠒⠒⠀⢴⡦⠤⠤⠤⠷⢤⠀⠒⠂⠉⠏⠀⠀⡰⠁⢸⡀⠀⣀⠀⡀⣸⠀⢀⣀⠀⠈⠢⣈⡉⣉⣉⣉⣉⣉⣉⣉⢉⣁⠔⠁
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠑⢄⠀⣞⡂⢂⡴⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠋⢃⠀⢠⠤⢄⠀⢙⣂⣀⣐⡃⠀⠀⠈⣇⣀⣀⣺⠁⠀⠀⢹⣂⣀⣐⡃
⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠑⠁⠀⣈⣉⣉⣉⡁⠀⠀⠀⣏⣉⣉⣹⠀⠀⠀⢨⣉⣉⣉⡇
⠀⠀⠀⠈⠑⠒⠠⢤⣇⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⢡⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⡎⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠀⠀⠀⠀⠀⣆⣠⠇⠀⠀⠀⠀⢱⣀⡘⠀⠀⠀⠀⠀⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠃⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠊⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠐⠒⠚⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢠⡄⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠠⠠⣤⡄⠄⠀⠀⠀⠀⢠⠄⠇
⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣸⣀⡀
⠀⠀⠀⠀⠀⠉⠒⠒⠢⠤⠤⠀⠤⠤⠤⠠⠀⠤⠤⠐⠒⠉⠀⠀⠀⠀⠯⠠⠀⠄⠄⠀⠀⠀⠀⠠⠀⠀⠤⠀⠄⠄⠀⠠⠄⠠⠀⠀⠀⠀⠠⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡠
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠉⠀⡀⠀⠁
⣄⡀⠀⠀⡐⠁⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣉⠀⠀⢀
⠳⢮⣑⠨⡢⢄⡀⠀⠀⠀⠀⠄⠁⠀⢀⠀⠀⠈⠀⠀⠐⠀⠀⣜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠓
⢤⣀⠉⠛⠢⣄⡀⠀⠠⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠆⠀⢉⠀⠀⠀⣀⡀⠸⠉⠀⠀⢠⠅
⠑⠉⠻⢦⣄⡀⠉⠳⢬⣐⠩⣂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠛⢩⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠙⠳⢤⣀⠈⠛⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⢛⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠀⠀⠀⠁⠀⣄
⠀⠀⣶⠶⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠽⠄⠀⠀⠀⢀⢦⠀⠀⠀⠀⠀⠀⠀⠑⡢⠀⢀⡤⠀⠈
⣠⠀⠀⡠⠋⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢓⠀⠀⢀⢢⣿⡳⠄⠀⠀⠀⠘⠃⠀⠀⠀⠀⠢⡄⠑
⠀⠀⠘⠁⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡈⣁⠀⠈⢷⣽⣝⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⠸⡆⠀⠳⣵⣝⠳⠄

⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢿⣿⣿⡷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣆⠶⣿⡿⣦
⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣦⣹⠆⢋⣾⣿⠞⠁
⠀⠀⠀⠀⠀⠈⢿⣿⡿⠲⣦⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣿⡏⠀⣰⣿⣯⠋
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡦⣄⡀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⢿⣮⡂⠀⡀⣿⣏⡇
⠀⠀⠀⢠⣤⣻⣿⡿⢆⣷⣿⣿⡾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⣦⠝⠉⠛⠈⠘⢿⣷⢀⣴⣿⡗⡁
⠀⠀⢀⡦⣿⣿⣿⣀⠀⠀⠙⢿⣳⣼⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣉⣣⣤⣴⣶⣦⣔⣠⣤⡞⠉⢹⡿⠝⢄
⠀⠀⠀⠲⠙⡿⢻⡏⢴⣿⣿⠿⡻⠛⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡯⠿⠿⠛⠛⠼⡻⠟⡿⡻⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠢⣄⢠⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡈⢑⠀⠈⠀⠀⠀⣀⠀⢆⡀⠙⡿⠛⠁
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠨⠄⣶⣿⠁⠀⠰⣤⠺⠝⠋⠀⠀⠀⠀⢀⣤⣾⣯⢹
⠀⠸⣿⣏⢛⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⣴⣛⡯⢰⡯⣽
⠀⠀⠘⣿⣿⠩⠭⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣅⣿⣗⡏
⠀⠀⠀⠘⣷⠖⠂⣀⣀⣀⣀⣱⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣯⣷⣈⣷⠙⣧⣀
⠀⠀⠀⠀⣿⡛⠻⠋⠉⢉⣩⣿⢿⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⡹⠿⠿⣿⣿⣧⡽⣳⠖⠛⠃
⠀⠀⠀⠀⠹⣧⣀⠘⢀⣾⡿⠃⢸⡇⠀⡈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣄⠺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠛⢻⡏⠠⠊⣸⡇⢀⢀⡤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡛⠂⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣘⣧⣼⣠⣧⣟⡻⣧⠀⠀⠀⠀⠀⠀⠀⠉⠩⠛⠛⢉⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠛⠻⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⡠⢬⠀⢠⠮⠥⣤⣴⣾⣿⡇⠘⠂⣀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠀⠀⠀⠐⠞⠻⠛⠛⠛⢼⣀⡤
⠀⠀⠀⠀⠀⠀⠀⣠⢰⡆⠃⠀⡙⠀⢉⠀⠀⠀⠈⢨⣽⣷⣷⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡾⠞
⠀⠀⠀⠀⠀⠀⢰⠻⠘⣷⣤⣤⡆⠀⠈⢀⣀⣤⣶⣿⣿⡟⢡⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠶⠶⡯⠷⠀⠀⡰
⠀⠀⠀⠀⠀⠀⣭⣤⣭⣭⣭⣥⠤⢤⣤⣤⣤⣤⣤⣤⣄⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠶⠀⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣥⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠠⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢠⠠⠰⡃⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠠⠀⢾⡅⣯⡒⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⠀⠀⠄⠘⠂⠚
⠀⠀⠀⢣⡘⣱⡐⡒⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠋⡀⠀⠀⠆
⠀⠀⠀⠀⠳⢜⡶⠿⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠨⠭⠈⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⠂
⠀⠀⠀⠀⠀⠘⠛⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣖⣒⣒⣃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡌⡇⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠀⠀⢀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⡁⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣆⣀⣀⣄⣦⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠉⠉⠉⠉⠉⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠁⠀⠀⠀⠀⠀⠀⠀⠰⣆⠰⠀⠀⠀⠀⡼⢅⡾⠉⠉⠉⠉⠹⣏⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠤⠓⠀⠀⠀⠀⠀⠀⡜⠁⡾⠀⠀⠀⠀⠀⠀⢰⡎⣦⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠰⠄⠈⠓⠁⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠲⣀⣠⡶⠆⡄⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⣤⣶⣶⡄⠀⠀⢠⣼⡃⠀⠀⠀⠀⠀⢉⢁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⠖⠂⠀⠀⠀⠀⠀⠀⢪⡝⠛⡙⡆⠁⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠙⠛⠉⠀⠀⡘⠈⠛⣳⡀⠀⠀⠀⠀⠀⠾⡍⡀
⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠈⠀⠀⠀⠈⠉⢈⡽⠛⣃⣤⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠃⠉⠘⢋⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡿⠋⠉⢹⠟⢷⡄⡄⢠⡄⢀⠔⠀⢀⡴⢿⠉⠉⠉⠳⡄⠀⠀⠀⠈⠀⠈⢛⡂⠋⣙⡇⠀⠀⠀⠸⠀⠠⠰⠛⠃⠀⠀⠀⠀⢀
⠀⠀⠀⡎⠀⠀⣴⣧⡀⢈⡇⢘⣚⡖⠁⠀⠀⣾⠀⠘⢧⣄⠀⠀⣷⠀⠀⠀⠀⠀⠀⠘⢀⣈⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣶⡾
⠀⠀⠀⣇⠀⠀⠉⠀⠁⣨⠁⠘⠛⠁⠀⠀⠀⠱⡀⠀⠈⠋⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⠀⠀⠀⢹⠁
⠀⠀⠀⠈⠓⠦⠤⠤⠞⠁⠀⠘⠛⠀⠀⠀⠀⠀⠙⠲⠤⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠭⡭⠯⠟⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣚⣽⡶⠾⣷⣶⣬⣍⠓⢤⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢚⣉⣀⣀⡀⠀⠈⠉⠻⣿⣦⣝⢦⡉⠲⢤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠚⠉⠉⠀⠀⠉⠙⢿⣶⣄⠈⠙⢿⣧⣳⡄⠀⢳⡀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⣃⠀⠐⠶⣤⣀⡀⠀⠀⠈⠻⣷⣦⡀⠙⣿⣿⠀⠀⢷⡄⠀⢿⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣴⠾⠋⠙⠛⠶⣿⣿⣻⣧⡀⡈⠱⡄⠈⢻⣿⣦⠸⠟⠀⢠⢸⡇⠀⣸⣧⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⠍⠋⠁⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⣷⣿⣿⡿⣿⣶⣌⠀⣈⣀⣿⣼⡾⣿⣷⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡵⠓⠛⣓⠶⢶⣤⣄⠀⢄⣀⠀⠈⣿⣿⣿⡞⢖⣯⣷⣻⣿⣿⣿⣿⣿⡿⠃⣠⣏⣡⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠉⠉⠙⠳⢾⣿⣷⣬⣛⣹⣷⣾⣿⣿⣿⣾⣽⢯⢿⡿⢟⣿⣿⡿⠶⠏⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣠⣲⣽⣿⣿⣾⣿⡻⡟⣿⣿⠙⠖⢛⣸⣿⡿⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡣⠖⠛⣉⣉⣙⠺⣷⣿⢻⢿⣿⢟⣟⣀⣿⣷⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣴⣶⡶⣾⣿⢿⣺⣷⣯⣴⡾⠿⠝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣙⠿⠞⣛⣵⣾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉