Fruit tree Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⣦⣄⠀⠀⠀⠀⣦⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⢰⡿⠘⢠⡶⠀⠙⠿⠆⠀⠀⠀⠛⡰⣫⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣼⡇⠀⠀⠀⣙⠊⠁⠀⠀⠀⠒⢛⣭⡎⠓⢤⠔⠚⢄⢉⣛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢰⣆⠘⠛⠛⠤⠄⠀⠀⠀⠀⢡⠆⠀⠀⢠⣿⡿⠁⠀⠈⡇⠀⠀⠸⢧⠄⠀⠀⡆⠀⢠⡶⣠⣶
⠀⠀⠀⠀⠀⠀⣠⣤⡝⠀⠤⠤⣀⡀⠀⠀⠀⠀⡎⣠⡤⠀⠈⢁⡀⠀⣀⢀⣹⠀⠈⢿⣦⠀⣠⠴⠓⢦⡈⢐⣛⠁
⠀⠀⠀⠀⠀⠀⠉⡀⠁⣰⡇⠀⣀⣈⣙⡲⣄⡀⡇⠀⠀⠀⠀⣀⣙⣉⡀⠀⢸⡇⠀⠀⠉⢰⠃⢠⣶⣤⣶⡅⠙⠃
⠀⠀⠀⠀⠀⠀⢀⣉⣃⠉⠀⠸⣿⣿⣿⡇⠀⠙⢷⡀⠀⠀⠀⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⢸⡀⠘⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠴⣿⠿⠟⠀⣄⠀⠉⠉⠋⠀⠀⠀⠀⠙⣦⠀⠀⠙⠛⠋⠀⠀⠀⣷⠀⠸⣦⢸⡇⠀⠀⠀⠀⠀⠀⣴⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠲⣤⣠⣤⠤⠤⠤⠤⣄⠘⣧⠀⠀⣀⠀⠀⠸⢆⡇⠀⠀⢈⣼⢀⣀⣀⣀⣞⣠⣄⡉⠺⠛⠁
⠀⠀⠀⠀⢠⡄⢸⡇⠀⣩⠔⢈⣡⠀⢠⣤⣀⠀⠀⠀⠙⢿⡆⡾⠟⠀⠀⠀⣸⣷⠞⠛⣭⡉⠉⠉⠉⢹⣄⠀⠘⣿⣷⡄
⠀⠀⣶⠀⢀⣀⣉⡲⡄⠁⠀⠈⠁⡶⠈⠻⣿⣆⠀⠀⠀⠘⣧⠀⠀⠀⣠⣾⣏⣀⣀⣀⡈⠁⠀⠀⠀⠀⠙⠀⠀⠈⠉⠛
⠀⣀⠻⠀⣿⣿⣿⣿⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⡀⠀⢰⡟⠁⠀⢀⣀⡀⠉⠳⡄⣛⡋⠀⠀⠀⢠⡄
⠀⠙⠛⠢⠬⣛⣛⣁⣀⡤⠷⠶⠒⠓⢲⡶⢶⣤⣄⡸⠇⠀⣿⡇⠀⣿⠁⠀⠐⠛⢛⡅⣴⣶⣶⣦⠀⠚⠒⠃⣿⡇⣴⡗
⠀⠀⣰⣾⠇⢠⠀⠀⠀⠀⠀⠀⣒⡂⢊⡀⠀⠈⠙⠻⣶⡄⢹⣷⣸⡏⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⣩⠨⣭⠄
⠀⠈⢛⣥⡄⠀⠦⠤⣄⠀⠀⠾⠛⠀⢸⣷⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⢀⣀⣀⡰⠋⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⣞⠋
⠀⠀⠘⠋⠀⣾⣷⣾⣦⠙⠦⣄⡀⠀⠀⠁⢀⣠⡴⠶⢿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⣷⠶⠶⠶⠶⠛⠓⠤⢾⠀⠻
⠀⠀⠀⠀⠀⠻⠿⠿⢋⣠⠠⠤⠭⠿⠗⡚⠋⡁⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣬⠆⣀⠀⠀⣾⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠇⠀⢸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⠏⢰⠙⠃⠀⠹⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⣼⣿⣿⣿⣇⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⣀⠉⠉⢦⣀⡈⢐⠒⠢⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢖⠀⡀⢀⠒⡈⠥⢻⡉⠈⠁⢂⠩⠐⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢷⢴⡈⠗⢒⡐⢨⣛⠽⣉⠐⠦⠀⠘⠑⠛⠩⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡋⠣⠒⣈⠁⣤⣈⠱⠄⡀⢰⣍⡛⢦⠀⠀⢚⠀⠈⠁⠷⢀⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠩⢷⣒⡳⡆⣊⠙⡐⢈⡃⣍⠓⠀⠈⢰⠗⠠⡐⠛⣖⣜⠂⠤⠉⠌⢣⣶
⠀⠀⠀⠀⠀⠀⠀⣘⣾⠂⠦⠘⢣⡅⠰⣭⡴⠦⣘⣖⠂⠀⡸⠈⠀⠁⣩⠭⠬⠵⠤⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⢉⣇⠰⡶⠀⠪⡇⠀⠀⠐⣶⢌⡉⠀⠀⠇⠀⠀⡴⠃⠘⠖⢄⢀
⠀⠀⠀⠀⠀⠀⡸⠪⠀⠗⠀⠀⠀⠙⠄⠀⠀⣿⠘⠁⠀⠀⠀⠀⠚⠁⠀⠀⠀⠘⠈⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣈⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⢠⠀⠌
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⣼⠃⡆⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡀⠀⢂⢿⡿⠷⠄⣈⡌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠤⢱⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣺⢥⣿⣂⣃⠣⡥⣁⣀⣃⣰⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢇⣡⠒⡀⣴⡏⢯⣉⠁⡷⣟⣤⣸⡗⣬⡝⠧⣀⣲⠊⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡀⠀⠀⢄⡀⡄⢀⡤⢄⡠⣀⣰⢉⡀⠤⡇⢈⢷⣍⡿⠣⣤⣆⠼⣽⢁⣹⣵⠔⢽⣶⣿⠚⢆⡁
⠀⠀⠀⠀⠀⠀⠠⣤⣀⠠⣗⣇⣁⣷⣶⣖⠫⢭⣾⢿⠌⣡⣉⢹⡾⣟⠋⢡⣾⢰⡿⠾⣧⣼⣜⣿⣷⣽⣩⣿⡶⠾⣿⣿⠾⡨⢱⣔⣤⢄⢘⢓⣠⡖⠏
⠀⠀⠀⠀⠀⠀⡸⣿⡩⢿⡖⠌⢱⣞⡏⢻⡼⢶⣷⣶⣦⣼⣿⡛⣶⣿⣷⣞⣻⣻⣜⢹⣾⣿⡿⠾⣿⢟⣟⢫⣤⣿⣿⣶⡶⣿⣧⣴⣏⠷⣻⣷⡂⣥⡦⡆
⠀⠀⠀⠀⠀⡀⠈⠱⡾⣉⢑⣼⣾⣿⣧⡞⣿⣿⣻⣿⣿⣿⣿⣷⣿⣭⣿⣿⣿⣿⣿⣿⣿⢯⡟⣛⣵⢿⣿⣷⣿⣿⣿⣿⣿⣿⣷⢋⣟⣴⡿⢿⣍⠃⠁
⠀⠀⠀⢀⢹⣿⢀⣰⣾⣮⣙⣿⣾⢏⣟⣿⣿⣿⣻⣯⣽⡿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣿⣶⣾⣿⡿⢲⣿⡟⣿⣬⣻⢿⣾⣿⡟⠋⢿⣷⣬⢫⡾⡿⢧⠀⢠⣀⢲
⠠⣠⡷⢻⣾⡻⣫⣄⣰⢨⣻⣿⠿⠿⣿⣿⢿⣿⡿⢻⣧⢐⢟⢩⡹⣿⣿⢿⣿⡿⠿⢿⣿⣮⣿⣿⣧⡟⢛⡿⠟⢾⡹⣮⣯⢛⣫⣿⣿⢾⣿⣿⠃⡈⢓⡐⣟⡞⠜
⠀⠀⢈⣙⣏⣁⣿⣟⠿⣾⣽⣽⢲⣦⣽⣽⣿⣻⢿⣿⣇⠘⠷⣧⡄⣾⣹⣧⣱⡏⢸⣿⣟⣿⣟⠛⠻⡟⣈⡤⢠⣿⣷⣟⣧⣿⣿⢟⣿⣟⣿⣵⣻⣿⣿⡧⣾⣷⠁
⠀⡀⠤⣦⣿⡟⢷⣿⢳⣿⠻⡿⣄⠡⡿⣇⣸⣭⣬⣿⢟⡿⢦⣼⢻⣿⡀⣻⣧⡽⢟⢛⡭⣵⠘⢳⣿⣣⣿⢿⣻⡴⣯⡷⠿⣯⠿⠛⠿⣿⡛⠻⠿⠿⣿⢃⠈⠉
⠁⠙⡿⣏⣛⣊⣽⢿⡁⣹⡟⣿⡷⣿⠷⣾⣿⣏⢩⡝⠻⣷⣺⢿⣵⣟⡁⣶⣙⣦⣜⣿⡾⣿⣾⠫⡮⡏⠉⠀⠛⠒⢮⡷⣚⠁⣰⣾⣺⣿⡏⣔⣶⣐⣿⢘⠂
⠀⠀⠀⣠⡸⣿⣿⡾⢿⢅⣹⠟⠃⠀⠀⠈⣿⣿⣿⣿⠒⢿⠭⠷⢶⢏⣝⣿⡟⢛⣯⣟⣯⢛⢶⠛⣥⣅⢒⣀⣘⣴⣀⣀⣉⣿⣯⣬⣽⡗⣿⠻⠿⢽⣳⢡⣄
⠀⢠⣽⣿⢻⣿⣋⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⢻⣳⠞⣆⠀⠙⢰⣶⣷⣟⢯⢽⡿⠃⠛⣻⠅⣵⠍⢂⡉⠉⡷⡚⠿⢥⣄⣀⣈⣱⡿⣼⣽⣓⡾⠷⣿⢉⡀
⠀⠈⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡝⣦⠾⣮⣿⣿⣿⠏⣨⣋⣈⢟⠩⠿⡇⠫⢓⡈⠂⠈⠃⠀⠀⠈⠙⠖⢢⡸⠿⣇⡻⣗⡾⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣐⠫⠈⡿⣿⡿⠀⠀⠉⠀⠀⠤⠀⣃⠳⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡏⠀⠐⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⣠⣿⡟⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⣿⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡽⠐⢸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⢘⢳⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣼⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢧⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠖⣸⣿⣿⣄⢠⣴⣼⣿⣷⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡤⢠⠁⠁⣰⣿⣿⣿⡧⠺⠉⠉⠀⠛⢠⡤⢼⠄⠀⣤⠀⣤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⣣⣦⣀⣄⣧⣴⣏⣸⣾⣿⣟⢿⣿⣿⣤⢁⢠⣴⣧⣧⣆⣀⣈⡩⢽⡟⠉⠉⠉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠛⠈⠉⠉⠙⡉⠘⢿⠈⣻⣭⡉⣙⠲⠢⠴⠿⠻⠆⠀⠒⢿⡉⠋⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⠻⢾⣷⡄⣠⡤⢉⣤⣴⣶⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣰⣿⣿⣇⡈⠟⠻⡟⠉⣄⢛⠡⡶⢾⣉⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣆⡈⣡⢉⣭⡝⣵⠏⣴⡖⢠⣾⣿⡆⢻⡾⡻⣿⡿⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⣿⣿⣿⣇⡿⣫⢀⣰⠆⠼⣷⠎⢻⣿⢃⣸⣿⣣⣼⠏⢨⣙⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡼⣿⢲⣾⡟⢫⣾⠅⠟⢸⣿⣿⣦⣾⠈⣿⡷⣂⣛⣨⣭⣰⣿⣿⣿⣙⣯⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣖⠶⣌⠻⢿⣷⠟⣷⣞⢛⣻⡛⢹⣿⣐⠻⡆⣩⢭⡇⣬⣿⠻⣿⡏⢉⣽⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣿⣿⣷⣘⡩⠾⣃⣶⣼⣏⢀⣼⣿⣗⢠⣅⣿⣴⣿⣿⡼⠟⣿⣧⢙⡏⣱⠟⣡⣥⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⡋⢿⣜⢻⡇⢾⣿⣿⡷⣛⣽⣟⣁⢸⡟⣿⣧⠹⣿⡿⠷⠗⢈⣁⣉⣰⣭⠼⣿⣿⡿⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⢈⣘⡡⢬⠉⣭⣴⣤⢛⠯⣥⣎⣰⢽⢋⣴⣶⢂⣾⣡⠄⢩⡉⣉⡹⢶⣤⣭⣘⢻⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣧⠞⣈⣉⣍⠘⠓⣠⣾⡟⡏⢳⣿⣿⣿⣠⢆⡄⠩⣬⡁⣴⣾⣿⣿⡻⠖⢤⣽⣛⡻⠥⠍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠏⣌⣽⣿⣿⡆⢛⣫⠄⣾⣢⡴⣼⢖⡋⣿⣿⠠⣬⣉⠻⣿⣿⠟⢘⣛⣋⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⣻⡛⡡⠛⣥⣴⠶⣅⢰⣦⢸⡇⢙⣃⣝⠎⣩⣼⡳⠤⠼⡿⠟⣭⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢉⣵⣾⠷⣠⣤⣮⣯⠻⣤⣿⠸⣿⡙⠏⢏⣴⣿⣼⣦⣀⡻⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⠙⣷⣄⠁⣿⣆⣀⣁⣴⣿⡏⠈⠃⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⠿⠿⠿⠿⠷

⠀⠀⠀⠠⢤⡈⠇⠀⠀⠀⠀⠀⠀⠰⣂⠂⠞⡀⣠⢆⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⡀⢰⢂
⠀⠀⠀⠀⢹⣷⣬⡄⠀⢀⠘⢧⡖⢻⢐⡱⠔⠉⢸⢁⠹⡵⢡⣶⣄⣀⣐⠀⡀⠀⠀⠀⠃⠹⠟⠟⠙⠘⠁
⠀⠀⠀⠠⠊⠉⠉⠀⠀⢸⣹⢾⣿⠒⡲⣇⡠⣂⡡⢨⠔⢡⠀⡡⠙⠅⡼⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢀⣌⠋⣼⢿⣳⣯⠲⢤⢴⡄⠐⡿⣯⣖⣎⠉⠵⠤⣴⣃⠜⠭⣰⢀
⠀⠀⠀⠀⠀⠚⢊⣴⣿⣷⣤⢯⠃⡎⢰⣴⠭⣻⠾⢿⣿⣷⣧⣶⣰⣯⣨⣭⣏⣩⣿⠄⠀⠀⠀⠀⠀⠲⠦⢀
⠀⠀⠀⠀⠀⢞⣷⣏⣡⣿⠛⢻⣿⣯⢧⣷⣤⣿⣦⣼⣿⠛⣽⣦⡸⣾⣶⣿⡿⠻⠾⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠙⣧⣿⣿⣏⣹⣿⣿⣾⣿⣤⢿⣿⠿⣿⢻⡟⠻⡯⣼⠿⣿⣴⡏⠳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠚⠜⣟⣻⠿⡛⠉⢿⡏⠿⣬⠨⠪⢸⣇⡡⠞⠋⠁⠳⢞⠀⠙⠁⠀⡠⠀⠀⠀⠀⠠⣤⠴⠾⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠐⠳⣄⠁⠀⢀⡜⠝⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⣁⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⠉⠀⠀⠀⢠⣴⣾⡿⢹⡴⠶⠴⢿⣯⢷⡄⠀⠀⡼⠋⠉
⠀⠀⠀⠀⠀⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣦⠉⠀⠀⠀⢠⣿⡿⡇⣀⡜⠀⠀⠀⠀⢻⣿⠇⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⣴⠀⠀⠀⣸⡇⠉⠀⠀⢸⣿⠷⣫⣿⣇⠀⠀⠀⢀⠸⣿⣄⡀
⠀⠀⢠⣶⣋⣿⠗⠄⣀⣀⣴⠟⠃⠀⠀⠰⠿⠀⠤⠀⠀⠀⠀⢠⣿⣿⣿⡟⠿⠛⠁⠀⠀⠈
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡐⠐⠂⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠐⠂⠢⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠀⡀⠂⠀⠠⡔⠀⠀⠀⠀⠀⠀⢀⠄⠒⠰⠒⠢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⢠⠐
⠀⠀⠀⠀⠀⠀⡀⠁⠐⠀⠐⠈⢑⠈⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⢆⢀⠀⢀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⠈⠙⠢⠤⠴⠋⠀⠀⠀⢠⠀⠈⠁⠔⠒⠤⠀⢬⠀⡀⠀⠰⡁
⠀⠀⠀⡈⠀⠀⠀⠀⢃⠂⠄⠀⠂⢨⠁⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⠨⠀⠀⠀⠀⢀⠇⠀⠰⢀⠄
⠀⠀⠰⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⢘⠀⠐⢄⣠⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠑⢦⡤⠔⠋⠀⠰
⠀⠀⠀⠀⠀⠆⠀⠑⠉⠑⡄⠀⠀⠀⠑⠒⠛⠃⠀⢀⠦⠶⡋⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠓⠂⠀⠠⢀
⠀⠀⠀⠂⠀⢃⠀⠀⠀⢀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢳⠀⣧⠀⠀⠀⠳⣄⠀⡀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⢀
⠀⠀⢸⠀⠀⠀⠙⠒⠒⠁⠀⠈⠀⢀⠤⠤⠜⣹⠀⠀⠀⠀⠈⡆⠸⡆⠀⢰⠃⢀⠁⢀⣀⠄⠈⠉⠣⢴⠃⠀⠀⠀⢠⠁
⠀⠀⠘⠀⠆⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⢹⣄⣀⣀⡤⠖⠃⠀⠙⠶⠋⠈⢸⠀⠀⠈⢆⡀⠀⠀⠀⠀⠄⠈⠀⠜
⠀⠀⠀⠀⠰⠀⠀⠠⣄⣀⠑⣀⣓⢀⡀⠀⠐⠠⠬⠭⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠉⡏⠑⠢⢀⠀⢂⢺⡅
⠀⠀⠀⠀⠠⡀⠀⠠⠀⠀⡋⠀⠈⠀⠈⢣⠀⡄⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠋⠀⡏⢰⡤⣘⠀⡁⠸⠆
⠀⠀⠀⠀⠀⠑⢄⡀⢠⠀⠱⣀⠀⢀⣠⠃⡀⠀⡀⠀⣀⣼⠀⠀⠀⠐⠀⠐⠀⡶⠦⡤⠴⠶⠊⢰⠁⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢈⠉⠉⠀⡍⠀⠀⠈⠁⢀⠂⠀⠀⢀⠀⠀⠀⣸⠇⠀⠈⠒⠒⠒⠉⠢⣀⣀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠃⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠤⢀⣄⣀⣠⣏⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠬

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⠠⡍⣧⣼⣿⢟⣶⢲⡞⣾⣿⣥⣄⣤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣟⠯⣿⢿⣿⣿⣿⠻⣬⠃⡼⢋⣾⡳⠻⠎⣽⣮⣵⠇⠺⣣
⠀⠀⠀⠀⠀⠀⣀⣜⠆⡟⡞⢻⡷⢺⡋⢫⣜⣿⢿⣳⣿⣤⣾⢿⣟⣤⢬⡏⢟⣚⡿⣩⣻⣆
⠀⠀⠀⠀⡠⣴⣿⣫⣶⠶⢏⣿⣥⣵⠹⢽⣿⣷⣾⢯⣿⣿⣿⢿⣿⡛⣷⣷⢞⢿⢿⡯⡅⢫⢌⣦⠠⠄
⠀⠀⠀⢀⢵⠭⡋⣹⣟⠿⣾⣿⡿⣿⣳⣿⠿⡽⢽⡮⣗⣹⣿⣆⣋⣘⢱⣻⡿⣿⣿⣣⢼⡗⢺⣯⣶⣦⡄
⠀⠀⢠⣞⠛⢿⣙⢽⣁⡟⣿⣿⡽⠹⠼⡿⢿⣤⠿⣤⣟⣆⢿⡟⣽⡿⠻⣉⣻⠿⣙⡝⠻⣏⣿⢻⡶⣳⣀
⠀⠀⢈⢷⣾⡛⢹⣿⣿⣿⠿⠗⣱⠺⢬⣶⣶⢿⡜⣿⣿⣿⡧⡞⣺⣷⡾⣾⡟⠛⠾⡸⣽⠿⣷⣻⡤⢻⣺⠆
⠀⠀⠚⣶⣿⣿⣺⣏⣣⣤⣮⣾⠟⣻⣿⢉⠟⣛⡏⢹⣝⣟⣿⣿⣽⢿⡿⣻⡯⣾⣇⣘⣿⣷⠿⡛⢣⠞⣧⡀
⠀⠀⠀⢩⣯⣻⣿⡿⡿⢿⣷⡾⣾⣽⣷⣽⡻⣿⣿⣶⣶⡿⢟⣫⣽⣭⣷⠻⣽⣯⢿⣫⢿⡽⣿⣧⣮⣶⠻
⠀⠀⠀⠀⢼⣜⡁⣖⣿⣿⣬⣿⣅⣟⣻⣿⣹⡮⡻⠇⠉⠳⠉⠙⢟⣿⣿⡁⠹⣿⠟⣿⣿⡻⢍⡳⣹⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠋⠛⠊⠒⠫⠃⠀⢂⠘⠐⢐⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠙⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠡⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡠⠶⠀⠆⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣸⢷⢻⣟⠃⠀⠀⠐⡤⠆⢀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠋⠽⣻⣿⣯⡰⠠⠀⢰⠀⠀⢸⣜⠀⠂⠀⠈⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣰⢨⣤⢰⣧⠘⠏⢿⣁⣀⠀⣠⣸⠟⡯⠙⢦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⣗⢩⣝⠈⣻⣿⣿⣧⣌⣋⣈⢃⡺⠉⠀⣷⡀⠀⠐⠨
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣛⡷⣻⣿⠏⣿⡿⠭⣾⠻⣻⣦⣾⢿⠛⠻⡿⣿⡦⠀⠄⢀⠎⠓⠈⠡⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢈⣯⣷⣾⣿⣽⣓⣿⡃⢖⡋⠀⣴⡷⣜⢔⡀⢀⡤⣿⠃⠄⠀⢀⠐⠠⠀⠐⠛⠒⠀⠀⡤⠀⠘⢃
⠀⠀⠀⠀⠀⠀⢀⣼⣵⣻⣿⣿⣿⣥⣿⡟⡮⣴⣤⠀⠂⢈⡈⢘⡷⣞⣿⣄⠐⠀⢸⣥⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢈⣝⢩⣿⣿⣴⠋⣼⣿⡆⡠⣽⣿⣷⡴⢂⠀⠿⠅⠛⡦⠘⣣⣶⣶⣦⣤⠀⠀⢀⠰⡏⠀⠀⡀⠀⡃⠀⠆
⠀⠀⠀⠀⠀⠀⣀⣟⢻⣿⠟⣥⣄⡔⣌⣿⠿⠏⠙⢻⣷⠦⢀⢛⣂⠆⠀⢀⣩⡴⠑⠏⠸⠋⠚⠀⠀⠄⠄⠀⠉⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠐⠫⣿⣓⣿⣆⡾⠿⣓⣛⣯⡈⡀⠱⣆⡿⠳⠿⣮⣭⣅⡬⣅⣿⣿⡆⣦⡘⠺⠃⠀⠀⠀⠀⣶⠀⡀⠄⠀⠀⠇
⠀⠀⠀⠀⠀⠠⠞⣻⣿⣽⡏⠛⣶⣿⣷⣿⣖⣡⢀⢀⣀⢲⡀⣀⣸⣾⣷⢯⠝⣿⠓⣿⣿⣴⠂⡀⠀⠀⠀⣻⡐⠙⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⡿⣿⠿⣌⣻⣽⠗⠶⣷⣎⣽⣷⣿⠇⠹⣿⠀⢠⡏⠀⠉⠘⠛⠛⢶⢮⣠⠏⠣⢸⣦⠐⣄⠙⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠿⣿⣾⣿⣿⣷⡿⢋⡵⢺⣟⣛⠋⠈⢷⣤⣿⣃⢰⠇⠀⠀⠀⠀⠀⠀⢠⣹⡆⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡂⠘⠀⠀⠀⠀⢹⠆⠀⠀⠀⠉⠋⠀⠀⠀⠁⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡰⠱⢀⠀⣀⢰⠀⠀⢠⠚⣇⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠣⠼⡧⠿⡽⠿⠺⠁⠀⠀⠇⠫⠏⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣰⣟⣈⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⡿⠯⠥⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⢰⡆⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠐⠉⣠⠶⢋⣼⠖⠂⣩⣿⠯⡐⠒⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠖⣘⡛⠋⠙⠿⢇⣀⡴⠊⠁⣰⠟⡁⢀⡾⠉⢙⣦⠉⠳⣶⡂⠀⠙⢾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣄⠉⠑⠚⣔⣤⠙⢶⡤⡾⠛⢄⣠⠟⠠⣴⠛⠙⣦⡙⢦⠙⠲⣤⣀⢙⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣤⠛⢁⣙⢷⣯⡀⠀⠉⠻⣦⣰⡇⣿⣆⠻⣶⢚⣡⠶⢋⠉⡳⣮⢂⣀⡈⠛⣆⣰⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⡿⢿⡗⠚⠿⣥⡼⢁⣽⠿⢧⡾⠦⣭⣿⣿⣈⢶⣤⠍⠑⢾⢾⡟⠹⣛⠉⢟⣳⣦⣬⣽⡿⢯⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢾⡟⠻⠒⠚⠁⠀⠀⢸⣇⣸⣦⡞⠛⠛⠂⢤⠾⢿⣇⠢⡙⢦⡁⠀⠸⣿⠀⣹⠟⠉⠹⠇⠀⠈⠙⣶⡃⠨⢻⡄
⠀⠀⠀⠀⠀⠀⢠⢏⢺⡧⠲⠀⠀⠀⠀⠀⢸⣿⣻⠏⠀⠀⠰⠛⠛⠀⠀⠙⣶⡉⠄⠙⢦⣄⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠉⢳⡀
⠀⠀⠀⠀⠀⠀⣿⠂⢸⣧⣤⣘⣠⡐⠦⢠⡾⣷⣿⡄⠀⠀⠀⡀⠀⠀⠀⠀⣿⢻⣤⣀⠀⢻⣌⠏⠻⣇⠐⠀⠀⠀⠀⠀⣈⠏⢱⠆⠩⡗
⠀⠀⠀⠀⠀⢀⣯⣤⣿⣤⣙⡙⣿⠟⠲⣎⡃⠈⢻⣷⣥⠀⠀⡁⠀⠀⠀⣴⢿⣿⠛⠛⠷⣧⣽⣶⣆⡈⢻⣦⡄⢠⣤⡴⢿⡶⡄⢻⡄⣿
⠀⠀⠀⢠⣤⣼⠋⠀⠀⠰⠏⠙⢿⣧⢖⡈⠓⢤⡀⠸⣿⣿⡴⣶⣧⠶⢾⣧⢏⣠⣴⡟⠑⣿⠁⠉⠽⣿⣄⠉⢻⣤⠉⣀⡤⠤⢈⣋⡱⡿⢠⣴⠂
⠀⠀⠀⠘⣧⡿⠀⠀⠀⠀⠀⠀⠀⣿⢦⣁⠠⠈⢿⡀⢏⡉⠛⠖⠶⣦⡀⠙⢻⣿⠉⠉⠀⠀⠀⠀⢀⣿⣦⣑⠄⠻⣦⠋⣀⣴⠟⠁⣀⡴⠋⡴
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢠⣟⡀⠙⠳⣮⣤⡙⣜⠳⡄⢀⠙⢤⠉⠳⢾⣿⠃⠄⠀⠀⠀⠀⢠⣿⠾⠛⡷⣶⣬⣿⡟⠁⠄⣰⠋⡠⣤⠃
⠀⠀⠀⠀⠀⢻⡷⣤⣀⡀⣀⣴⢟⠉⣻⠷⢞⣶⣾⣿⣟⡆⠙⢦⡁⠈⣷⢦⣤⡍⠻⢶⣾⣤⠐⣨⡿⠷⠚⡍⢻⡏⢡⡏⢀⣱⠞⠁⡬⣲⠏
⠀⠀⠀⠀⠀⠀⠛⢆⣉⠋⠹⣧⢸⡇⠘⣶⡞⠁⠀⠀⣽⠙⠳⣀⠙⡴⠛⡀⣠⠶⢋⣴⠋⣩⠟⠁⣶⠖⠉⣴⣿⠀⣾⢠⡾⠁⢀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠙⢳⣴⣬⣳⣤⠀⣿⠃⠀⠀⠀⠀⠀⠀⢻⡎⢠⡬⠎⠁⣠⡞⢛⡟⢁⡤⠚⠁⢠⡞⢯⣹⢀⣿⣎⣴⣶⠛⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡋⠤⣬⡁⠈⣙⠰⢿⡁⠀⠀⠀⠀⠀⠀⣬⡖⢋⣠⣤⣼⠿⡄⣋⡴⣋⣤⠶⠞⡿⠇⣨⠿⠋⢉⣤⡤⠤⢈⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠑⠶⢷⣄⠑⢆⣀⠀⠀⢀⡼⠿⢋⣽⠟⢋⣀⣐⣿⣟⡓⠉⢀⡴⠏⣰⡞⢁⣤⡾⠋⠁⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⡀⠉⠳⢼⣿⠻⡙⢯⡁⠀⠙⣴⠟⠉⠉⣩⡬⠉⠉⠳⣏⠔⠚⠉⣡⢀⣹⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠻⢿⣗⠒⠿⠳⣜⡀⠙⢷⣬⠏⡀⠀⠘⡀⠀⠀⠀⠀⢿⢠⠿⠃⣀⡾⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⢳⢤⣈⠳⣄⠀⠹⡷⢀⠀⠀⠉⠀⠀⠀⠀⣼⢁⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠛⠳⠶⣜⣷⣤⣀⡀⣀⣀⡰⡶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠙⠳⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠙⠦⠀⠖⠀⠱⠶

⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣉⣟⣛⣛⣙⣋⣻⣎⣛⣹⣋⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣿⣭⣭⣭⣿⣿⣭⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠰⠐⡷⠀⠀⢠⣄⠐⡿⠂⢠⣦⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⡐⠃⠲⠃⣀⠘⢻⡔⠀⢠⣘⠋⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣴⠄⡘⠗⡈⢋⣁⢫⡴⠛⢤⡄⠰⢼⠛⠀⠀⠈⠛⣚⡁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣠⣿⣦⣝⢦⣩⢱⡇⣬⠛⢻⠁⣿⣿⣿⡆⣼⠛⠀⠀⠿⣾⣩⡄⠀⠀⠫⡀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠡⡹⣿⣿⢏⠠⠟⠉⢹⢷⣠⢘⡇⠙⠛⠋⢠⣿⡟⢡⣤⣠⡏⣨⣴⣯⡀⣤⣸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢷⠀⣦⠐⠟⠀⣄⢸⣷⠀⠀⣤⢠⣬⣹⡇⢦⠐⠂⢠⣄⣣⣦⠙⣟⠀⢻⣿⣿⠇⠠⣼⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣊⠀⠀⣠⡞⠉⠿⠙⢒⡶⣟⠁⢉⢹⣷⣣⣤⢀⠀⣤⣻⡷⠞⠛⠁⠀⡉⣁⠻⣢⠾⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠉⢀⠀⠶⣀⠮⡁⢸⣴⠝⠿⢿⡟⠉⠘⢃⢉⣹⣇⣴⡆⠀⠸⣷⣸⠾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⢛⣤⣹⣇⠰⠠⣄⢺⣋⣙⣶⣿⢸⣿⠀⠀⣤⡱⠻⢿⡉⢠⣦⢠⡞⠁⣤⠀⢀⣰⡿⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡄⠀⢠⡀⠙⠋⢴⡿⠁⢰⡏⠩⡅⠸⠏⢻⣿⣿⡇⢸⣿⣿⡧⠈⣿⣤⡽⠾⠳⣾⠉⠹⠯⠉⠳⣄⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣄⣿⡿⠀⠀⠀⢠⡄⠐⠛⣄⣉⠽⠶⣾⣿⣿⡇⠈⠻⠟⢁⣼⠟⠁⠀⡾⠂⣶⠀⢰⡶⠂⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢭⡙⡇⣠⡆⠰⡆⠁⠀⢰⣿⣷⣶⠀⠈⣿⣿⣧⢀⣠⣴⠟⢱⡄⠀⠀⢂⣠⠋⠀⠀⠀⠀⠙⡻⠟⣱⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣆⡉⢷⣫⡅⠀⣠⡖⠳⡈⠿⠿⠃⢠⣄⢻⣿⣿⣿⠟⠉⢰⣷⠀⢀⣀⣼⣁⣤⣸⠇⠀⠀⣾⡏⣠⣞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠘⢿⣥⣾⠁⠀⡀⠹⡄⠀⡀⢨⣍⢾⣿⣿⣧⡾⠃⣴⠟⠛⠛⢋⣥⠀⢻⠯⠉⣩⡍⠉⠣⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⡤⠉⣉⣀⠀⣠⢹⣦⣀⣀⣻⣴⣿⣜⡇⠈⠛⣿⣿⣿⣏⣠⣾⣁⠸⡇⢸⣿⣿⡷⠈⠓⣴⠛⠁⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⢀⢀⣱⠾⠚⣻⡋⠉⠉⣩⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⢠⣍⢁⣴⠎⠛⠛⣁⡀⠀⢠⡄⣠⡄⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠁⢤⡠⠞⠁⠟⠐⡿⠃⠀⠸⠿⠋⠀⣙⣿⣿⣿⣿⣿⡟⠀⣹⣷⠊⢰⡿⠀⣸⠿⠃⣀⣀⣥⢟⣃⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠹⣿⣿⣿⣿⣿⣿⡿⢿⣟⡛⠛⣿⡟⠛⠛⠠⢄⣀⠛⠆⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠁⠀⠘⠿⣿⠀⠉⠋⠀⠀⢰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣠⣽⣿⡗⣱⢂⡀⠀⠀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⡴⣯⢿⣿⣿⡩⠼⣿⣴⢾⣿⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣿⣛⡹⣿⣿⣿⣌⢂⠑⣩⠊⣻⣤⣾⣇⢄⢬⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠄⢀⢀⣠⢮⣿⢿⣿⣧⣬⣩⣿⢞⠁⡀⢢⢿⣿⣞⣿⣿⠺⠘⢘⣻⡁
⠀⠀⠀⠀⠀⠀⠐⠀⠠⢄⠸⣧⣾⢿⡿⣟⢪⣯⣽⣷⠒⢀⣿⣿⣧⣿⣷⣿⡧⠽⠍⡉⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣆⢈⣿⠙⡘⡭⠿⠫⡯⢷⣿⣖⢻⠿⣿⣯⣬⣻⡇⡊⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣈⢏⡿⣼⣴⣾⣷⣧⣿⣿⣅⣟⣿⣯⣿⢿⣭⠌⠩
⠀⠀⠀⠀⠀⠐⠀⣀⡄⢱⣿⣆⣨⡋⢓⣭⣧⣿⠿⢳⡛⣖⣰⣯⣿⣴⣿⡏⣿⣞
⠀⠀⠀⡀⠀⢀⡴⡟⢻⣯⣿⣷⣻⣾⠌⣛⣋⢾⡒⢋⡳⠚⣤⣼⡿⠿⡟⣿⣿⡟⠐
⠀⠀⠀⠀⠈⠉⢹⣿⡷⣷⣾⡿⠟⣹⣿⣶⣿⣸⣷⣾⠔⡀⢈⣿⣧⣳⣸⠽⡮⢽⣶⡆
⠀⠀⠀⠀⣠⣤⣽⠏⣿⣋⣙⣝⢿⣭⣬⣿⣿⣿⣿⡿⠀⠛⣽⣻⣿⣯⣭⣶⢃⣻⠛⣻⡇
⠀⠀⠀⠀⡘⣛⢷⣡⣏⣯⣿⣿⢿⣿⠻⣟⣿⣿⣿⣟⢠⡼⡿⣿⢿⣋⢟⣑⣼⣷⠥⣟⡗⣶
⠀⠀⠀⠀⠙⠁⢻⣿⠬⢛⣈⣿⣯⢧⣾⣀⢸⣿⣷⠟⡤⢼⢦⠾⢾⣯⣽⠿⣦⣄⡏⢡⠗
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠛⠋⠀⠈⠁⠤⢿⠇⠀⠁⠀⠀⠀⠈⠙⠩⡠⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⢲⣂⣀⡔⣢⢶⣾⠙⡗⢶⡿⣉⠉⣉⣀⡀⠀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⡙⠁⣠⣙⢽⠿⠀⢿⠟⠛⠻⠟⠿⠷⠦⠶⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠘⠌⠸⠭⠝⠃⠛⠦⠦⠂⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⡄⠰⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠂⠀⠀⢀⠔⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢌⠒⢀⢁⠀⠣⠀⠰⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠤⠎⠀⠒⠐⡡⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣁⠀⠀⠉⠀⠃⠀⡀⢦
⠀⠀⡀⠀⠀⠫⡑⢄⠀⠀⠀⠀⠀⠆⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄⢊⠔⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠂⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡴⠀⠄⠡⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠨⢀⣀⠀⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠃⠀⠑⠈⠀⡤⡄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠁⢉⠔⠁⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⡠⠂⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠐⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠆⠐⡀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡄⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠢⡈⠢⠀⢂⠀⢀⠖⡀
⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠈⠀⠀⠐⠂⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡅⠐⡑⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠀⣀⠄⢢⠎
⠀⠀⠈⠀⡀⠀⠀⠀⠀⢨⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠅⠀⠀⠀⠠⠊⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠
⣀⡀⣀⣀⣀⣀⣀⣀⡀⣀⣉⣉⢉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠈⠁⠀⠁⠀⠠⠀⠠⡀⠀⠀⢀⠀⠠⠆⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠢⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠊⠓⠀⠔⠢⠤⡠⠘⠂⠀⠀⠀⠋⠉⢠⠠⢄⠀⣀⡀⠂⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠅⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠓⠂⡀⠠⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠥⡬⠄⠠⡄⠀⠀⠀⠀⠀⠀⠂⠐⡄⠀⠀⠀⠀⠀⠸⢀⡠⢄⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠠⠓⠀⡀⠀⡤⠓⠢⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⠃⠀⢀⡀⠠⠂⠀⠀⠀⠁⠀⣄⡀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠷⡀⠀⠀⠀⣠⡎⠀⠀⢀⠀⠀⠄⠠⠤⠀⠀⠑⠐⠂⠀⠦⠀⠐⠀⠀⠈⡄⠀⠀⠀⠁
⠀⠀⠐⠀⠀⠀⠸⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠴⠤⠴⠀⠰⠉⠙⠒⠚⠃⠀⢠⠀⠀⠀⠆⣀⠀⠀⡔⠉⠉⠛⠉⠙⢢⠀⠤⠀⠀⠚⠄⠀⠀⠀⠀⠅
⠀⠀⡀⠀⡎⠀⠀⠀⠀⠀⠃⡀⠐⣀⠀⠒⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡊⠁⡀⠀⢇⠀⠀⠀⠀⠀⢠⠄⠀⠀⠧⢀⠄
⠀⠐⠀⠔⠁⢀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠘⢄⠀⢀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠠⠀⠀⠀⠈⢦⣄⣀⣀⠴⠋⠀⡀⡆⠀⠘⠂
⠰⠀⠀⡸⠂⠀⣀⠤⠠⢤⠤⠤⣄⠁⠀⠀⠀⠐⢄⣠⣤⡭⠇⠀⠀⢀⠀⣀⡜⠳⡖⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠁⠀⠀⠀⢀⠤⣤⠤⠀⠀⡄
⠠⠀⠀⢧⠀⠀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠞⠉⠙⣆⠀⢱⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⢀⡀⠀⠐⠁⢠
⠐⠀⠘⠠⠉⠀⠘⣄⠀⠀⠀⠀⣴⠃⠀⡄⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠸⡄⢈⣇⠀⠀⠀⠀⠗⢢⣀⡀⠆⠀⠀⠠⣀⢀⠜⡀⣀⠁⠀⠀⠀⠘⢀⠀⠈
⠀⠀⠀⢤⠀⠀⠀⠈⠙⠒⠒⠉⠀⠀⠀⠁⠀⣀⡰⢄⡤⠊⡏⠀⠀⠀⠀⠀⠀⣧⠀⢻⡆⠀⠀⣸⠀⠀⡇⠀⡀⢀⠄⠀⠀⠈⠣⣴⡝⠀⠀⠒⡄⠀⡌
⠀⠀⠀⠸⠠⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣀⡤⠿⠀⠀⠿⣦⡼⠃⠀⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⢀⡇⠀⠄
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⡀⠀⢁⠀⠀⢠⡀⠀⠀⠀⠀⡀⠈⠛⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠤⡴⢄⣠⠀⠀⠀⢠⣀⡼⠀⠂
⠀⠀⠀⠒⠀⡀⠁⠀⠀⠀⠣⠒⠂⡠⠐⠠⠤⠤⠤⣄⠀⠈⠁⠀⠀⠀⠲⡄⢀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠⠇⠀⡇⠀⠈⠀⡀⢀⡠⠀⡹
⠀⠀⠀⠀⠀⠑⢆⠀⠀⠠⠀⠐⢈⡇⠀⠀⠀⠀⠀⢸⠄⢠⠄⠀⠀⠀⠀⢹⡄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⣰⠇⣘⡥⢄⡉⠤⢄⠀⡹
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⡄⠀⢣⡀⠀⠀⠀⣠⠞⢀⠀⠀⡀⠀⢀⠀⣼⠀⠁⠀⢀⠁⠀⠀⠐⠑⡶⠤⣤⡤⠤⠴⠞⠁⢸⠁⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⣁⡀⠀⠈⠓⠒⠋⠁⠰⠈⠉⠉⠉⠂⠉⢉⠇⠀⡀⠀⠀⠀⠀⠂⠀⢠⡁⠀⠈⠳⠤⠤⢦⠤⠻⣄⠀⠀⠀⠀⣠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠢⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⡘⠀⠐⠀⠀⠘⠀⠆⢰⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠀⠀⠄⠀⠀⡜⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢃⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⣸⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣧⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⠣⢰⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢂⠛⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡄⠀⡄⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢰⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣓⣲⣤⣼⣦⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣒⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡿⠿⡿⠛⠿⠿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠘⢿⣆⠀⣀⣤⡄⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢃⣀⡀⢿⣷⣴⡿⠀⣀⢀⠔⠒⠲⡇⠰⣯⣅⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠿⢿⡦⢤⠶⠿⠛⠁⠀⠀⡁⠀⠀⢨⣿⣦⡄⠀⠘⡆⢮⡭⠓⢤⡘⢁⠀⢀⣴⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠈⣱⠟⠛⠉⢙⡓⠾⣦⣄⡘⠿⠿⠃⠀⢀⡿⣿⣿⡇⢸⠇⠘⢧⡿⠋⠀⢠⣿⢀⡀
⠀⠀⠻⣦⢠⣿⡿⠃⠀⠀⢰⡇⠰⢶⣶⣬⢡⠖⠉⣯⡙⢷⣄⠀⢀⡼⠁⣉⠉⣰⠿⡶⠦⣔⠠⢶⣶⠼⠏⠘⣷⢀⣀⣀⣀
⠀⠀⠀⠈⢛⣋⣄⠀⠀⢀⣤⡷⣀⠀⣀⡔⢻⡀⣿⣿⣿⡇⠻⣷⡟⠀⢀⣽⠟⣅⣼⠇⢠⣼⣿⡅⠀⢀⠤⠐⣩⠙⠛⠛⠁
⠴⣶⣶⣇⠸⣿⣿⠃⠠⠿⠟⢀⡴⠛⢓⣴⣆⢳⡜⢛⣛⡀⠀⢿⣷⣶⡟⠁⢷⠙⢃⣀⡈⠿⠿⡷⠊⢉⣳⣾⣋
⠀⠀⠀⠈⠓⠦⢥⣤⠴⠶⢤⣿⠁⠀⢻⣿⣿⣼⠟⠉⢩⡍⢳⣸⣿⡟⣐⣭⡝⢇⠹⠿⠇⠀⣰⠃⣄⢺⣿⣿⣿⣇
⠀⠀⠀⠀⣠⣼⣾⣤⡀⠀⠀⡙⢧⣄⣀⣉⢱⡇⠀⠀⠸⣿⠀⢻⣿⡇⢸⡋⢁⣾⣠⣤⠴⠊⠁⠸⣿⡌⠻⠿⠟⢸⡇⢀⣴
⠀⠀⠀⠀⢿⣿⣿⣿⠓⠶⠼⢃⣀⡈⣭⠉⠛⢷⣄⠛⠛⠁⢀⣿⣿⣇⣠⡶⣛⣭⡝⢩⠍⠓⠢⠤⠈⠱⣤⡻⠶⠮⠱⠟⠋
⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⢀⠛⠋⠀⠘⠴⠟⠀⠙⠻⠶⣾⣿⣿⣿⣿⡏⠀⢿⣿⣿⣄⡴⠚⠉⠉⠳⣤⣀⠁⢀⣠⡂⢀⣴
⠀⣤⣄⡀⠀⠀⠀⠀⣠⠴⠾⠶⠤⢤⣤⠷⠦⠤⢤⣤⣀⠈⣻⣿⣿⣿⠷⠦⠤⠽⢊⡾⠁⢰⡄⢈⣷⣿⡌⠉⠉⠀⠈⢫⠁
⠀⠀⠉⣡⡤⠴⠖⢻⣡⡄⠀⠀⡞⠉⠉⠻⣦⠄⠀⠀⠙⢷⣿⣿⣿⣿⠀⠀⢀⣴⠟⠐⠲⠾⠃⣿⣿⣿⣿⡇⠀⣦⣀⠊
⠀⠀⢀⣿⡗⠀⠀⣾⣿⠀⠀⢸⡅⠀⠀⣾⣿⣿⠆⠀⠀⣸⣿⣿⣿⣿⣶⣾⣿⣿⣶⣤⡴⠊⣀⠈⠿⢿⣟⠀⠸⣿⣿⠇
⠀⠀⠀⠛⠁⠀⠀⠈⠱⣦⡤⠲⢿⣤⣀⣈⣛⣫⣴⠾⠿⣿⣿⣿⣿⣿⠟⠩⣾⣿⡦⠈⢉⡳⢬⡳⠶⠿⠟⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠈⠉⠉⠉⠁⠀⠀⠀⠘⣿⣿⣿⡏⠀⠀⠙⠛⢁⣀⡘⠁⠀⢳⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⢩⡽⠦⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠⠀⠠⡀⠀⠠⠀⠂⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠀⠐⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠰⠈⠀⢀⠢⣀⠀⠀⠀⠀⠀⡖⠉⠉⠁⠈⠂⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠁⠊⢀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠵⣄⠀⢀⡠⠀⠀⠀⠀⠀⠠⠀⣈⢀⣂⡐⠄⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠤⠀⡄⠀⠀⠰⠒⠒⠑⠊⠀⠀⠈⠁⠀⠀⠂⠀⠈⠄⠀⠈⠀⠈⠀⠈⡆⠀⢀⠈
⠀⠈⠄⠁⠀⠀⢀⠀⠂⠀⠀⠀⢸⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⠴⠃⢠⠀⠘
⠀⠀⠀⠀⢠⠄⠀⠔⠂⠌⠀⠀⠀⠂⠴⠾⠁⠀⢀⡠⡔⠓⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡔⠤⠀⢀⠐
⠀⠀⠁⠀⠀⡀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠹⡀⢧⠀⠀⠀⢢⡀⠀⡀⠀⠀⠀⠀⠃⠁
⠀⠀⢄⠀⠀⠈⠒⠒⠊⠀⠈⠀⢀⠤⢠⠜⡏⠀⠀⠀⠀⣇⠘⣆⠀⢠⠁⠈⠁⣀⡀⠀⠉⠳⢤⠂⠀⠀⠀⡈
⠀⠀⠘⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠤⠔⠋⠀⠙⠶⠃⠀⢠⠀⠀⠱⣄⠀⡀⠀⠀⠀⠈⢠⠂
⠀⠀⠠⠀⠖⠀⠀⠢⠤⢀⠠⢑⡀⣀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⡇⢹⠉⠑⠀⠀⠀⢺
⠀⠀⠀⠀⢲⠀⠀⠀⠀⢈⠀⠀⠀⠀⡧⠰⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⢀⡼⠀⠧⠬⠤⢄⠘
⠀⠀⠀⠀⠀⠑⠀⠀⠆⠘⠢⢄⠤⠜⡁⠤⠀⠀⠤⢰⠃⠀⠀⠀⠀⠀⢨⠛⠳⣖⠛⡉⢠⡇⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡟⠀⠀⠈⠁⠈⠁⠈⠢⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠄⠀⢈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠸⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⠀⠀⠀⠀⠀⠀⠀⠘⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠄⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠱⠀⠀⠀⠠⠀⠀⠀⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣣⣤⣠⣄⣀⣮⣠⣀⣀⣀⣀⣀⣀⣠⣤⣴⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠃⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠀⠘⠁⠄⠀⠀⠆⠀⠂⠁⠀⠤⢀⠁⢆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⢘⡄⠀⠀⡙⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⠀⠀⠐⠐⠄⠀⠀⠀⠀⢄⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠈⠘⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠊⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠀⢠⣧⡀⣹⢿⡇⠠
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⣆⡀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠙⢏⠙⠌⣷⠀⣦⠂⠀⠀⠀⢀⣀⠠⠄⠀⠤
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠶⠀⢂⠀⢸⣷⠇⢠⡴⠚⠁⠀⠠⢦
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠠⡤⠀⢀⡀⣀⡈⠁⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⣨⠷⠦⢥⣄⠀⠀⠀⢠⡆⠀⠉⠿⠀⠀⣀⣤⣴⡦⣤⣤⣄⡤⠄⠈⠀⠀⠈
⠀⠀⠀⠀⠳⠀⠀⠀⠀⡤⠀⠄⢀⠀⠀⠈⠀⠀⠐⢊⡀⠀⠀⠀⠉⠑⠦⣀⠉⠁⠀⠀⠀⠀⠀⠟⠉⠉⠁⠣⠀⡀⠈⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⢄⣈⠀⠀⠘⠸⣇⠀⠀⠀⠀⠀⣿⡆⠀⣴⢦⣀⡀⠀⠀⠀⠀⠀⠂⠀⡁⠠
⠀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠑⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠑⠀⠏⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⠀⠐⠂⠀⠀⠀⠀⡠⢿⡋⠙⠋⠉⠉⠉⣒⣶⡶⣞⡓⠂⠀⠀⠀⠒⠿⣤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⣤⠁⠈⠃⠀⠘⣁⠔⠁⠀⠀⠉⠑⠦⣤⠀⠀⠀⠉⢲⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈
⠀⠀⠀⢰⡀⠀⠀⠀⠄⠀⠁⠀⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⠀⠀⠉⡉⠁⢈⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⣅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠃⠈⠁⢀⣈⣉⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢈⣄⡀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⡉⠁⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠘⠅⠢⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⣽⢇⣆⡀⠀⡀⠀⠐⠲⠛⠛⠛⠗⠤⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⣀⠀⠀⣠⠀⠀⠀⠀⠹⢿⡄⢀⣤⡄⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢋⣀⡀⠹⢿⣴⡿⠀⣄⣠⠒⠒⠲⡀⢶⣧⣄⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠻⠷⠆⡐⠛⣛⣁⣀⠀⢀⠀⠀⣸⣿⣷⡄⠀⢱⡰⣬⡛⠲⣌⢁⡀⢀⣴⠀⠀⣠
⠀⠀⡀⠀⠀⣠⣴⡆⠀⠀⣨⠟⠉⠉⠉⡟⠛⠶⢤⣜⠿⠟⠀⠀⣸⢻⣿⡿⢀⡏⠀⠙⠞⠋⠀⢰⡿⢀⡀
⠀⠀⠻⣆⣼⡿⠟⠀⠀⠀⣿⠀⠛⠿⠶⢱⠋⣀⣷⣈⢻⣦⡀⣰⠃⢠⣄⣠⠟⣒⠒⢶⣀⡻⠷⠺⠃⠘⣇⣠⣤⣤⠄
⠀⠀⠀⠀⣭⣴⣆⠀⢀⣴⡾⠢⢄⡤⠖⠸⣄⢿⣿⣿⠃⠹⣿⠃⢀⣴⢟⢱⣼⠏⠀⣾⣿⡇⢀⣤⡂⢈⡴⠈⠉⠁
⠘⠿⠿⢧⡹⠿⠏⠀⠘⠋⢀⡶⠉⢩⣷⣧⢹⣎⡭⠥⢄⡀⣿⣿⡿⢁⣘⣃⢡⣴⣄⠙⠛⡗⠁⣠⣽⣿⣥
⠀⠀⠀⠀⠉⣟⡲⠛⠋⠛⠺⣇⠀⠘⠿⠟⡾⠁⠀⣼⡆⢱⣿⣿⠃⣱⡷⢘⡄⠛⠃⣀⡼⠁⣦⠹⣿⣿⣿⢠
⠀⠀⠀⠀⣾⣿⣿⣷⣀⡀⣠⠙⠳⢤⣤⣼⣇⠀⣠⣼⠷⠀⣿⣿⡇⠿⣠⡾⠶⠶⠯⣁⠀⠀⠻⠇⠉⣍⣁⢸⢀⣶⠏
⠀⠀⠀⠀⢻⣿⣿⠏⠈⠉⢡⣴⠆⢸⢆⣠⠝⢶⣬⣀⣀⣼⣿⣿⣷⡞⢡⣾⣿⡔⠂⣠⡭⠭⣅⠈⠳⠌⠉⠁⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣄⠀⠀⠀⣊⡁⠀⠀⠈⠙⠻⣿⣿⣿⣿⣀⠈⠻⣿⢧⡞⢁⡀⠀⣌⣿⠲⠤⠴⠚⠤⠸⠛
⠀⠛⠓⢄⠀⣀⣠⡴⠋⠁⠉⢉⡽⠛⢯⡍⠉⠙⠛⢶⣄⣿⣿⣿⡏⠉⠉⠉⣠⠟⣀⡘⡇⣰⣾⣿⣧⡀⠀⡀⢀⠇
⠀⠀⢠⣾⡇⠁⢀⣵⡏⠀⠀⡏⠀⠀⣨⣽⣤⡀⠀⠀⢻⣿⣿⣿⣧⣠⣴⣾⣏⣀⣀⡩⠀⠹⣿⣿⡿⠁⢰⣿⣶
⠀⠀⠸⠿⠁⠀⠈⠛⣁⠀⣀⣳⣄⠀⠘⠿⠟⣁⣤⣶⣾⣿⣿⣿⣿⡿⢻⣿⣏⠛⠳⢤⡐⢦⣨⣼⣶⠆⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣤⡈⠙⠛⠶⠞⠛⠉⠉⠉⢻⣿⣿⣿⡏⠀⠸⠿⠟⠀⠀⠇⠈⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠈⠛⣲⣄⣀⠜⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷
⣿⣿⢿⠿⡻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⣤⣴⠒⠀⣴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⣛⣬⣝⣳⣜⢑⡯⣾⡯⠿⣶⣟⡤⢠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣍⣾⣧⣜⢇⣷⡙⣭⢑⣠⢗⡶⢻⠓⠲⣿⢿⣶⠤⣼⣴⠴
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢿⣼⣿⣿⡏⡯⠿⢦⠴⢭⣟⡦⡗⠛⢾⢉⣴⠧⣙⢶⣿⣿⠃⣦
⠀⠀⠀⠀⠀⠀⢐⣦⡛⣭⣿⣿⣿⣷⢹⢧⡤⣷⡋⠙⡏⢿⣽⣗⡍⢉⠿⣷⢮⢮⡩⡞⢿⢷⡇⢀
⠀⠀⠀⠀⠠⠷⠾⣢⣿⣿⣦⣼⣟⠿⣼⠓⣆⣰⣽⣻⣞⡿⣿⣷⣯⣇⢼⣬⣾⣇⣸⣽⣏⢉⣿⣯⡀
⠀⠀⠀⠀⢰⣼⣮⣿⠛⣿⣿⣿⣽⣧⣏⣲⣽⣧⣀⣿⣴⣈⣿⣿⣿⣻⣏⢙⣿⣿⣵⣿⣿⡿⣯⣗
⠀⠀⠀⠠⣭⣺⣿⣿⣿⠿⣿⣤⣾⣻⣿⡋⢻⣿⣿⣿⣿⣿⣿⣿⣦⣿⢛⣷⣽⣿⢻⡿⣏⣶⡁
⠀⠀⠀⠀⠹⣻⢿⣿⣿⣤⣿⣿⡿⣛⣿⣿⡟⢿⢿⣍⢹⣤⢿⠺⢹⣏⠽⣏⡳⣟⠿⣧⣜⠃
⠀⠀⠀⠀⠘⠹⢫⣿⣨⠿⠫⢋⡈⠻⣇⠚⠓⡖⠐⠛⠀⣿⣤⠞⠋⠁⠀⠉⠛⠧⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠉⠉⠙⢷⡀⡇⠀⠀⡼⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⢸⢏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠛⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠁⠺⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠉⠁⠂⠉⠀⠀⠐⢀⡀⠀⠀⢀⠄⠤⠆⠠⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⡀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⡠⢄⡀⠢⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡠⠂⠴⠘⣆⡠⠐⡤⢄⡠⠖⠂⠀⠀⠀⠃⠉⢢⡀⣀⠀⣀⠀⠤⢀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣈⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠀⠳⠆⠀⢀⣀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⢘⡀⠀⢴⠎⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡄⠀⠀⠠⠈⠐
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡆⠈⠁⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣀⣋⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢘⡀⢀⣄⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠐⠀⠀⠀⢀⠾⠀⢀⠀⢀⠹⢤⡀⠀⡀⠀⠀⢠⠀⠀⢾⠁⠀⠀⠁⠀⠀⣷⠀⠀⠀⠀⠀⠆⠠⢆⠁⠐⡀⢀⡄⠀⠀⠈⠃⠀⣀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣀⠦⠀⠀⠈⠀⠉⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⡀⢀⡀⠈⠐⠣⠤⢄⠀⢠⡀⠀⠀⠈⠑⢄⠀⠀⠈⠐⢀
⠀⠀⠀⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣄⠃⡜⠳⠦⠤⠴⠋⠁⢄⠀⠈⠠⡌⠀⠀⠁⣠⠒⠒⠶⠔⠦⢤⠀⢀⡄⠀⠠⢎⠀⠀⠀⠀⢸
⠀⠀⠄⠀⡐⠉⠈⠀⠀⢀⡺⠄⣐⡇⠀⠠⠤⠒⡏⠉⠋⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⠝⠋⠀⠀⡇⠀⠀⠀⠀⠀⠈⡗⠀⠀⢠⠀⢈⠀⠀⠀⠀⠀⢰
⠀⢠⠢⣀⠃⠀⠀⠀⠀⠀⠀⢲⠀⠈⠁⠀⠀⢰⠅⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠂⠀⠃⠀⠰⣄⠀⠀⠀⢀⡼⠃⠀⣀⠉⢀⡇
⢀⠀⠀⢱⡄⠐⠀⠀⣀⡙⠀⣀⠀⠼⠀⠀⠀⠈⡄⠀⢈⣒⣤⠎⠀⠀⠀⠀⠀⣰⣁⡤⠀⠀⠀⠀⠈⠀⠀⠀⡠⠉⣛⠖⠛⡉⠀⠀⢀⠉⠀⠈⠀⠀⢀⡀
⠆⠀⠀⡆⡀⠀⠰⠏⠀⠈⠋⠀⠙⣦⠀⠀⠀⠀⠈⠉⠙⠟⠉⠀⠀⢀⡶⠶⢾⡁⠈⣇⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⠀⠀⠓⠀⠘⣋⠙⡋⠀⠀⡼⢀⠀⠀⠀⠘
⢠⠀⢸⡉⠦⠀⠸⡀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⣧⠀⢻⡄⠀⠀⠀⠈⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠘⠀⡇⠀⠀⠀⠀⡇⠀⠀⡄
⠀⢀⠀⠈⠀⠀⠀⠹⢦⣀⣄⡠⠞⠁⠀⠻⠀⠀⠀⠀⠀⠠⢶⠆⠀⠀⠀⠀⠀⢸⡆⠘⣷⠀⠀⠀⢠⠃⠙⠖⠚⠉⠀⠀⠀⠲⠴⣥⠂⢰⠁⠀⢀⠀⠀⠈⠆⠀⢀
⠀⠀⡁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠚⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡁⠀⠘⣆⠀⢀⡆⠀⠀⠀⠀⠦⢴⠃⠀⠀⠀⠈⠛⠃⠀⠀⠉⡌⠀⠸
⠀⠀⢁⠈⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠠⠀⠀⠈⠀⠀⢧⡀⣀⣀⠠⠄⠛⠁⠀⠀⠙⠓⠊⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⡀⠀⠀⠀⠄⠀⠀⠐⡞⢀
⠀⠀⠀⠀⠀⠑⣤⠀⡀⠀⣤⠀⡀⠖⠋⠘⠲⠄⠐⠀⠀⠁⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣟⠑⠲⡄⠀⠀⠲⠢⢴⡁⠉
⠀⠀⠀⠈⠐⣎⠀⠠⠂⠀⠈⠙⡉⣴⠊⠉⠛⠋⠙⠲⡄⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠄⣀⣀⣀⡴⠏⠀⣿⢀⡄⠀⣬⠤⠐⠀⢺⡁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⠀⠈⠀⣮⠀⠀⠀⠀⠀⠀⡗⠀⠛⠀⠀⠀⠀⠀⣿⠀⠆⠀⠀⡆⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⢀⣰⠃⡤⠛⠓⠶⠒⠒⢄⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⠀⢴⠀⠘⢦⣀⡀⣀⣠⢞⢁⣄⡀⢠⡀⢀⣤⢠⡟⠀⠀⠀⠠⠙⠀⠆⠘⠈⡟⠓⢶⡖⠒⠛⠋⠁⢸⡃⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⡀⠀⠈⠉⠉⠀⠈⠇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡀⢀⠀⠀⠀⠀⣸⡅⠀⠀⠙⠒⠚⠳⠖⠙⢧⣀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠐⠂⠐⠊⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⠋⠀⠇⠸⢸⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⡰⠁⠀⠀⢠⠀⠀⠀⡏⢱⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠁⠀⠀⠀⠀⠀⠀⢀⢹⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡟⢣⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⢷⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⠀⡄⠀⠀⣰⠀⠀⠀⠀⠀⢀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣼⢻⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡿⠄⡻⠀⠸⠀⠀⢠⠁⠀⠀⠀⠀⠾⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠐⢀⠇⠀⠀⠐⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠁⢸⠀⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠈⠀⣸⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠤⢦⣠⣾⣀⣀⣼⣣⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠤⠶⠗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠠⠄⡀⠤⢀⠀⢀⢀⠤⠄⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⡠⠤⠤⢀⡡⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢺⡇⠒⠄⠀⠘⠀⣀⠤⣔⡤⢄⠀⠀⠀⠀⠈⠢⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡠⢒⡿⢈⠑⡀⠀⠀⠠⠐⠀⠀⠀⡀⠀⠀⠐⠁⠀⠉⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢥
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠀⠀⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⡑⠠⠀⠊⠀⠀⠀⠀⠡⣀⠀⡰⠔⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠂⠔⠒⠈⡀⡄⠁⠁⢀⠤⢤⣧⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠩⠿⠉⠑⡀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⣀⠜⠋⡉⠐⠂⠑⢄⣀⠀⠀⢀⢢⣨⣀⠀⠀⠀⢊⢀⡄⠁⠀⠀⠁⠀⠀⠀⠀⣀⠀⢀⠸⡘⠆⠀⠀⢠⠣⢄⠀⠀⠀⠈⠱
⠀⠀⠀⠀⡊⢀⠔⠐⣴⢃⠲⠄⠀⠀⠎⠁⠘⠚⠀⠈⢳⠐⡀⠈⠢⣀⠀⠀⠈⠀⠀⢠⠤⠎⠀⠉⠃⠀⠈⠀⠐⠀⠁⣀⠀⡍⠉⠀⠀⠀⢇
⠀⠀⠀⢀⠅⠈⡄⠀⠀⢠⡁⠄⠀⠀⡀⠑⡀⠀⠀⠀⡘⠀⠉⠂⢀⠄⡀⠠⠀⠀⠀⠀⢄⠀⠀⠀⢀⠠⢴⡤⢄⠀⠊⠀⠹⠏⠙⣦⢄⠀⠀⠇
⠀⠀⠀⠸⡀⠀⠈⠢⠐⠒⠊⢀⠀⠀⠈⠂⠌⠄⠠⠚⠀⠀⢠⠒⠁⠀⠀⠀⢀⠊⠀⠽⠎⠁⠢⠀⡆⠀⠈⠁⡀⠁⢠⡀⠀⠈⢂⠃⠀⠁⠚⡀
⠀⠀⠀⠀⠇⠀⢀⣀⡠⠄⡠⢬⡎⠉⠑⡀⠀⠀⠀⠀⠀⢰⣾⠒⠢⠄⠀⠀⣸⡀⠀⠀⢀⡓⢠⠁⠐⢄⢀⣀⡠⠂⠀⠈⠉⠉⠁⠀⠀⠀⠐⠥⡀
⠀⠀⠀⠀⠱⠀⡇⠈⠀⢸⠐⠄⠀⠀⢀⠇⠀⠀⠀⢠⠉⡀⠋⠀⠀⢸⠋⠛⠀⡑⢠⠄⠬⠴⣧⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⣀⣄⡀⡀⠀⠀⡀
⠀⠀⠀⠀⠸⠊⠀⠀⠀⠀⠑⠂⠀⠒⡚⠀⠀⠀⠁⢈⠠⡑⠂⢀⢀⠌⢀⠐⠊⠠⠁⠀⠠⠊⡠⠑⡄⠀⠀⠀⠀⠠⡜⠀⢠⠫⠈⠛⠀⢸⠀⠀⠱
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⠀⠉⢇⠈⡄⠈⠀⠀⠠⠐⠁⡠⠊⡀⠘⢣⣀⠀⠀⢀⠔⠀⠀⠀⠢⢗⣀⣀⠜⠀⢀⠜
⠀⠀⠀⢐⠁⠀⠀⠀⠀⠤⠰⣸⠆⠠⡀⠀⠀⠀⢠⠈⠡⡀⠀⠈⡄⠰⡟⠀⠀⠀⢀⠌⡠⠊⢀⠔⠁⠈⠑⠒⠁⠀⠀⠀⢀⠀⠀⠀⡠⡀⢀⠜
⠀⠀⠀⠈⠢⠤⡄⠀⠀⠀⠀⠉⠀⠀⠁⠀⡰⠒⠃⢄⠀⠈⠶⡉⠃⠀⠀⠀⠀⠀⠟⠋⢀⠔⠁⠤⠂⠤⠤⠔⠀⠂⠤⠐⠁⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠣⢀⣠⣀⠔⠉⠋⠀⠀⠀⠀⡱⢄⠀⠉⠒⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠊⠀⠁⠈⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠉⠓⠊⠁⠊⠉⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠒⢴⠶⡲⢏⠣⢄⣀⢠⠦⣤⢀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⣒⠣⣤⠑⢿⡉⢁⠼⣟⠢⢾⠂⡴⣤⢰⡋⡻⡝⠏⣌⠱⠦⠤⢠
⠀⠀⠀⠀⠀⠀⢠⠔⠒⠚⣇⡀⣉⠶⡈⡄⢭⠏⡴⡀⡰⢆⡤⢦⢞⣢⠐⢚⡴⢋⠐⡀⠒⠷⠄⡅
⠀⠀⠀⠀⠀⠀⢨⠒⢛⣫⣡⣍⣨⡋⣱⢙⣪⠹⣍⢿⠐⡬⣴⡜⢶⡙⣗⢂⡤⢝⡛⠛⠯⡄⠳⠰⣄
⠀⠀⠀⠀⠀⢠⢀⣈⣰⢦⠛⡵⢙⣨⣏⡀⠛⡝⠻⣌⣿⠆⡐⡚⢛⡿⣥⢾⡻⢭⡿⣤⢳⠤⡯⣰⠋
⠀⠀⠀⠀⠀⡼⢁⢳⢯⢁⣀⡽⠀⢀⢝⢶⡰⠃⠄⢎⣻⢼⢉⣷⣮⣾⡵⠈⢗⠜⠠⢜⣷⡼⡗⠽⣈⡅
⠀⠀⠀⠀⠀⢩⡚⠹⣁⠓⠿⣴⣈⣑⣦⠖⡩⢳⣤⣆⣿⡎⣽⣣⣾⢫⢒⣸⣿⣀⣫⣨⠴⣊⢳⡆⢧⡑
⠀⠀⠀⠀⠀⠀⣟⣠⠉⡅⠉⣁⠄⡲⢉⠹⠷⠶⢶⣬⣻⣧⣿⣣⣴⡿⢍⡉⠣⠩⠟⢒⡐⡯⠬⠙⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠀⠀⠀⠀⠉⢿⣿⣿⡟⠁⠀⠀⠁⠀⠐⠀⠀⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠿⢿⣦⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠀⠀⠀⢀⣀⣠⣄⣀⡰⣶⠇⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠐⠋
⠓⠆⠓⠒⠂⠩⡤⠄⠒⠂⠸⠀⠀⠀⠀⠀⠀⠸⣤⣼⣧⡝⢁⣤⠀⠀⠀⣴⣯⣭⣶⣋⡱⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢐⡶⠾⣇⡔⠓⠀⢀⡈⣻⣿⣿⠟⠁⠀⠀⠀⣩⣿⣹⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⢾⣷⣶⠿⠿⣿⣇⠀⡄⠐⠒⠁⠀⠀⠀⠀⠀⠈⠟⡀⠀⢠⣦⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⡃⠶⠋⡋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⡒⢛⣶⣧⠤⠆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣶⣼⣿⠲⢦⣄⣘⣁⠀⡀⠀⠀⢡⠄⠀⠁⠀⠀⠙⠋⣿⣏⢛⡿⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢀⡉⠄⠘⣿⣁⣴⡄⠀⠙⢿⣿⣿⣅⠒⠚⢂⡀⢻⡆⠀⠄⠀⠀⠈⠉⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢈⡁⢀⠀⠉⠉⠉⠁⠀⣀⣶⢾⣿⣿⡷⣾⣿⡟⠻⡏⠀⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢄⠀⠀⠻⢿⣬⡽⠉⠀⠀⠿⣷⠚⢁⠀⠀⠀⠀⠀⠀⠢⢴⣖
⠀⠀⠀⠀⠀⠀⠀⢊⠀⠠⠀⠀⠀⠀⠐⠚⠙⠒⠀⠂⣠⠶⣴⣷⣧⣶⣄⣠⠀⢐⡒⠀⣏⢀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⢋⠀⠀⢶⣲⣏⣋⠀⢀⡤⠚⢛⢧⠸⡟⠋⢀⠘⠉⠃⠡⠀⠹⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣹⢻⠿⢪⣦⣓⠲⠄⠀⠀⢰⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠛⢯⣄⣀⠀⠀⢼⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣦⣄⣀⢀⣆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣴⡏⣧⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠞⠉⠀⢀⠀⣠⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢰⢀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⢸⣿⣄⠈⡟⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢻⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⠤⡄⠀⢾⣿⣿⣆⡄⣀⢠⡷⠄⠀⠀⠀⢠⣶⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣰⠇⠀⠈⠈⣿⡇⠅⠉⠀⠀⠀⠀⠀⠀⡸⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠠⣶⠲⠀⠀⠟⠀⠀⠀⠀⠀⠀⢠⡏⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠷⠖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣶⣄⠀⠀⠀⢰⡄⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣄⣿⠃⠡⠞⢁⣈⡛⢀⠀⠀⢈⡱⢭⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⡀⢰⣄⣿⠇⠀⠀⠐⠎⢀⢀⠀⠀⠉⣡⣾⠀⠙⣖⠉⠱⢀⡬⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠉⠀⠋⠀⠀⠀⠀⢠⠇⠀⠀⠸⠟⠃⠀⠀⠸⡄⠀⣬⡙⠂⠀⠘⢇⠀⠞⣱⡿⠁
⠀⠀⠀⠀⠀⠐⠛⠷⢀⡍⠁⠒⠢⢄⡀⠀⢸⠘⠛⠀⠀⠐⠦⠔⠂⠒⣧⠀⠘⠿⢄⡞⠁⣈⣑⡀⠰⣦
⠀⠀⠀⠀⠀⠀⠲⠦⠸⠁⢰⣿⣷⣷⠈⠳⢼⡀⠀⠀⠀⣾⣶⣿⡆⠀⢿⠀⠀⠀⢸⠀⢸⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣾⡿⠂⡀⠀⠻⠿⠟⠀⠀⠀⠙⣆⠀⠀⠻⠿⠟⠁⠀⢸⠀⠀⣤⢸⡇⠀⠉⠙⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠦⣀⣀⣀⡤⠤⣤⣀⠘⣧⠀⠀⠀⠀⠀⢦⣸⠀⠀⠙⣸⠁⠀⠀⢠⠖⣀⠘⠵⠿⠋
⠀⠀⠀⠀⣤⠀⣿⠀⢉⡄⢂⣉⠀⢡⣀⠀⠀⠈⠑⢾⡆⣾⠟⠀⠀⢀⣿⡴⠖⣟⡉⠉⠉⠉⣭⡁⠀⢿⣷⣄
⠀⢰⣦⠀⣀⣈⣑⢄⠉⠀⠘⠁⠆⠘⢿⣷⠀⠀⠀⠈⣧⠀⠀⠀⣴⣿⣉⣀⣀⣈⠁⠀⠀⠀⠈⠃⠀⠀⠉⠛
⠀⣈⡻⠸⣿⣿⣿⠊⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡀⠀⣼⠏⠀⢀⣀⡀⠉⠑⠔⣛⠁⠀⠀⢀⣤
⠀⠉⠉⢒⠩⠭⡩⠤⠴⠛⠛⠛⠛⡻⠓⠶⣦⣌⡇⠀⣿⡇⢰⡟⠀⠀⠙⠋⠵⣴⣶⣶⡆⠀⠛⠊⢸⡿⣴⠟
⠀⢀⣾⡟⠁⠆⠀⠀⠀⠀⢀⣭⠀⣤⡀⠀⠀⠙⠻⣦⣸⣷⣼⠇⠀⠀⠀⣀⠀⠙⠿⠿⠃⠀⠀⢠⣠⠂⢲⣂
⠀⠀⣱⡶⢉⣉⣑⣒⢤⡀⠉⠁⠀⠻⠇⠀⠀⣀⣀⣹⣿⣿⣿⣠⣤⣤⣤⣭⣄⣀⣀⣀⡀⢀⣴⠋⢀⡀⢾⠁
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠉⠒⢦⣤⣀⣠⠶⠛⠉⠙⣿⣿⣿⣿⠟⠉⠁⠀⠉⠉⠹⡉⠉⠉⠉⣡⣄⣭⡂⠈
⠀⠀⠀⠀⠀⠉⠉⠱⠞⠉⣩⡏⠉⣴⣶⣶⡄⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⣴⣿⢁⠶⡄⠐⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠻⣿⣿⠃⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠰⠟⠁⠘⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠠⠀⠀⢄⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⣀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⡐⠈⠀⢀⡀⠀⠁⠒⠁⠈⠰⡄⢃⡀⠠⠤⠥⠀⠀⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⢀⢢⠠⢀⠀⠀⠀⡊⢀⠛⠀⠈⠀⠀⠀⠐⠈⠹⠏⡉⠂⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠐
⠀⠀⠀⡄⠀⠠⠀⡀⠤⠂⠀⠀⠀⡂⠀⠋⠰⠄⠀⠀⠀⠐⢄⣀⠀⠔⠀⠀⠀⠠⡀⠀⢠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⢄⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠑⢄⣀⠤⠔⠀⠠⠠⠔⠀⣀⣠⡄⣀⠀⠀⠀⠀⠂⠀⠁⠀⠀⡠⠀⣼⠔⢤⠀⠀⠀⢈⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⢀⠆⠂⠠⠠⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡎⠀⠘⠃⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⣅⠀⠀⠀⠁⠐⢄⠈
⠀⠀⠀⢠⠂⢁⠤⣄⠄⠠⡀⠈⠀⡀⠂⢰⡼⠉⠐⠤⠀⠀⠡⡑⠀⠀⢀⠌⠀⠀⢀⡠⠈⠐⠄⠁⠑⠤⠤⠤⠊⠀⠉⠂⠢⠀⠀⠀⡐⢈⠂
⠀⠀⠀⠈⠀⠇⠀⠈⠀⡃⠀⠀⠀⡀⠠⠀⠀⠀⠀⡀⠀⠒⡀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⡄⡀⠀⡔⠉⢰⡗⠲⣀⡀⠀⢐
⠀⠀⠀⡁⠀⠈⠢⠀⠄⠕⠁⠀⠀⠈⠠⠑⠀⠀⠔⠁⠀⠀⠔⠁⠀⠀⠀⠠⠂⠑⣦⠂⠠⡀⠐⠁⠘⠃⠈⠁⢂⠀⠀⠐⢀⠋⠈⠂⢆
⠀⠀⠀⠸⠂⠀⠀⢀⠄⢀⢼⣔⠒⠢⡀⠀⠀⠀⠀⠀⢠⡧⠄⢄⠀⠀⠀⠃⠀⠀⠀⠐⠀⡅⠐⢄⠀⠀⢁⠄⠀⠑⠒⠂⠁⠀⠀⠀⠸⢄
⠀⠀⠀⠐⡄⠈⠉⠁⠀⡁⠌⠁⠀⠀⠀⠀⠀⠀⢠⠊⠙⠋⠀⠀⠑⠂⠊⢈⠦⡤⢄⡣⢜⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠇
⠀⠀⠀⠀⠖⠁⠀⠀⠀⠐⠠⠤⠐⡰⠀⠄⠀⠐⡈⢄⠐⠀⢀⣀⠀⡄⠐⠁⠔⠀⢀⠔⢁⠔⢄⠀⠀⠀⠀⠀⠔⠁⠀⠊⠘⠓⠀⠱⠀⠈⢂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠘⡅⠰⠀⡇⠀⠈⠄⠊⢀⠔⢁⠔⠓⣄⠀⠀⠀⠄⠁⠀⠀⠢⡒⠀⢀⠌⠀⡠⠊
⠀⠀⠀⡎⠀⠀⠀⠀⡠⠀⣎⡖⠠⡀⠀⠀⠀⠐⠈⠡⡀⠀⠰⠀⠲⠃⠀⠀⠀⡐⢁⠔⠁⡠⠊⠀⠑⠒⠉⠀⠀⠀⢀⠀⠀⠀⡠⠀⠀⠅
⠀⠀⠀⠑⠀⢄⠀⠀⡀⠀⠀⠠⠄⡀⠀⡐⠒⠃⢀⠀⠈⢆⠈⡄⠀⠀⠀⠀⠘⠉⠀⡠⠈⠀⠐⠀⠀⠀⣀⠂⠀⠐⠁⠈⠀⠉
⠀⠀⢀⠀⠁⢉⢁⠈⠑⠤⢤⡠⠔⠁⠉⠀⣀⠀⠀⠱⢄⠀⠁⠃⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣐⠑⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⢁⣦⠄
⠀⠀⠈⠀⠀⠀⡻⡎⠠⠀⠀⠈⠁⠈⣀⣈⠁⠉⠀⠀⠈⣂⠀⠀⠀⠀⠀⠀⢠⣁⠤⡄⡤⠐⠿⠋⢫⡄⣉⠁⠀⣀⣀⠀⠀⠠⠠⣰⡿⠉
⠀⠀⠀⡀⡄⠀⢈⢽⡗⠈⠀⠀⠀⠀⠀⠀⣀⣄⡆⠠⠄⠀⢆⠀⠀⠀⠀⠀⠂⠀⠦⣼⠇⡁⢠⣮⡼⠛⠿⠁⢂⠀⠀⠀⠀⠀⣀⣻⣁
⠀⠀⠁⢚⢯⣁⣄⣀⠀⠄⠀⠐⠂⠀⠀⠀⠉⣿⡣⠅⠀⠀⠐⠀⠀⠀⠀⠀⠀⣄⣂⠀⠀⠡⠈⠃⠀⣃⣀⠠⣦⢴⠎⡑⢄⠀⢰⠌⠁
⠀⠀⠈⠉⣺⠏⠀⡅⠀⠀⠀⠀⠀⠀⠀⠠⠤⠬⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠉⠁⠉⠉⠁⡠⠐⢁⡀⢸⠄⢈⣦⠃⢹⣾⠂⠀⢀
⠀⠀⠀⠉⠙⠁⠔⠓⠯⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠘⠤⢉⠀⠐⠂⠀⠉⡗⢈⡀⢰⠘⣥⠘⠋⣐⢄⡀⣡⢀⣂⡀
⠀⠀⢀⡤⢀⣄⠤⢀⠀⢂⡔⠀⠀⠀⠤⢠⠤⡤⠤⡀⠀⠀⡌⠀⠀⠀⠀⠀⡀⠀⡦⢸⡡⢀⡀⠀⠀⢨⠀⢀⠀⣆⠱⠈⠙⠋⠙⡏⡘⠰⠟⠇
⠀⠀⠀⠘⠉⠛⠀⠂⡇⠉⠀⠀⠀⠀⠐⠉⠛⠁⢄⡅⠀⡰⠀⠀⠀⠀⠀⠀⢡⡈⠀⠈⠁⠀⠨⠀⠉⠈⠁⢷⡖⠺⡦⢱⣄⣐⠜⠑⠄⠀⡀⠄
⠀⠀⠀⠐⠄⣀⡀⠠⠁⠀⠀⣀⣀⡀⠈⠢⣀⣀⣠⠦⢠⢡⣀⠠⣀⡀⣀⠤⠤⢷⣄⠀⠀⠣⠂⠀⠀⢰⠀⡀⠀⠀⡀⠀⠀⠀⢀⢀
⠀⠀⠰⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠤⠄⠀⠑⠠⠀⠒⠀⠀⠀⠀⠀⠁⠉⠉

⣿⡻⢟⣛⣿⢛⡛⣛⣛⣛⠛⠻⣿⠛⠛⠛⠛⠻⠟⡛⠻⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠉⠍⢅⣤⠂⠃⢸⣶⡀⠉⠐⠢⠀⠀⠂⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣠⡋⣑⠠⠀⠈⣳⡄⠀⢻⠃⠋⠀⠀⠀⠉⠶⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⣿⢸⣿⡼⢢⡀⠉⠉⢹⣄⡨⡴⠁⣨⠁⠀⡄⠀⠹⣿⠁
⣿⢠⡉⠀⢸⡷⠀⠲⣿⡏⠀⠈⠀⢀⡉⢢⣌⢉⠞⠉⠀⠀⠀⠀⠀⠀⠀⠠
⣿⠀⠀⠀⠸⠇⠩⠂⠀⠁⠀⠀⠀⢨⠀⠀⣿⡇⠂
⣿⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⡌⠛⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣀⣀⣀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣦⠐⠠⠶⣙⠛⡀⢙⣿⣇⠀⠰⣀
⣿⡤⠀⡀⠐⠦⠄⠀⣰⣿⣶⣿⠄⢳⠃⠀⠀⠀⠀⠀⠀⣀⠀⠈⢿⠀⠀⣼⡯⠁⠀⣨⡱⡆⠀⠀⣿⣇
⣿⠰⠗⢽⠂⠃⠀⠀⣿⡇⠅⣿⠶⠿⠶⣤⣄⠀⠀⠀⠀⣁⡕⠐⠘⠂⠒⢻⠓⠀⣟⠛⣹⠓⣤⠈⡏⣀⠀⠀⣀
⣿⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⢌⣷⡊⠀⠀⠀⠀⠀⠀⠓⠐⢿⣶⣿⣾⣏⠀⠐⠛⠛
⣿⣓⡂⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡒⢅⣢⣔⣬⠦⠭⢩⠉⠂⠀⠀⠀⠀⠀⡖⠒⣶⢻⡟⢹⡏
⣿⣒⡪⠭⢕⣒⡈⠤⢀⣐⣠⠤⠴⠖⠒⠉⠉⠁⠂⠀⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡯⢸⡇⣸
⣿⠶⣒⣫⡭⠶⠒⠋⠉⠁⢀⣀⣀⠀⠤⠂⠀⠀⠄⠀⠃⠀⠳⣄⠠⠀⠀⠀⠀⠀⡇⢨⣇⣸⣇⣿⠔⣠⡄
⣿⠋⠉⠤⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⡀⠀⠢⠶⠀⠀⢀⠐⡿⢄⠀⠀⠀⡀⠀⣀⣀⣸⡏⠀⠉⣬⠛⠁⠀⠠
⣿⠀⠀⠄⠀⠀⠀⣰⣴⡄⠀⠀⠠⠄⠁⠀⠀⠀⢀⠐⠀⢀⠀⠀⠀⠀⠀⠀⡁⠠⠊⢈⡽⠇⠀⣰⡿⣭⣄
⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⡠⠐⠀⠀⠚⠁⠀⠀⠀⠀⠠⠾⠶⠀⠀⠀⠄⠈⠀⠀⠀⠩⠄⠀⠀⠀⠆
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤