King cobra Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣲⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠣⡬⡄⢤⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣤⣆⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣿⣿⣛⣿⡽⠿⠛⠛⠛⠛⠛⠳⠷⢿⣿⣗⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣥⣤⣤⣤⣀⠀⠀⠀⠀⣀⣀⠀⠸⡿⠃⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠁⠀⣨⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⣜⠁⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢭⠭⠷⣯⣿⣯⣍⣛⣏⣉⣫⡯⠽⠟⠋⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⢰⡅⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⢠⣾⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣾⣿⣿⣫⠆⠀⢀⣿⠇⠀⢀⣀⣤⣤⣴⣶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠄⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⣠⣾⣷⣾⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣠⡼
⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣸⣿⣿⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⣠⣴⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠉⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢠⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⠿⠛⣁
⠀⠺⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣿⣟⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠾⠿⠿⠾⠾⠶⠚⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠂⠐⠇⠐⣰⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡟⢛⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⠛⠋⠀⡿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠼⡿⠀⠀⠿⠇⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣤⣠⣤⣀⡀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⣭⣧⠿⣟⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡙⣿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣗⡀⣘⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣦⣤⣤⣿⠆⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡛⣾⣿⣿⣿⠿⣿⣿⣿⡿⢯⣽⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣧⣙⣿⠟⠛⣛⣿⣏⡓⢲⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠠⢝⠷⠶⣾⠉⣟⣶⣿⣟⣟⣿⣯⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣧⡆⣤⣶⣴⣤⣷⣿⣿⣿⣷⣟⣿⣿⢻⡋⢹⣈⣭⣉⣕⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⣿⠻⣾⢿⣿⣿⡿⠙⢝⣓⣾⣿⡿⢥⡍⣯⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢋⡧⢹⡁⡟⣻⠛⡖⣶⢶⡞⣗⣶⡿⣧⠧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢥⣾⢡⣿⣻⣎⣷⢈⡾⣯⣼⢿⡽⠁⠉⠉⠙⠫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠛⠚⠁⠛⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠐⠀⠐⡀⡀⠀⢠⠄⠀⠀⠀⠀⠀⣀⣠⣤⣤⢶⣶⣦⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠠⠴⠙⠀⠀⠈⠀⠀⠄⠻⡋⣮⠶⠻⢷⠀⠀⣰⣿⣿⣴⣿⣷⠂⣽⣿⣁⠻⢟⣶⣤⡀
⠀⠀⠀⠀⠠⠞⣁⣺⣂⠄⢠⠄⡤⢥⠷⣴⠐⣆⣂⠰⠋⠀⠀⠘⠻⠿⠾⠿⢿⣾⣟⣯⣷⣦⠀⣶⣹⣿⣶⡄
⠀⠀⠀⣰⣤⣾⠿⠊⢲⡘⢄⡤⠖⣻⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣕⣘⣓⢻⣯⣹⣯⣿⡿⣿⡄
⠀⠀⢠⣿⣟⣿⣶⣈⠚⠓⠀⣠⠞⠩⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣞⣶⣥⣬⣿⣻⢣⣶⣿⣿⣷
⠀⠀⣿⣿⣯⠄⠓⠈⠀⠀⣾⣯⡀⠄⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡽⣿⣯⣧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⡟⢱⣾⠃⠀⠀⠀⠽⠻⣿⠳⠠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣳⣿⣰⣥⣿⡿⢿⣟⣇
⠀⠀⣿⡟⡸⠿⠂⠀⠀⠀⠀⠀⡋⠈⠆⢆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⠿⢿⣿⣿⣿⣿⠗⣻⣿⡇
⠀⠀⢹⣿⠣⢤⡀⠈⠀⠀⢀⠀⠹⡀⠓⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣾⣿⣾⣿⣟⡆
⠀⠀⠘⠟⡦⢄⡈⠉⠉⠉⢀⠀⠓⢏⠙⠦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠁
⠀⠀⠀⠰⢳⠬⡉⠉⣉⣉⡀⠀⠊⣸⡀⠳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⣟⣿⣿⣿⣿⣾⣿⡏
⠀⠀⠀⠀⢻⡦⣄⡀⠀⠀⣀⡠⠾⢋⣏⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠈⢧⠦⣙⠋⢙⣁⣠⠴⠋⣻⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⢿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢾⣯⣉⢉⣁⣀⡤⠞⣻⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡞⢷⣿⣿⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢨⠀⣌⢉⣉⣁⡠⠖⢛⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⣱⣿⢿⡷⢎⣿⠁
⠀⠀⠀⠀⠀⠀⣼⣲⡀⠈⠉⢁⣠⠔⠛⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⣹⣿⠲⠜⡡⢻
⠀⠀⠀⠀⠀⣼⣿⣹⡇⠉⠉⠁⡠⠔⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠠⢿⣏⣑⣘⡙⣇
⣶⣶⠶⠶⠾⣿⣷⣿⣿⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣿⣶⣿⣿⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣴⡶⢲⢾⡻⣿⠟⣦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⣤⣩⣥⣤⣙⣂⢀⣷⣶⣶⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢠⣧⣼⣼⣿⣾⣿⠛⠻⣿⣯⣿⡟⡿⢿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⠩⣿⣿⣾⣿⢻⣧⠴⣠⡿⣿⣿⣻⣷⣶⠄⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡻⣧⢈⠻⡿⣿⠘⣿⠿⣿⢏⣿⣿⣿⡿⢊⣡⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣻⣔⡔⣿⡆⠈⠉⠁⣼⣿⢙⢡⣸⢾⡫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢜⢿⣿⡇⠀⠉⢰⣟⣾⡶⡻⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⠇⠀⠀⣾⣟⠥⠋⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣹⡛⠶⢶⡟⢡⣶⣶⣤⣀⢤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢈⣤⣴⣶⣤⣿⠀⠀⢸⣇⣈⣿⣿⡟⠫⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠐⢿⡟⠓⠒⢺⣿⠀⠀⣽⣿⣛⣩⣥⣶⣾⣿⠿⠃⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡀⠑⠀⠀⣘⣿⡀⠀⢻⣧⡍⠛⠛⠛⠉⠁⣀⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠿⣿⣿⣿⣿⡿⢷⣄⠀⠻⢿⣷⣶⣶⣾⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠶⠶⠶⠶⠿⠟⠻⠶⣶⣶⣴⡶⠶⠟⠛⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠒⠒⠶⠤⣄⣀⡀⠀⣠⠴⠶⠶⢶⠒⠲⠒⠒⠴⡏⠀⡴⠒⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣠⠴⠶⠶⠶⠶⢤⣌⡉⠉⠁⠀⠀⣀⣀⡁⠀⠀⠀⠰⣼⡞⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢙⠂⠀⠀⠈⠙⢉⣹⣆⡀⠀⠐⠛⠃⢄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⠃⠀⠀⠀⠀⠀⠉⠐⠦⣠⣏⠀⢀⣀⣀⣘⣒⠘⠋⠀⠀⠶⠀⠀⠈⡆⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⠀⠀⣷⢀⣾⠟⠷⢦⡀⣀⡤⠶⡆⢑⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢸⡆⠹⡇⢀⠚⡄⢸⠀⠀⡇⢨⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⡇⠀⠀⠀⠀⠒⠒⠦⢤⣀⠀⠈⢧⠘⡟⠀⢹⡾⠀⡇⠃⣠⠞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠾⡆⢳⡴⢲⣙⢄⣰⠊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⢿⡀⠀⢻⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠑⠚⠬⠓⠮⣺⡁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⠲⠤⠬⢷⡀⠀⠙⢆⠀⠀⠉⠙⠲⠦⠤⢤⠴⡏⠉⡻⠋⢩⠟⠀⠈⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⢾⣷⣄⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊⠉⠀⠈⠳⣤⠀⠀⠙⠢⣀⠀⠀⠀⠀⠄⢄⠀⢟⠉⠙⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠠⣖⣉⣙⣦⣄⠀⠈⠢⡀⠀⠀⠀⠀⠃⠸⣤⠊⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣤⣤⣤⣈⣳⣦⡀⠑⠀⠀⠀⣀⡤⠤⣷⡀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠀⠈⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠤⠒⠒⠻⡄⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢠⡀⣸⣤⣴⠁⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⢸⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠙⡁⠀⠈⠑⠤⣄⣀⣀⡈⡇⠀⠀⠀⠀⠀⠀⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠉⢉⠇⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠾⠋⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣤⣤⣤⣤⣤⡤⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣾⡿⢿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡙⢿⣿⣿⣿⣟⣠⣼⣿⣛⣭⣙⣛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣾⣿⣿⣿⣿⣿⢟⣕⣡⠟⠻⢿⣿⣶⣝⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣾⣍⢯⢿⣿⣷⣸⣏⣉⣀⣤⠞⢣⡹⣿⣿⣷⣜⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧⡻⣿⣿⣿⢩⣍⣁⣤⡴⠞⢳⡘⣿⣿⣿⣯⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣞⣿⣟⣾⣿⣤⣤⣤⡴⠞⣧⢹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠻⣿⣿⣿⣿⣤⣤⠤⠶⢿⡄⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡧⠶⠶⠶⢾⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡧⠶⠶⠶⢾⡇⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠶⠶⢦⣾⡇⣿⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠶⠦⣤⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠳⠦⣤⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣏⣙⣳⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣯⣙⣶⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⠴⣒⣩⣭⣶⣶⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⢀⣤⣖⣛⣷⣼⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⣠⢖⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣰⣿⢯⠃⠀⢀⣴⣯⣤⣴⣿⣿⣿⣿⠿⠛⣉⣀⣀⡀⠀⠀⢀⣴⣿⣾⣿⣿⣿⣿⣿⠿⠋⠙⢯⠽⢿⢿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣟⡇⠀⠀⣼⢁⣤⣤⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⢀⡼⠤⢼⡇⣿⣿⣿
⠀⠀⠀⠀⡎⣿⣷⣷⣤⣤⣼⡋⠀⢀⣹⣿⣿⣿⣷⣾⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣴⣛⣦⡤⣞⣼⣿⣿⠃
⠀⠀⠀⠀⠐⢜⣿⣿⣿⣿⣿⡻⣟⠋⠁⣙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠈⠛⠿⢭⣀⣤⣿⣛⣛⣿⣿⠿⠟⠛⠉⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠄⠀⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡀⡀⠀⢀⢀⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠘⠛⢧⣄⡽⠛⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢴⣄⠀⠀⠀⣠⡆⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢳⣍⣀⣤⣈⣭⡆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣿⣿⣿⣿⣿⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠉⠉⠉⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⢺⠀⠉⣹⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⢽⣿⣧⠀⠀⠀⢸⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠋⡉⡉⣒⠚⠿⢾⢶⣷⠀⠀⠀⢘⣇⣀⣉⢙⠓⠲⢤⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠠⠸⣿⠽⠿⣿⣷⣵⣖⣂⣿⠀⠀⠀⢰⠓⠻⠭⢝⣛⠾⣤⠈⢣⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣱⠀⠉⠑⠤⢤⣌⣙⢫⣽⣯⣤⣀⣀⡞⠀⠀⠀⠀⠈⠙⣎⣧⠂⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⡪⠦⣄⣌⣄⣶⣤⣮⡰⡠⡴⡄⡉⠓⠶⠤⠤⠤⠤⠖⠉⠀⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠳⠿⠶⠯⠭⣭⣛⡺⠦⣌⣦⣒⡀⡔⡀⡶⠱⣟⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠚⠭⠭⠭⠵⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠦⠈⣄⣠⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡤⠤⠒⠊⠉⠁⣀⠀⠀⠀⠀⠂⠠⣤⠄⡴⠾⣶⡀⡀⠀⠂⣠⡟⠉⠉⢠⡘⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⠀⠀⣦⠀⣿⣀⣿⣿⡋⠁⠐⢦⣤⣀⠀⠄⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠶⣾⣄⠀⠎⠀⠈⠉⠉⢥⣁⠀⠀⠀⠀⠙⠃⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣴⠶⠛⠩⠛⠋⠉⠝⠻⠟⠛⠉⠽⠛⢛⣹⣿⣦⣈⣿⠛⢗⠰⠄⢶⣶⣾⣿⣷⣤⣀⣠⠶⢺⠟⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠠⣴⠊⠁⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠦⢤⣄⣀⠈⠉⠙⠓⢄⡈⠻⣄⠀⣿⣿⡟⢹⣿⠃⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⣓⣶⠶⠉⠙⢶⡈⠳⣽⣿⡇⠸⠏⡄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠒⠚⣛⡟⠋⠀⠀⠀⠀⠀⢻⡄⠹⣿⠁⡄⠆⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣦⠄⠀⠀⠀⠀⠤⣤⣤⣀⣀⣀⣀⣀⣀⣤⢴⡾⠋⠀⠀⠀⠀⠀⠀⢀⡾⠻⣆⣽⡇⢈⣠⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⣹⣷⡁⢼⣡⡾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠻⡀⠀⠀⠀⠠⣤⣤⣀⣀⣀⣀⣠⣤⠶⣿⡔⠂⠀⠀⠀⠀⠀⣠⠏⠀⣠⠞⠃⠈⠛⠦⠤⠶⠋⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡘⣧⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⢀⡼⡏⠀⠀⠀⠀⠀⠀⡴⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠢⢀
⠀⠀⢠⡔⣈⡁⠤⠶⠤⢀⣀⡈⢷⡀⠀⠀⠀⢿⣄⠀⠀⠀⠀⣀⣀⣀⣠⡴⠛⠀⢣⢀⡤⠂⠀⠀⠘⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀⠁⠹⣦⠀⠀⠈⠙⠁⠀⠀⠀⠀⢀⠾⡇⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠟⠱⣄⠀⠀⣠⣤⣤⣴⠶⠋⠀⢿⣀⡖⠁⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠉⢷⣄⠀⠙⠁⠀⠀⣠⠞⠀⠻⡄⢠⢿⣏⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⠠⠀⠀⠀⠀⠈⠛⢶⣄⠚⠉⣷⣤⠒⠻⠏⠁⠀⠀⠀⢹⢧⡸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠄⠀⠀⠙⠷⠶⣿⣿⣿⠿⠿⠷⣤⡀⠘⠳⣄⠀⢀⣀⣠⡴⠟⠀⠻⣿⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠳⡈⠙⠁⠀⠀⠀⣠⠏⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣄⠀⠀⠀⠴⠶⠛⠉⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠒⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠏⢻⡄⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠒⠚⠉⠁⠀⠀⢻⡄⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⢠⡾⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢀⣠⡴⠏⢿⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠛⢶⣤⠄⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠉⠉⠁⠀⠀⠘⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢣⠀⠀⠀⠀⠀⠈⠛⠶⢶⣄⣀⣀⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⠀⠀⠀⠀⠲⠶⠶⠞⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⡀⠀⠀⢀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠒⠦⠤⠴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠶⢶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣀⣀⣀⣀⣀⣀⣀⣈⣳⣶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣄⡀⠰⡄⠸⠀⣄⣦⠂
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⠀⢨⣉⢠⡀⢠⠀⣩⠄⢀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡌⢿⢻⣶⣾⣿⡟⣰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⢿⡼⣿⡿⣿⣿⢱⠿⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣇⠀⠀⠹⠿⠈⠁⠀⠀⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣷⣶⣤⣀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣟⣉⣩⣿⣿⡟⠿⣿⣿⣿⣦
⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣏⣀⣤⣾⠇⠀⠀⠀⠀⠀⠇⠈⠙⢿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠀⠀⣨⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠟⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢤⠤⠤⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢸⣆⠀⠀⢸⠀⠀⢀⣼⡁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠓⢄⡀⠘⠟⡑⡶⢺⠳⡖⢋⠟⠁⠀⡠⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⠖⠋⢉⣷⣦⠤⠴⠗⠚⠓⠷⠤⠤⢴⣞⠉⠓⢦⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣀⢀⡼⠦⣼⠁⠀⠈⡿⠁⣄⣐⡂⣈⢹⡋⠀⠀⢱⡤⠼⣁⢀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢉⡏⠀⢠⠞⠒⠲⢶⡉⠀⠐⠒⠒⠒⠉⣳⠶⠒⠚⢦⠀⠘⡏⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢄⣠⠗⠒⡏⠀⠀⠀⣆⡈⠉⠉⠉⠉⠉⠉⣨⣄⠀⠀⣸⠖⠺⢅⣠⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⡇⠀⢠⠏⠛⠛⠙⣄⠀⠉⠉⠉⠉⠉⠁⣀⡌⠉⠉⠙⡆⠀⢸⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢹⠒⠛⣄⣠⡤⢮⠀⠈⠁⠀⠀⠀⠉⠉⠀⡸⠦⢤⣤⡟⠒⢻⠀⢙⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠙⣦⣤⣇⠀⢀⣬⠉⠁⠒⠒⠒⠒⠂⠉⠁⢰⣤⣀⣠⢧⣤⡞⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣷⠀⢈⠏⠁⢸⠑⠢⠤⠤⠤⠤⠤⠔⠒⢫⠀⠀⢹⠀⢀⣧⢴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣻⠙⢧⡠⠼⡦⢀⣀⣀⣀⣀⡀⠠⠤⢾⠢⢤⡞⠙⣏⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⢦⢼⠀⠀⣣⣀⡀⠀⠀⠀⠀⢀⣀⣜⠀⢠⠧⡼⢹⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣤⡟⠉⠙⣄⣈⡉⠉⠉⠉⣁⣀⡎⠉⣯⣠⢿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⠀⠀⠹⣇⠙⡶⠺⣇⠀⠈⠉⠉⠉⠁⠀⡳⢶⠃⣸⠎⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⣩⠥⠖⠛⠁⠀⠀⠀⠹⣷⢧⣠⣏⠉⠁⠒⠒⠒⠋⠉⣣⠾⣞⠏⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣤⡏⠉⠓⠒⠒⠒⠒⠉⢱⣄⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⢀⡴⠋⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣨⠗⠢⠤⠤⠤⠤⠤⠤⢾⣿⠛⠉⠙⠓⠒⠲⠤⠤⠤⠤⠤⠤⠖⠂⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⡞⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⠹⣾⣀⠀⠀⠀⠀⠀⠀⠀⣨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠦⣄⣀⣠⠤⠴⠚⠋⠁⠀⠀⠀⠀⠀⣇⠈⠉⠉⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⠑⠲⠤⠤⠤⠤⠤⠖⠊⢹⠒⠒⠲⠶⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⠀⠀⠀⢀⣀⣀⣠⡤⠖⠚⠉⠈⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠙⠒⠒⠚⠉⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⠟⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣶⣿⣆⣀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⣉⣉⡛⠛⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠸⢀⠄⣠⣾⣿⠿⠛⠛⠛⠛⠛⠻⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣶⠾⠛⠛⣛⣛⣫⣾⠟⠋⠀⢠⡄⠙⠛⠶⠶⠤⠄⠀⢈⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣠⣿⠇⠸⢿⣷⣶⣶⣦⣤⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⣰⣶⣤⣄⣉⣉⠙⠉⠀⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢀⣀⠙⠛⠿⠿⢿⣿⠟⠁⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢾⣿⣿⣷⣶⣶⡤⠀⢀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢰⣤⣄⣉⡉⠛⠋⢀⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⠿⢿⣿⣿⠏⢠⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣶⣤⣤⡀⢀⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⠛⠛⠃⢸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡆⢹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠷⠆⠀⣠⣶⠿⢶⣦⠀⠀⣶⡶⢶⣶⡀⠀⣾⡶⠶⣶⡀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⢀⡀⠀⣿⣇⠀⢠⣿⠂⠀⣿⡟⠛⣿⡄⠀⣿⣷⣶⡿⠃⠀⣰⣿⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠈⠛⠛⠛⠁⠀⠀⠛⠛⠛⠛⠁⠀⠛⠃⠈⠛⠂⠐⠛⠁⠀⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⠶⠶⠶⠦⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣒⡿⠋⠉⠠⢤⡽⣆⣀⣀⣀⣀⣀⣀⣀⠀⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⣀⣄⠌⠱⠁⠔⣾⣿⣿⣿⣿⣿⣿⣛⠋⣽⣷⣦⣀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠞⠀⠀⡼⣧⠿⠁⣤⣾⡧⢹⣿⢟⢿⠿⣿⣿⣿⣷⠤⠙⠻⢿⣷⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⣀⣴⣶⣿⣿⣿⢏⣾⠴⠃⠀⠀⠼⣫⣿⣶⣿⡄⢹⣿⣾⣿⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⣓⢻⣻⡈⡟⣿⣿⠏⡾⣳⣤⠤⠖⠀⠀⠈⣿⣿⣿⠧⠈⡻⢿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⡿⣸⠆⢛⣻⡦⣤⠤⠔⠋⢻⣿⣶⡇⠀⣿⣿⣿⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⡵⠋⢷⠀⣿⣧⡀⠀⢀⢀⡼⢿⡿⠗⠀⣻⣿⠏⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡆⠀⠘⡇⢸⠇⠉⠉⠉⠑⣿⣿⠁⢀⣼⣿⠏⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⣦⡇⠀⠀⣇⣼⢤⣀⣀⣀⣼⡿⠃⢠⣿⠟⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⡿⠁⠀⠀⠀⣶⣾⣶⣿⠟⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠒⠢⠤⢴⣿⣿⠟⢁⡴⠊
⠀⠀⠀⠀⠀⠀⢀⣶⡿⣫⣭⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⠿⣄⡀⠀⣸⣿⣿⠟⢁⡴⠋
⠀⠀⠀⠀⠀⠀⣽⡿⠀⢹⠃⠀⠀⠉⠷⠀⠀⠀⠀⠀⢰⡏⠀⠀⠉⣽⣿⠟⢁⣴⣯⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢿⣷⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⣰⠟⠙⠒⠦⢼⡿⠃⣠⠞⠁⣀⢀⡀⠐⢦⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣷⣤⣤⣈⣙⠛⠛⠒⠒⠚⢛⡿⠤⣄⣀⣰⡟⠁⣰⣷⢯⣟⡷⣫⣾⣿⠟⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢠⡞⡅⡀⢰⣦⣦⣈⡍⢙⠛⠲⠶⢤⣾⠀⠀⠀⢰⣿⠁⢠⣿⣿⡿⠿⠿⢛⣋⣡⣤⡤⠶⠶⠞⢛⡛⠛⠻⠶⣦⣄
⠀⠀⠀⠀⣾⣾⡻⡗⣀⡙⠿⣷⣿⣯⣷⣛⣶⣶⡏⠉⠛⢒⣻⡇⣰⢸⡷⠶⠶⢚⡛⢋⣭⣁⡴⢦⣴⣋⣶⣿⣿⡆⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢟⢿⣿⣯⣻⣽⣧⠶⢌⣩⣍⢉⣉⣹⣇⣀⣀⣸⣿⡇⣿⡄⢷⣿⣶⣿⣽⢟⣷⣞⣽⣿⣶⣿⣿⣿⣿⠇⢀⣴⢶⣇⣻⡇
⠀⠀⠀⠀⠈⢻⣹⣿⣿⣿⣾⣿⣭⣵⣞⣛⣶⣿⡇⠀⠀⣶⣾⣷⢹⣷⡀⠻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⠴⡇⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣼⣿⡻⣿⡿⣿⣿⣿⣿⣿⣷⡤⠴⠿⢟⣻⣿⣿⣿⣯⣠⡉⠛⠻⠿⠿⠟⠛⠋⢉⡀⣰⢖⡟⣺⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠾⠿⠿⢮⣻⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣶⣷⣞⣣⡴⠶⣤⡖⣦⢮⣭⣏⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣾⡿⢟⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⣟⣵⠿⠿⠿⠿⠿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣀⣀⣀⣀⣀⣠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢡⠖⣦⠨⠀⢈⠁⠠⢀⡖⢳⠙⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⢠⠸⠓⠥⠂⠒⠀⠈⠂⠠⠕⠛⢀⠄⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣋⠇⣤⣴⣀⡀⢤⡸⣤⣶⣿⣷⣦⡼⣀⠄⣠⣰⣦⡄⢥⡑⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣧⣴⣿⡟⡟⠛⣿⣇⣿⣿⣿⣿⣿⡇⣾⡟⠛⡿⣿⣿⣦⣇⠈⣆
⠀⠀⠀⠀⠀⠀⠀⣘⡝⢹⣿⢻⡅⡸⡉⠢⠸⣿⣿⣿⣿⣿⣿⣿⡿⢡⠞⡹⡀⡸⢻⣿⡉⣏⡆
⠀⠀⠀⠀⠀⠀⠀⡇⣰⣿⡿⢅⡸⡀⡸⡆⢀⢹⣿⣿⣿⣿⣿⣿⢃⠆⡸⠄⡸⡀⡸⣻⣷⡄⡇
⠀⠀⠀⠀⠀⠀⠀⢫⠸⣿⢇⡸⢄⡸⣀⡭⠀⡅⣿⣿⣿⣿⣿⡏⠈⠀⣅⡸⣀⡸⣀⢼⣿⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡸⢇⡸⢄⡼⣗⠀⢰⢹⣿⣿⣿⣿⠣⠃⢐⡿⢆⡸⢀⠼⣰⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣹⣇⡸⢆⡸⣄⣬⡁⠈⢆⠻⢿⡿⢃⠎⠀⣨⣄⡸⢄⠼⣀⣼⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⢆⡸⢄⠼⢼⠤⠀⠀⠉⢸⠃⠉⠀⠠⢼⡼⢆⠸⢄⠼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⢆⠜⢄⢼⠒⠀⠀⠀⢸⡀⠀⠀⠐⢺⢆⡜⢄⠜⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢢⠜⢼⡋⠂⠀⠀⣸⡇⠀⠀⠊⣹⠜⢣⢜⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣠⠚⣯⡁⠀⠀⠁⠁⠀⠀⣈⣽⢣⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡗⠀⠀⠀⠀⠀⠀⠀⠐⣿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⡀⠀⠀⠀⠀⠀⠀⢈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄⠀⠀⠤⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣴⣿⡄⣤⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣸⡇⣾⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣡⣾⣿⡿⢛⡭⢧⣴⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠹⠿⠇⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠛⠛⠶⣿⣿⣧⣾⣿⣷⢾⡋⣯⣿⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⣿⣿⢾⣭⣭⣽⢛⣍⡧⠿⡜⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣿⡿⣿⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣿⣿⣟⠛⠛⠛⢼⡽⠶⢷⢛⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢛⠿⠛⠓⠒⢶⠳⡇⠾⠺⠈⠋⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣶⣴⣶⡶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠷⢤⠟⠀⠀⢸⠟⠲⠦⣤⣼⣷⠁⠀⣼⢰⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⢤⣀⣸⠏⠈⢾⢀⡄⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠛⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣸⡍⠙⣠⠌⠠⣡⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣾⣿⣶⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣠⡍⠰⠀⠀⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣻⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣈⡭⠡⠀⡻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⣐⢀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢹⣿⢀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⠿⣿⣿⣻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣋⣁⠀⠀⠈⣿⡟⠉⠀⢹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠈⠦⣀⣀⣠⣶⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠁⠀⠀⠂⣼⣏⡀⠁⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⣠⠀⠀⠀⠀⣿⠿⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠺⡛⠀⠀⠀⠡⣿⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠁⠀⠀⠀⠠⢽⡇⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣿⡀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢿⣧⣾⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣷⣤⣠⣤⣴⣿⣯⣿⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣀⠀⠀⢀⣀⣤⣴⣶⡶⣿⣿⡿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⢢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⠿⠿⠿⠟⠛⠛⠛⠛⢿⡽⣽⣿⣿⡿⣟⣷⣸⡍⠙⠻⢿⡿⣱⣟⢻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣽⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣞⠛⣿⡙⢿⠿⡿⡟⢻⢻⣷⣶⣦⣤⣀⠀⠀⠹⣞⣋⡉⣩⠥⢖⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⢶⣾⣷⣆⠸⣿⣾⣷⣿⣷⣽⣈⣽⡷⣻⠟⢁⣦⠀⢹⣿⠒⢒⣻⠩⣻⡆⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⣧
⠀⠀⠀⠀⠀⣰⡿⢿⡏⠙⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣟⣿⣿⣿⠇⣰⣿⣿⣷⡈⣿⡅⠀⠶⢚⢩⡇⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠿⢿⠄
⠀⠀⠀⠀⢰⣿⣷⡋⢰⠠⠹⢿⡿⠋⠁⠀⠀⠀⠉⠙⠻⣿⣿⠇⣼⣿⣿⣟⣿⣿⣿⢃⢈⣉⣭⠴⣇⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣧⣴⡱⣮⢼⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣛⡯⡿⡿⠄⠄⢒⣚⣩⡇⠀⠀⠀⠀⠀⠀⢸⣿⣧⡛⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⣣⣿⡞⣧⣾⣿⣷⢦⣄⣀⠀⠀⠀⠀⠈⢻⣿⣽⡾⣿⣿⠫⢭⡭⠽⢶⡇⠀⠀⠀⠀⠀⢀⣿⣿⣏⢩⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣽⢟⡚⣷⠟⣫⠛⣧⡿⣹⡟⣷⣦⣤⣀⣀⠹⣿⣿⣻⣽⣟⠿⡳⣮⠽⣇⠀⠀⠀⣠⣴⠿⡃⠿⠙⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡏⣿⣽⣮⣴⡿⣗⢰⠂⠧⠘⠺⠟⣹⣿⣿⡿⣿⣿⣿⣯⣿⡟⢲⣗⣺⣿⣶⡶⠿⢿⣫⣴⢋⣠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢿⣿⣿⣯⣿⡿⡿⣿⡟⣤⣅⠘⠃⡭⠟⢹⣆⣿⣼⣿⡛⣿⣻⣿⣿⣿⠞⢛⣶⢈⠋⣹⣽⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣾⣿⣿⢶⣿⡿⡾⣷⣦⣷⡀⣺⣽⣿⣿⢿⢝⢻⣣⣺⣹⣋⢏⣞⣿⣿⣶⣌⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣾⣷⣾⣿⣿⡁⣿⣯⣿⣷⣿⣷⣿⣽⣟⣯⣿⣻⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⢴⢂⡈⣿⢦⡀⢰⣾⣿⣾⣿⣿⣿⠃⣠⡞⠿⠀⣌⡃⢄⠀⠈⢁⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣶⣶⣇⠘⢏⣀⣇⠈⣿⣈⣙⣛⠛⠛⣛⣣⣤⡿⠀⢠⠀⡜⠀⣼⡿⠿⢿⣿⣿⣷⣦⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⣿⣶⣶⣽⣿⣤⠚⣤⡟⠒⣎⢉⡁⠉⠉⠉⠁⢀⠅⣠⠉⠱⠆⣁⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣄⠄
⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⡩⠈⠩⡀⢁⣤⣶⣶⣤⣀⣠⠀⠀⢠⣾⠟⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆
⠀⠀⠀⠀⠀⠀⢸⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣄⢻⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⡆
⠀⠀⠀⠀⠀⠀⡎⢸⣿⣿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣖⠈⢾⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⡟⢻⣿⣿⡟⢀⡽⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⡇⢣
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⠘⣧⡜⢿⣿⣯⣿⡏⠻⠰⠆⠈⢸⣷⠚⣿⡟⢰⣾⢀⣿⣿⠿⠉⠀⠀⠀⠀⠀⠘⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠓⣿⣷⡼⣿⠈⢿⢿⡀⠀⠀⢠⢿⡏⠀⣿⢱⣿⣿⢉⡿⠋⠀⠁⠀⠘⠀⠀⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⡃⣿⣿⣷⣽⡆⠸⣧⢳⡄⢠⠟⣼⠁⣸⢷⣿⣿⣿⡘⣁⣤⣤⣀⡀⠀⢀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠂⢀⣾⣿⣿⣿⣷⣾⢻⣿⣿⣿⣿⡄⠹⢆⣷⡾⠈⠇⣰⣿⡼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣄⠸⠀⠀⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣸⣿⣿⡽⣿⣿⠆⢨⣹⢤⣤⣴⣿⣿⢡⣿⣿⣥⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠰⡈⠀⠀⠠⠀⠘⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⢿⡿⣇⠘⣿⣾⣿⡿⣫⠟⣿⣿⡟⢸⣿⣿⣿⣿⣿⠿⠁⠀⠃⠀⢠⢡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠙⢻⠿⠿⠟⠃⣸⣿⣿⡀⠙⠓⠦⡀⠶⠒⠋⠁⢀⣿⣿⣧⠀⠉⠛⠛⠏⠁⠀⠀⠀⢀⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⡟⠒⠒⠒⣷⣠⠐⠉⠉⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢮⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⢀⠀⠀⠀⠀⣠⣼⣿⣷⣀⡀⣠⣿⡞⣀⣀⣠⣾⣿⢳⣦⣀⠈⠀⠀⠄⠀⣀⡴⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣻⣶⣶⣦⣶⣶⣿⣿⡇⣿⣿⡉⠉⠋⢋⠍⠀⠀⢠⣿⣿⣸⣿⣿⣿⣿⣿⣿⡿⣯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⣿⣿⣿⣿⣿⣷⢿⣿⡷⠤⠤⠤⠴⠒⠒⢾⣿⡏⣿⣿⣿⣿⣿⣿⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣸⣿⣇⠀⠀⠀⠀⠀⢀⣼⣿⣧⣿⣿⣿⣿⣟⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⢻⣿⡿⠉⠉⠉⠉⠉⠉⢻⣿⡺⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⣼⣿⣷⣀⣀⣀⣀⢀⡤⣾⣿⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⢸⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡇⡿⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣺⣿⡷⠲⠶⠒⠒⠒⠒⠻⣿⣏⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣿⣿⣀⣀⣀⣀⣀⣀⣀⣠⡿⠿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠄⠀⠀⠤⣀⡀⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠒⠊⡉⠀⠀⠠⠀⣄⣠⡴⣤⡀⠀⠀⣠⠞⠚⢍⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠉⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀⡀⠰⠀⠰⡄⢪⣼⡿⠏⠉⠲⠤⣄⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢀⣀⡤⢾⡿⠿⠿⣿⡿⠿⣿⠿⢯⣝⠛⣷⢬⢀⣀⣀⣤⣷⣄⠀⠀⣌⣤⠤⠖
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠠⡶⠦⠬⣤⣀⡛⠛⠛⠯⣀⠺⡄⢹⣿⡿⣿⡟⠈⠀⡙
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣴⡃⠀⠀⠀⠀⠠⣤⣄⣀⡀⠀⠀⠀⢉⣙⡶⠖⠉⠳⣌⠳⣿⡇⢹⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⡏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠉⢉⣩⡼⠁⠀⠀⠀⠀⣸⣆⢻⡄⠊⢰
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢻⠁⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⣹⠋⠀⠀⠀⠀⠀⡴⠃⢘⣿⡁⣖⣠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠘⡄⠀⠀⠀⢦⣤⣀⣀⣠⠤⢺⡷⠂⠀⠀⠀⠀⠔⢀⣴⠏⠀⠙⠶⠶⠋⠹⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣠⠛⡄⠀⠀⠀⢀⠊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⡉⠂
⠀⠀⠑⠀⠉⠉⠉⠉⠓⠻⢦⡀⠀⠙⣦⠀⠀⠒⠚⠛⠉⠀⢀⣷⠋⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⢦⡀⠘⠱⣄⠀⢤⣤⠤⠖⠋⠸⣆⠄⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⠀⠈⠙⢦⣄⠘⠷⣄⠁⣀⣠⠖⠁⠘⣦⡞⣿⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡘⠁⠠⠀⠘⠤⣤⣶⣶⣿⡷⣄⠈⠳⢌⠁⠀⢀⣠⠞⠓⣿⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡇⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠑⠈⠋⠀⠀⢀⡏⠻⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠐⠉⠁⠀⠀⢘⢦⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠤⠖⠋⠈⢣⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡴⢤⣄⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⣀⡤⠚⢧⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⠛⢶⣀⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠘⢦⡀⠀⠀⠀⠈⠙⠓⠶⠶⣿⠀⠀⠠⠤⣤⠴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠑⠒⢚⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠤⠤⣤⡤⠤⠼⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣥⣠⡽⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠛⠽⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠒⠂⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠐⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣀⠔⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⢸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⢫⣷⢲⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡛⣯⣻⣫⣿⣴⣧⣼⣧⣽⣽⣷⣦⣤⣄⣀⣀⣀⣀⣠⠄⣿⣿⣿⠏⠙⠛
⠀⠀⠀⠀⣰⣿⣿⣿⠿⣿⣿⠿⠛⠛⠻⠿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣾⣿⣿⣶⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⠃⣴⠟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⢏⣡⣶⣿⣿⣿⡿⣿⣿⢿⣿⢿⣿⢿⣿⣟⣷⣄
⠀⠀⠀⣿⣿⣿⣿⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡿⣿⣿⣿⣩⣷⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⣿⣿⣿⣿⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣴⣾⣿⡿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣿⣟⣼⣿⣿⣽⡿⢛⣿⣿⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⠿⠛⠛⠛⠓⠒⠟⠥⠥⠄⣿⣿⣿⣷⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣟⠥⠖⠋⠁
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⠦⢤⣤⡀
⠀⠀⠀⠀⠀⠹⣿⣿⣄⡀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠤⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣨⡛⢒⣇⢦⣀⣗⢽⣿⣿⣶⣚⠲⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠻⣿⣿⣷⣤⡀⣉⣁⣈⠁⠈⠉⢀⣠⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢻⠯⣥⣻⣿⣷⠑⣒⡶⠾⣟⣻⣽⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡬⢶⣾⣿⣿⢟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢠⢊⡽⣫⣴⣿⣿⣿⡿⠻⠟⢿⣿⣿⣿⣿⡵⠠⡟⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠪⠉⠀⠉⣿⣿⡿⣿⣿⣖⠒⠊⢻⣿⣽⣿⣷⠤⡉⢰⡀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⡀⠀⠀⠀⢹⣿⡁⠸⢿⣿⣇⠈⠉⢹⣿⣽⣿⣧⠋⢲⠀⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠸⣇⠀⠷⢀⠿⣿⡏⠈⠉⢿⣿⣻⣿⠓⡆⠈⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠀⠇⢰⡄⢸⢦⣻⣿⠒⠒⠺⣿⣿⣿⠠⠉⡎⠀⣞⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠁⣀⣨⣤⣤⣗⣶⠀⢳⠀⣽⣿⡦⢀⡀⣿⣿⣿⣸⢤⠉⡆⠙⢀⠀⠛⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⣴⣿⡿⠟⠛⠛⠛⠚⠁⡄⠈⢯⣿⡧⠀⢀⣽⣻⣿⡿⠞⢠⠁⡄⡈⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠈⠢⠉⢠⠀⣿⡇⠀⠀⢹⡿⣿⣇⢤⠊⠠⠰⢿⣿⣵⡀
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⢊⣿⠁⠀⠀⠀⠀⠀⠀⣀⠀⠠⢂⡈⠑⣿⡏⠁⠐⢺⣿⣿⣿⠞⢠⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⢸⣟⠀⠀⠀⡀⠀⠀⠭⠏⠀⠀⠀⡳⣴⣿⠃⠀⠠⣼⣽⣾⣿⣤⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢸⡀⢂⠀⠀⢿⡠⠐⠃⠀⣀⠀⣀⣤⣴⣾⣿⡷⣩⡟⠂⠤⢀⣾⣿⣻⣏⠄⠈⡄⠀⠀⠠⢮⠋⠀⠀⣰⣼⠃
⠀⠀⠀⠀⠀⠀⠘⣷⠈⠀⠠⠊⠀⠀⠄⣴⣽⣿⡿⠛⠛⠉⠀⠀⢐⡷⠀⠀⢀⣿⣿⣿⣏⠨⠸⠋⠀⠀⠀⠀⠠⠒⣩⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡆⢡⠄⠀⢀⣾⣿⠏⠙⠻⠉⠉⠉⠌⠀⢀⠃⠄⣀⣲⣾⣿⡟⣼⡇⢀⠀⠀⢠⣀⣥⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠀⣠⣿⡟⠁⠉⠳⠷⠶⢶⣶⣶⣶⠟⠄⠀⢸⣷⣿⡆⣼⡏⠂⣼⣷⣾⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡁⡀⠀⠀⠌⠻⠷⣦⣤⣀⣄⣠⢢⠄⢊⠘⢄⠀⢰⣯⣿⣹⣽⡟⢀⠈⠉⠀⠑⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⢢⢀⠀⠂⠐⠬⠲⠓⠀⢐⢪⡔⠻⠀⢀⣦⣛⡿⢿⣿⢏⡀⠁⠀⠀⠀⠰⠒⠂⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣍⣀⠐⠒⠰⠂⠈⡇⢀⣣⣴⣾⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣿⣷⠶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠯⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠛⠻⠛⠛⠋⠈⠁

⠀⠀⠀⢠⠦⠂⢶⣶⠄⢀
⠀⠀⠀⠈⠡⣈⡀⠉⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢸⣿⣆⠀⠰⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣿⣿⣷⠀⠈⣥⠀⠂⠂⣺⡄
⠀⠀⠀⠀⢐⣾⣒⣿⠄⠀⢻⠄⠀⠸⠶⡗
⠀⠀⠀⠀⠘⣟⣂⣿⠀⠀⠰⠂⠐⢘⣉⡇
⠀⠀⠀⠀⠠⡏⣿⣿⠁⠀⢘⣿⡆⢨⠅
⠀⠀⠀⠀⠈⣧⢡⡟⠀⠀⠰⠉⢠⢴⡇
⠀⠀⠀⠀⠀⣟⢹⣯⠀⢀⣭⡄⢥⡿
⠀⠀⠀⠀⠀⢓⣾⡿⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢸⣿⠯⠀⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢰⡿⠀⠀⣖⡿
⠀⠀⠀⠀⠀⢸⠇⠀⢨⣽⠇
⠀⠀⠀⠀⠀⢸⠀⠀⢼⣿
⠀⠀⠀⠀⠀⢸⠄⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⠀⠀⢈⣿⣀⣀⣀⣀⠀⠀⠀⠀⣀⣠⣴⣦⡶⡐⠤⠤⠀⠀⢡⣤⣀⡀
⠀⠀⢀⣴⣾⣿⠁⠀⠀⣿⡁⣩⣟⠁⢀⣤⠞⠛⠋⠉⣩⣿⡿⢷⡌⠀⠀⢀⣼⡇⠀⠈⠑⢂
⠀⢠⡟⠉⠉⣿⣏⡀⠀⠘⣿⣿⣿⣿⠟⠀⣤⣦⣾⣿⠿⢫⡅⠂⠀⠀⣠⣎⣩⣿⠅⠀⠐⠏
⠀⡄⠇⠀⠀⠈⢿⡵⢆⠀⠈⠙⠿⣷⠀⢨⣿⡟⠉⠈⠁⠀⠀⠀⣠⡾⠋⠁⠉⠁⠀⢀⡾⠃
⠀⠘⠮⣢⡤⣄⣼⣿⣾⣵⣤⢀⡀⠀⠀⠘⣿⣟⣧⣀⡀⠠⠐⠛⣿⣿⣷⣶⣶⡒⠋⠁
⠀⠀⠀⠀⠈⠉⠉⠋⠉⠉⠀⠉⠉⠉⠈⠀⠄⠉⠙⠛⠛⠒⠓⠛⠉⠀⠀⠉⠉⠉⠻⠒⠚⠛⡩⠙⠛⠲⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠳⣶⠆⠀⢀⣠⣴⣶⣶⣤⣄⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣠⡧⠟⠀⣠⣾⡟⠋⣹⣯⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣲⣶⣿⡋⠀⣀⣠⡴⣋⣥⣿⣰⡯⢼⣗⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡼⢻⣿⣿⣯⣽⣟⣭⣶⠏⠀⢸⡟⣤⣾⣿⣿⢿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⡇⠈⢿⣿⣷⣿⣿⡿⢃⣤⣶⣿⡳⣙⠿⠋⠀⡰⣺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡝⢢⢈⡉⠛⠋⢉⣴⣿⣿⠟⠋⠙⠫⣖⢤⣽⠷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣦⣪⣉⣛⣛⣘⠛⣋⡯⢖⡒⣠⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠙⣿⣿⣿⣿⣿⣿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣋⡄⣀⠤⣙⡛⠿⡛⢿⣿⣿⣿⣿⣉⠛⢌⠻⡽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣟⣿⣿⣾⣶⠖⠫⢴⢔⠻⡿⠿⣿⣿⣿⣿⣷⣹⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⢿⣿⣋⣁⡀⢀⣴⣿⢍⡎⠢⢀⠉⠁⠈⢹⠏⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢿⠀⣴⣿⡟⠛⠛⠿⠿⠟⣁⡀⠉⠪⣁⡌⣀⣮⣱⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⢂⠙⠿⠷⢶⣤⣤⣶⠾⠟⠷⣿⣦⣀⠁⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣷⣵⣀⣤⣤⣾⣿⡏⠀⠀⠀⡿⢏⡞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠊⠁⢸⠁⠀⠀⠀⠑⢶⡏⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠳⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⢠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⢋⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⡂⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢸⢀⠀⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢹⡄⠀⣿⣇
⠀⠀⠀⠀⠀⠀⡡⠈⠃⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢸⣿⠀⣀⣠⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠃⢄⠤⠄⠀⢀⣤⡴⢶⣶⡶⣦⣄⣀⣬⣤⣀⣀⡀⠀⠀⠀⠀⡀⢸⡇⢸⣿⠂⣀⠿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠐⡂⠐⠀⣀⣼⣿⢣⣾⣿⣿⣿⣿⣷⣶⣿⣟⡿⣿⣿⣿⣶⣦⣉⠁⣸⣿⣸⣿⠀⢀⣼⣿⣏⡀
⠀⠀⠀⠀⣀⣠⣀⣠⣾⣿⣿⣿⣸⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣾⣽⣿⣟⣛⣛⣳⡿⣣⡿⠃⠀⠉⠉⠛⠛⠛⠃
⠀⠀⠀⠀⠈⠯⣿⣿⡯⢹⣿⣿⣷⣝⠿⣿⣄⣀⠀⠀⠈⢙⣻⣿⣯⣽⣿⣿⣽⣽⣾⡋⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣷⡜⢿⣟⡻⣿⣿⣶⣭⣽⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠉⠉⠉⠁⠀⢀⣠⣪⣿⠏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠶⠶⠶⠶⠶⠾⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠺⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠛⠶⣦⡤⠴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢴⣶⡥⣀⡀⠰⡖⢦⡙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⢿⣿⣦⡈⠳⢷⠈⠉⢛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⢿⣼⢿⣿⣿⣄⠀⠁⣠⣼⡇⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡝⣿⣿⣿⣶⡿⢲⡇⢈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡿⠁⣹⠛⣦⡀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠿⡟⢿⠛⢿⣶⣄⡀⠀⣠⣿⠼⣫⣾⢟⣁⡾⠛⢫⣿⣳⡌⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠶⣦⣤⣀⠀⠉⣬⠅⣤⣴⠄⣶⠾⣛⣽⡿⢛⣿⡉⠉⢉⡷⣻⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⣠⣧⣴⣄⡝⢳⣄⠉⠆⢘⣹⠤⣴⣾⡛⢉⣠⣾⢟⡟⠛⠓⣻⣭⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⣿⣿⣿⣿⡷⢼⠈⡷⣄⠀⠀⠚⠉⠿⠛⣿⡙⠏⢸⠗⠦⣼⣋⡙⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡇⠀⣿⣇⢸⠳⣦⡢⣄⣀⣀⣠⣤⣠⠿⣄⠀⢽⡿⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣤⠀⠈⢻⣤⠿⣿⣿⣷⠀⠘⡨⡿⢦⣸⠙⢷⠿⠿⠿⠚⢧⣀⣤⣿⢯⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡆⣹⣆⠀⠀⠙⢿⣍⡹⠿⣷⣀⡀⠀⠈⠩⠑⢾⠧⢀⣱⣤⣀⣩⣽⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣁⡽⣄⠀⠀⠀⠈⠛⠿⣤⣼⣉⡟⠓⡶⠤⣤⣀⡀⠙⠂⠈⠳⠊⠹⡿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡿⡀⣸⣆⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢶⣧⣬⣏⣙⡷⠶⣤⣀⠀⠑⡉⠿⢷⣍⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣿⡁⡈⠙⠒⠶⠶⠶⠶⣶⣶⣶⣶⣶⠶⠞⠛⡋⢉⠙⠳⢧⣜⡛⣶⣄⠘⢹⢿⡆⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣆⣤⣤⠶⠚⠉⣁⣀⣴⣾⡇⡀⠀⣠⣽⢶⠛⢚⢛⠟⢻⣦⡛⣧⠀⣼⡇⠀⠠⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢉⡿⠁⠀⠐⣋⣩⡟⣻⡌⠀⣇⠀⢿⣳⣾⣿⣿⣿⣿⣿⣶⢻⡿⢀⡿⠁⠀⠆⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠁⢸⡇⠀⠀⠖⢋⣿⣿⢧⣏⡀⠈⠳⢤⣙⠛⠿⠿⠿⠿⠿⣛⣫⡴⠋⠀⠀⡀⢛⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢧⠀⠀⠈⠛⢼⣿⣼⣤⣥⣠⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⡄⢠⣏⣩⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠓⠂⠀⠀⠁⠀⠀⠀⠓⢺⠿⣦⣿⣘⣆⠠⠰⣆⠀⡠⣀⠀⠠⣤⣊⠒⡾⢦⣾⡿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠲⠂⠀⠀⠀⠀⠢⢤⣀⣉⠙⠋⠿⠿⠶⣤⣿⣿⣄⣈⣷⣾⣥⣽⣿⠿⠛⠉⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡂⢂⠀⣀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠶⠶⠶⠿⠿⠿⠟⠛⠋⠁⢀⠀⠀⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡼⣶⠂⣣⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⡠⢄⢀⡴⠣⣤⣏⣩⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣥⣵⣴⣈⣱⣤⣎⡙⣦⣴⣻⣄⣠⣿⣶⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢗⣠⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢍⣿⢽⣽⣿⣷⡿⠳⠃⢉⣁⣐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣭⣟⣿⡻⢭⣯⣤⣿⢛⣿⣿⡿⠟⣿⣿⣷⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡏⠉⠛⠒⠻⣿⣿⣿⡧⣾⣿⣿⣿⠟⣿⠋⣿⣼⣿⢷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠃⠀⠀⢸⣿⣿⣧⣟⣏⣙⣻⠷⢻⢻⣯⣸⣆⠚⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣼⣿⣿⣿⣿⡇⡾⢻⡉⣧⣰⣧⠻⡟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣿⣿⣷⣷⡅⠀⠀⠈⣚⢛⡚⢻⢉⡏⢹⡤⣷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠈⢻⠻⠟⠛⠛⠛⢻⣛⠻⡗⣿⠈⠿⠈⡗⢸⠏
⠀⠀⠀⠀⠀⠀⠠⠒⢛⣷⣀⣠⠇⠀⠀⠀⢯⠊⠲⢤⣀⣀⣸⣿⡰⠁⠀⢠⣟⣰⣧⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠉⠀⠀⠀⠀⢸⠀⠀⠀⠈⢙⣟⠋⡧⣴⠀⠘⠉⢹⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠶⣤⣼⣃⡐⠁⢛⠀⣾⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⣤⣷⡎⠈⣇⡴⠁⡠⢣⡾⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀⠀⣬⡹⢠⠎⠀⢥⣴⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⢁⠌⣴⣎⠄⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⣴⢷⢋⠁⣠⡞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣊⠉⣨⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⢿⣻⡇⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠿⠿⠡⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠂⠀⠂⠈⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠐⠀⠉⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡉⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣄⡀⠀⠈⠀⢤⣀⠀⠀⠀⠐⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⠀⠠⠋⠀⠀⣀⡤⠒⡿⠛⠛⠻⣆⠀⣯⢘⣩⣶⡄⠒⣖⡶⠂⢴⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠀⢀⢞⠁⠀⠀⠘⠄⠀⠀⠈⢦⠘⠸⡎⠣⠘⠊⠘⠀⠀⠈⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠐⠠⢌⣆⠠⠹⡆⠘⠢⠘⡀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢛⡀⠳⡀⢑⠀⣀⡑⠜⢦
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⡄⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⢀⠏⢡⠁⠀⠰⠃⠈⠂⢍⠊⠛⠛⢧⡅
⠀⠀⠀⠀⠀⠀⠇⠀⠇⠀⡇⠀⠀⠀⠄⢰⠋⠁⠀⠀⠀⠀⠀⠀⠃⠀⠫⣀⡤⠢⡀⡰⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⣅⠀⠀⠀⠀⣿⣠⠂⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⢹⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⡠
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⣆⠄⠀⠀⡁⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢀⡦⠋
⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠀⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⡐⠒⠆⠀⠀⣀
⠀⠀⡀⠀⠁⡀⠝⠐⣈⡁⠠⠄⠈⢶⠳⠀⣆⠀⠀⠀⠀⠀⠀⠠⢠⠇⡀⠀⠀⠐⠀⠀⠈⡳
⠀⠂⢀⠂⠠⠀⠸⠢⠅⠈⠉⠖⠚⠈⢳⣔⠸⡄⠀⠀⠀⠀⠀⠀⠸⠆⠠⠀⠐⠀⡀⠀⣠⠁⠰
⠆⢔⡈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠘⢦⣹⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠃⠀⠃⠀⠀⠐⠚⠁
⢦⠀⠀⠀⢀⣠⠴⠚⠉⡉⠃⠀⠀⠀⠀⠈⠘⠻⣏⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⢀⡅
⠀⠀⠁⢠⠎⠀⠔⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠹⣦⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠥⡀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⠌⢧⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡼⠁
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠂⠤⠀⠀⣸⠀⠁⠀⠂⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠐⠀⠀⡄⠁⠀⠀⠀⠐⠶⣄⠀⠀⠐⠂⠠⠤⠔⠀⠀⠀⠙⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣀
⠀⠀⠀⠀⠙⢤⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⣀⡤⠀⢀⡠⠖
⠀⠀⠀⠀⠀⠀⠉⠐⠤⣀⣀⠀⠀⠀⠀⠀⣁⡀⢰⡠⠤⠒⠈⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣾⣿⣷⣾⣿⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⣠⣉⣾⣏⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢹⣿⣿⠯⢠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠸⣿⠦⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⣽⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡸⡁⠈⠸⡁⣴⢀⡄⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⠰⢇⣸⣿⣦⠄⠀⠀⠀⢧⡀⠀⠀⠀⢰⡇⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠇⠀⠸⠇⢸⠻⠆⠀⠦⣀⠀⢻⣆⠀⢀⣿⢁⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣇⠀⠀⣸⠀⠀⠀⠘⣿⢷⣤⣿⣾⣿⣿⣾⠟⠃⣠⣴⣦⣀
⠀⠀⠀⠀⣠⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣶⣆⣀⣄⠀⢠⣄⣀⣸⣤⣾⣯⣆⣀⣇⢀⣀⣴⣤⣤⣌⢻⣿⣿⣿⣷⣾⡔⣻⣿⣿⣿⣿⣶⡀
⠀⠀⠘⢿⣿⡿⢿⣧⠀⠀⠀⠠⠤⠴⠞⠹⠷⠿⠿⠿⣿⡿⢿⣟⠻⢯⠹⣿⣽⣿⣿⣿⡿⢫⣽⣿⣿⣿⣏⠛⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠿⠃
⠀⠀⢀⣰⠞⣉⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠻⣿⣷⡀⠀⠈⣽⢿⢹⣧⠀⣿⢭⣭⣭⣭⣽⣿⣿⣿⣼⣾⠟⠶⢿⣿⣿⠿⣷⠦⡄
⠀⠀⠙⣯⣉⣩⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠦⣤⣿⣝⣿⣦⡀⠛⠛⠒⠛⠉⠀⠀⣀⡀⠲⠄⢀⣾⣿⣿⢤⡆⠀⠀⠁⠀⠛⠻⠇
⠀⠀⠀⠀⠙⢻⣭⣿⣯⣴⣶⣿⣶⠀⠀⠀⠀⠀⣀⡄⠀⢰⣶⣿⣿⣦⣬⣿⡶⢤⡀⣀⠐⠃⠀⢉⣄⣠⣤⣾⣿⣿⣿⢸⡇⢀⠀⠙⠛⠀⠤⣀
⠀⠀⠀⣤⣤⡜⠿⠿⣿⣿⣿⣿⣿⡿⠟⠒⣚⣿⡟⠛⡶⢸⣿⣿⣿⠿⠛⠛⠛⠀⠘⠛⠳⠀⣠⣿⣿⣿⣿⡟⣿⣿⠛⣻⣆⡀⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠈⠁⠀⠆⠀⠙⠛⠿⠋⠙⠯⠁⠀⠶⠅⠁⣬⣿⣿⣿⠇⢀⠀⠓⠀⠛⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣿⢿⢛⣿⣟⢋⠘⠳⢚⣩⡟⢋⡄
⠀⠀⠀⣠⣤⣤⣤⣴⣶⣿⣷⣿⣿⣶⣶⣾⣿⣶⣾⣾⣿⣿⣿⠏⢠⣭⣿⡶⣀⣴⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠁⢹⡇⢈⣶⠗⢊⣽⣦⡿⠁
⠀⠀⠀⠉⠉⠉⠻⣿⣿⠉⣛⣽⣟⣿⠹⣿⣿⡿⠛⠛⠛⠻⣿⠘⢞⡀⢫⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠟⠋⠄⣠⣴⢸⣷⣏⣤⡴⠟⣧⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⢳⡟⠛⠟⠙⠉⠀⠀⠀⠤⠀⢌⣱⣿⣿⠋⣿⢿⣿⣿⣿⣿⠟⠁⠀⠁⢀⣸⠟⣉⠘⣿⣿⣿⡁⠀⣼⠃
⠀⠀⠀⢠⢠⡀⣤⠀⢄⠀⢠⣤⣀⣾⡀⠀⠀⠀⠀⣠⠂⢠⣴⣶⠾⣿⣿⣿⠐⠃⠀⠈⣉⠉⠀⠀⣠⣤⣶⡟⠃⠀⡼⢶⢏⣻⠿⠛⣠⣿⡄
⠀⢰⣶⡄⠈⠃⠸⡁⢞⢁⣠⣿⣿⣦⣈⠇⠀⠀⠀⡀⢠⣿⣯⡉⠃⣿⣿⣿⣦⣀⠀⠀⢸⣾⣿⣿⣿⣿⣧⣀⡀⠘⠳⠎⠄⣹⣷⣿⡡⠾⣯⠆⡀
⠀⢰⡟⠧⣤⣀⡀⠄⠛⣾⣿⣿⡿⣿⣿⣦⡄⠀⠀⣿⢏⣩⣽⣾⡇⣿⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣶⣾⢿⣿⣿⣷⣤⡤⠿
⠀⠀⢁⣠⣬⣿⣟⣶⣷⢿⣿⣿⣷⣿⢿⣿⡷⣶⣖⠿⠟⣿⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣾⡿⠕⠈
⠀⠀⢿⣤⣿⣹⢿⣭⡿⢿⣿⣿⣿⡟⠋⢹⣷⠙⣻⣷⣤⣿⣷⡿⣿⡿⢿⣿⣿⠿⢿⣿⣿⣿⣷⣮⣙⣿⣿⣿⣿⢻⣿⡿⠁⠀⠀⣴⣶⠖⠒
⠀⢰⡎⢩⣿⣽⠶⣤⣝⢡⡜⣿⣿⣇⠀⠐⣹⣿⣿⣿⡏⣹⣿⣷⣿⣶⣿⣿⣿⣶⣿⣯⣽⣧⡴⢾⡉⠩⣿⣻⣿⣿⣿⣷⣶⣤⣄⠀⠉⠀⠂
⠀⠻⢟⣄⠑⠾⢖⣠⣿⣾⣿⣿⣿⣷⣦⣼⣿⣿⡿⠁⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣬⣼⣷⣾⣓⠒⣿⣿⣿⣿⣟⣛⣿⣿⣿⣦⡀⠠
⠀⠀⠀⣠⣤⠘⠟⡋⢉⣝⣛⣿⣿⣿⣿⣿⣿⣿⣷⣆⣼⣿⣿⣿⢉⣿⡟⣸⡿⢿⠂⣩⡾⠿⣿⣿⣿⡇⠛⣻⣿⣿⣿⣿⣿⣿⣯⣿⣄⣀⡀
⠀⠀⠀⠀⣿⡵⣾⡿⠂⢩⣉⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣵⢮⣱⣦⣿⡷⢊⣶⣷⣶⣿⣿⣿⣸⡷⢻⣿⣯⣿⣿⠛⠟⠹⣏⠕⠙⠿⠃
⠀⠀⠀⠀⠉⠐⠿⠰⣿⣆⠙⠿⢿⣿⣿⣿⣿⣿⢟⣵⣿⢿⣯⡿⠾⢿⣿⣿⣷⠾⠟⣿⣟⢿⣿⣿⣿⡟⢷⣾⣿⡅⠩⣝⡀⠆⠘⠛
⠀⠀⠀⢀⣀⣤⣀⣈⣽⠛⠓⠀⠈⢿⣿⣿⣿⠿⡿⣫⣿⡾⠃⣴⣾⠿⣿⡿⠛⠶⣾⡿⢘⣻⣿⣿⣿⠿⢞⣿⠽⣿⣴⣤⠷⠶
⠀⠀⣴⠟⠉⠉⢀⣉⣠⣝⢶⣤⣤⣬⣿⣿⣿⣷⣤⣿⣏⣁⡀⡀⠁⠶⣿⣿⣿⣿⣡⣷⡀⠀⠀⠀⠉⠈⠀⠀⠈⠁⠉⠉
⠀⣼⠃⣠⣶⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠙⠛⠻⢿⣿⣿⡿
⠀⠀⣸⣿⣿⣿⣿⠿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣯⣤⡉⠙⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⡉⠉⠉⣉⣉⣩⣵⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣿⣿⣿⣿⡿⠟⠛⠋⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⢤⣤⡖⠒⣖⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡛⠋⠉⠀⢛⢠⣥⣶⣻⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⡄⠰⠶⣿⣿⡿⢻⡀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⣀⣿⣧⡤⢭⣿⣻⣿⣴⣧⣀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⢰⠿⡌⠁⠀⠀⠀⠈⠛⠿⣷⣿⡷⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⢸⡝⡙⠂⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡻⣆⡡⢂⠌⡩⢃⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣝⣣⠎⣀⢁⠔⡠⡱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢮⣕⢮⡊⢔⠅⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣻⡤⢊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣤⣤⡀⠀⠀⠀⠀⢀⣿⣷⣏⢐⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣾⣿⡇⡯⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣫⠿⢓⡓⠶⢭⣙⠻⢿⣿⣿⣟⣽⣭⣴⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⡇⡜⠉⠉⠓⠦⣆⣋⢒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣝⣷⣤⣀⣀⣤⣤⣾⣿⣿⣿⢿⣻⡿⠿⠻⢹⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠷⣋⠤⠒⠛⠓⢮⣊⠽⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⢻⡽⣪⠥⠋⠁⠀⠀⠀⠀⢸⠂⢐⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢈⣉⠙⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⢀⡒⠀⣸⣱⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣾⣼⣵⣒⡠⡤⠤⡤⠀⢀⠀⡀⠄⠒⣉⣥⣾⣵⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠛⠿⣷⣾⣭⣽⣟⣓⣲⣾⣲⣷⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣶⣌⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⢭⡙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢗⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣯⣾⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡞⣯⣤⣾⣿⠿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠭⠽⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⣶⣄⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⠏⠀⣹⣿⡿⠿⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣤⣩⣿⣟⣿⣿⣶⣿⣿⢯⠞⣻⣿⣶⣦⣝⡻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣝⡻⣿⣿⢿⣿⣿⡛⣯⣵⠧⠞⠃⢈⣝⢿⣿⣿⣦⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡳⣼⣿⣿⣧⣿⣥⣤⠴⠶⠋⠉⣦⠻⣿⣿⣿⣦⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣎⢿⣿⣿⡏⣶⡤⠤⠴⠶⠟⠉⣧⠹⣿⣿⣿⣷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⣴⣻⣟⣣⣿⣿⣤⣤⣤⡴⠾⢻⡆⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⢿⣿⣿⣿⣿⣤⣤⣤⠴⠾⣷⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡤⠤⠤⢤⣿⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⣇⣠⣤⣤⣤⣿⠂⣿⣿⣟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⣀⣠⣿⢠⣿⡟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣉⣉⠉⣻⣿⢸⣿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⢹⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠙⠛⢳⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠙⠛⣶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢿⣄⣉⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢯⣉⣻⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⡤⣞⣯⣽⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠀⠀⠀⠀⢀⣤⣖⠛⣧⣼⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⣠⢶⣦⣶⣶⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣠⣿⣯⠏⠀⠀⢠⣞⣋⣉⣩⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣴⣯⣶⣿⣿⣿⣿⣿⣿⠿⠛⠻⣝⣻⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣼⣿⣟⡎⠀⠀⢠⡟⠉⢉⣹⣿⣿⣿⣿⢿⣷⣶⣶⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⣿⣀⣘⡎⣿⣿⣿⡇
⠀⠀⠀⠀⢠⢻⣿⡟⣄⠀⠀⢸⡶⠟⠋⠙⣿⣿⣿⣿⣮⣛⣻⣟⣛⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⢀⣠⣾⡉⢉⡽⢣⣿⣿⣿⠁
⠀⠀⠀⠀⠘⡜⣿⣿⣿⣿⣿⣿⣷⣠⣤⡶⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⣿⣿⣿⣶⣾⣿⣯⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠚⠿⣿⣿⣿⣿⣷⡻⣤⣀⣤⡶⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠛⠶⠦⠶⢿⣭⡭⠽⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠙⢛⠂⣀⣬⣌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣾⣿⣷⣾⣿⣿⣿⣿⣏⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠟⠿⢿⣿⣿⣿⣦⠀⠙⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠋⠀⠟⣿⣿⣿⡟⠀⠀⣸⣿⡿⠛⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢁⠐⣻⣶⣏⡇⠀⠀⣿⠟⠉⠄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠈⢠⠚⣿⣿⡃⠀⠀⣿⠀⠀⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠀⢂⣿⣟⡇⠀⠀⣿⡀⠀⠂⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠌⢿⣗⡇⠀⠀⣽⡇⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⢹⣿⡧⠀⠀⢸⣇⠐⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠻⣿⣛⠀⠀⢸⣿⠀⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢿⣿⠀⠀⠈⣽⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⠀⠀⠀⣽⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⢸⣿⠀⠀⠀⣏⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠐⠃⠀⢀⢸⡯⠀⠀⠸⣿⠀⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣰⣶⣿⠋⡼⠃⠀⢀⣾⡷⣶⣴⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡉⡀⢈⠉⡡⠞⠁⠀⢠⢶⡏⠀⠀⠈⠟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣥⣤⣤⣶⡾⠿⠿⢿⣷⣥⣉⣀⣠⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡻⠒⠅⡐⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠉⡉⠀⠀⠀⠀⠀⠄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⣀⣀⡀⠀⠂⠀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⡞⠁⠀⠀⠙⡇⡄⣘⠙⠉⠢⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠡⡀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠻⣔⠃⠀⠀⠀⠀⠀⠘⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⠹⠐⠤⠄⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠄⠀⢸⡓⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠔⠁⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠂⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠀⠀⠁⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠐⠀⠁⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⣀⠠⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢜⣮⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠈⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠠⡀⠀⠀⢀⡀⠌⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⠈⡈⠀⠂⠠⠀⠈⠙⠒⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣄⣴⡆⢲⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠁⠂⢄⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣀⡀
⠀⠀⠀⡀⣤⣿⣻⠿⠿⠶⠧⣀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠉⠓⠢⢄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⢹⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣤⣉⣉⠑⢠⣀⠀⠊⠈⠀⠂⠀⢀⠀⠈⢧
⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣭⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡠⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠦⠀⠆⠀⢀⠀⢻
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠁⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠴⠃⠀⡇⠐⠂⠉⠘⠘⡀⠀⢸
⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠤⠄⠀⠉⠛⠓⠲⠶⠶⠶⠖⢚⣛⠛⠛⠛⠙⠉⠉⠉⠀⠌⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⢈⡟
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣷⣔⠈⠀⠀⠂⠐⠀⡆⠀⢀⢄⠐⠙⡋⠟⠡⠄⠀⢘⢟⠄⠀⠉⢂⠀⠀⠀⠰⠘⠀⠀⣀⣴⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢓⣛⣷⣦⣈⠀⠀⠸⠀⠀⢈⢇⠀⠀⠐⠀⠀⠀⠀⠀⠊⠀⠀⠀⣀⣀⣀⣤⣤⠴⣶⠿⠿⢿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠛⠲⠦⣤⣤⣤⣬⣤⣤⣤⣤⠤⠴⠶⠶⠶⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣀⣖⠀⡶⠂⢰⡄⢀⡄⠀⠀⡄⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣀⣰⠀⠀⠁⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⣀⠟⢣⣼⣿⣿⡟⠛⠋⠉⠉⠉⡙⠛⠦⣴⡅⠰⠆⠀⠈⠂⠀⠀⠰⣿⣇⠀⣀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⣼⠋⡾⠟⣤⠟⠁⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠹⢦⣼⠛⠀⣱⣿⣷⣤⣀⣀⣀⣛⣡⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠛⢰⡦⢠⡟⠣⠀⠀⠀⠀⠀⠠⣀⣤⣶⣶⣶⣶⣦⣿⡄⠀⣿⠋⠛⣿⣿⠉⡟⢁⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸⡆⠾⠠⣿⠁⠄⣀⠀⠀⠰⣶⡟⣯⣽⣿⠿⠛⠋⠉⠉⠻⣦⢩⡀⠀⠈⢿⠎⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⡀⣤⠴⣟⠀⠀⠀⠀⠀⡞⢠⡞⣣⠚⠁⠀⠀⠀⠀⠀⠀⠈⠳⣿⣧⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⢨⡀⣿⠀⠀⠀⠀⢰⣭⡏⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⠈⡁⢸⡁⠀⠀⠀⣸⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠉⣀⢳⠒⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡉⢌⣗⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢏⣨⣄⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⣆⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣀⡴⢀⡆⢠⠐⠠⠖⠦⡀⢤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣾⣦⣷⣴⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣾⡟⣿⣾⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷⣿⢟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣩⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⡷⠿⢟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠲⠶⠭⠿⡭⣭⣽⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣀⡤⠶⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⢖⡤⢠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠛⠚⢿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡪⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢶⣲⡿⠟⠛⠛⠛⠛⠛⠛⢿⣶⡶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢋⣴⠞⢻⡟⠀⣶⣄⠀⠀⠀⢀⣴⡄⢹⡟⠻⢦⣍⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣰⠟⠀⠀⠈⣷⡀⠈⠉⠀⠀⠀⠉⠉⢀⣼⠃⠀⠀⠙⣦⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣰⡏⠀⠀⠀⠀⢸⡟⢦⣄⣀⣀⣀⣠⡴⠟⡿⠀⠀⠀⠀⠸⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠘⠿⠶⠿⠋⠀⢸⡇⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠈⣷⠶⠶⠦⠤⠤⠶⠶⢾⡇⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣼⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣽⣆⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠀⠀⠀⠹⣆⠀⠀⠀⢻⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⣰⠟
⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⣀⣤⣤⠶⠾⣧⠀⠀⢸⣆⣀⣀⣀⣀⣀⣀⣿⠀⠀⣴⣟⣳⣶⣦⣄⣀
⠀⣰⠟⠀⠀⠀⠀⣤⠾⠛⠉⠀⠀⠀⠀⠘⣧⠀⢸⡏⠉⠉⠉⠉⠉⢉⡇⠀⣼⠏⠈⠉⠉⠙⠛⠛⠻⠶⠦
⢰⡏⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⡷⠶⠶⠶⠶⠶⢾⡇⣸⠏
⣾⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣇⣀⣀⣀⣀⣀⣸⣷⡟
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⢹⣿⠁
⣿⡄⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠶⠶⠶⠶⠶⢾⡿
⢸⣷⡀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣀⣀⣀⣸⡇
⠀⢻⣷⣄⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠉⠉⠉⢸⡇
⠀⠀⠻⣝⠷⣄⡀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣄⣀⢸⡟⠲⠶⠶⠶⠖⢻⡇
⠀⠀⠀⠙⢷⣌⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣧⣄⣀⣀⣀⣠⣼⣧⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠳⣤⣈⠉⠛⠶⣤⣄⣀⡀⠀⠀⢸⡇⠈⠉⠉⠉⠁⢸⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠳⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠈⠉⠛⠛⠶⢾⡟⠛⠒⠒⠒⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⣤⣄⣸⣧⣤⣤⣀⣤⣤⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠈⣧⠉⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⣤⣤⣤⣤⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣀⣈⣛⣦⣄⣀⣀⣀⣀⣤⣤⣤⠶⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⣀⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣭⣁⣀⡀⣉⣠⣈⠖⠂⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⢉⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⡟⠛⠁⠀⡿⢿⣧⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣗⡡⣿⡗⠀⠀⢺⠿⢨⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡧⣃⡀⠀⣀⡀⠀⠀⣼⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣾⣿⡿⠿⣎⣷⣾⡗⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡷⣿⣿⣿⣭⣟⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢘⡟⠛⢂⡗⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠭⠄⢤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⣤⣤⣤⣤⣤⣼⡿⠀⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⢵⣷⣛⣿⣶⣿⣿⣿⣿⣿⣷⡖⣲⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣜⠹⣿⣿⡿⠬⢿⣿⣿⠿⢌⣽⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⠻⠳⣿⣋⣀⣠⠶⣿⣟⣲⣄⣼⣟⡿⡿⢛⡟⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡄⠉⠓⠚⠛⠋⠗⡀⣯⣶⣿⣿⢥⣧⣿⣷⣾⣿⣿⣟⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣷⡇⣦⣼⣷⣷⣶⣿⣿⣿⣿⣿⣿⡯⣿⣿⠏⡯⠀⠸⣠⣦⣤⣤⡌⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⣼⣿⠛⢺⠿⣿⣿⣿⠟⠉⢍⣎⣲⣿⣿⣿⢧⡆⢺⡥⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡬⢫⣇⠩⡇⢸⠛⣻⠿⣲⣶⡦⣶⢟⡧⢴⡿⣧⣾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢼⢃⣸⡇⣸⣧⣷⡐⣧⠘⣦⣿⡇⣿⢾⣗⠎⠁⠒⠙⠛⢗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠄⠻⡓⣟⣱⠏⣴⣟⣼⠿⠷⠌⠉⠀⠀⠀⠀⠀⠀⠛


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⣔⡂⣚⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠰⠓⢱⡟⣧⣏⣻⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣻⢘⠛⣄⣷⢋⠜⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡿⣼⣿⣿⡁⡶⣭⢾⡋⢻⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⣧⣻⣿⣿⣿⣿⠿⢳⠟⡾⣑⠗⣬⣖⣤⠎⠁⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣷⣽⣿⣿⡛⠛⣤⣹⣦⣬⣴⣭⣿⣴⢿⣭⣽⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣯⣻⣿⣿⣋⢠⣼⣿⡿⡟⣻⢟⣿⢿⣿⣿⣷⣦⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⣿⣧⠤⢾⣿⣿⣾⣿⣾⣿⣿⣼⣫⣾⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣻⣿⣄⣀⣀⠙⢉⣭⢩⠍⣠⡍⠙⣿⣿⡿⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠘⠃⢹⣿⣧⠸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢤⠊⠉⣰⣿⣿⣻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢲⠉⠀⢃⣀⣤⣶⣾⣿⣟⣽⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢆⣤⣤⣿⣿⡿⣟⣿⣩⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢄⣴⣿⣿⣿⣳⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣼⣿⣿⣿⣿⣿⠟⠁⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⠁⠰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⠋⠀⢻⣿⢟⣻⣿⣿⣿⣿⡏⣺⡟⣿⡿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣸⡉⠀⠀⣲⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡦⠄⢺⣿⣿⣻⣿⣿⣿⣿⣾⣿⣾⣟⣼⣿⡿⣟⣿⣿⣿⣇⠀⠀⢸⠉⠀⣀⡶⠛
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⢿⣎⣿⡷⠆⠘⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠉⠂⢠⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⢰⣿⣾⣟⣭⣟⣿⣦⣿⣿⣷⠒⠒⠈⢻⣿⣿⣿⣿⣿⣷⣶⣤⣾⣿⣿⣿⣿⣿⡿⠋⢠⡄⣾⣏⣿⡏
⠀⠀⠀⠀⠀⣿⣿⣿⡟⣹⣿⣿⣿⣿⡿⠋⠶⠒⠒⠀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣁⠀⠈⠁⢿⣿⣿⡷⡄
⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣾⠿⣿⣏⣿⢿⣟⣿⣿⣽⣿⣿⣿⢿⣿⣦⣄⣀⠘⠁⠀⠀⠘⣧⣿⣇⠸⣄
⠀⠀⠀⠀⠀⠡⠸⡿⠿⣿⣿⣿⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣟⣿⣿⣶⣶⣶⣾⣿⣾⣿⡆⣌⡂
⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠉⢻⡿⠿⠿⠿⣿⡿⠿⠿⠿⢿⡿⠿⠟⠿⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⡃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⢀⡁⠀⠀⠀⢁⡏⠙⠻⠿⠿⠿⢿⠛⠋⠙⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠀⠓⠒⠒⠀⠀⠉⠉⠉⠀⠁⠉⠑⠒⠀⠲⠤⣀⡀⣈⣀⡀⢀⠣⠄⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠶⣦⠤⢤⣤⣤⠤⢤⡶⠖⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⢿⢷⡄⣈⠀⠀⠙⠁⠀⢀⡀⣴⠟⢷⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⡟⢁⠀⡸⢦⡼⢁⠀⢠⠔⠚⠒⢤⠄⢀⠹⣤⠾⡀⢀⠙⣷⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⠊⠉⢁⠘⠆⠀⠀⠉⢁⠀⠀⢀⣀⣀⠀⠀⢀⠉⠁⠐⠀⠞⢀⠉⠉⠺⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣸⠆⣤⣴⣿⡀⣄⠀⢦⣠⢼⣦⣿⣿⣿⣿⣿⣦⣾⢄⡤⠆⢀⡄⣸⣷⣤⡄⢾⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⢹⠁⣤⣿⣿⣿⣿⠾⠿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⡿⠿⢾⣿⣿⣿⣧⣀⣹⠁⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣄⠴⣿⣿⣿⡟⠙⢤⠿⡄⠀⢻⣿⣆⢿⣿⣿⣿⣿⣿⣿⣇⣿⣿⠃⠀⡼⢧⠜⠙⣿⣿⣿⡷⢄⡸⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣰⠁⣰⣿⣟⡸⢇⢀⡼⣄⠉⢳⠈⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⠋⢀⠼⣄⣀⠷⣙⣿⣷⡀⣷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡷⣿⡿⣹⠀⠀⣯⠀⢸⣧⠈⢆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠎⢠⣿⠀⢨⡇⠀⢸⡹⣿⣷⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠞⢿⣿⣟⠁⢱⡎⠈⢲⠃⠘⠆⠈⠆⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠎⠀⠞⠁⢳⠊⠈⡖⠁⢙⣿⣿⠟⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⣿⠛⣤⠜⠣⣤⠞⢦⣼⠃⠀⢸⠈⣿⣿⣿⣿⣿⣿⣿⡏⢰⠀⠀⢻⣤⠚⢦⡤⠛⢄⡜⢻⣿⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢀⡾⡀⢀⢧⡀⡸⢧⡓⠀⠈⠆⢻⣿⣿⣿⣿⣿⣿⠁⠏⠀⠐⣃⠿⡀⡰⢇⠀⡸⡄⢸⣿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⢻⣯⠀⢨⡇⠀⣹⠀⠈⡟⠢⠀⢰⡀⢻⣿⣿⣿⣿⠋⣸⠂⠀⠚⡇⠀⢸⠁⠀⣿⠀⢈⣿⢋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣿⢲⠊⠑⡶⠋⢳⡞⡿⠦⠀⠀⠳⣄⡉⣿⡏⣁⡴⠃⠀⠠⠾⡟⣶⠉⠳⡖⠉⢲⢸⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠛⢤⡰⠻⣄⠜⠣⣿⠶⠤⠀⠀⠀⠀⢹⠃⠀⠀⠀⠠⠴⢾⡥⠛⢄⡜⠣⣀⠜⣣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣰⡇⠀⣼⡀⢀⣿⡦⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⣀⡠⣾⣇⠀⣸⡀⢀⣷⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⣏⠀⢹⡇⢸⣦⣀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣤⣾⠈⣿⠀⢈⡏⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢲⠋⠙⣾⣄⡀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⣀⣼⡞⠉⢳⠊⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢦⡰⢻⣅⡈⠁⠀⠀⠰⠀⠱⠀⠀⠈⠉⣁⣽⠣⣀⢞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣇⢸⣏⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⢀⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣨⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠂⠀⠀⠀⠀⠀⠀⠀⠐⢚⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⢀⣀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣆⣤⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠜⠁⠀⢘⢣⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⢀⢨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠬⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠩⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣖
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⣀⣤⣤⣤⣤⡀⠀⠐⠲⠶⢶⣦⡤⠀⡀⠀⠀⠀⠀⢸⡄⠀⠹
⠀⠀⠀⠀⠀⣠⣄⡆⠀⢸⣿⣿⠛⠋⠀⠀⠀⢀⡶⡄⠀⠈⠛⢲⡦⢤⣦⣄⣀⣿⠃⡀⠁
⠀⠀⠀⣠⠂⠙⣇⣿⡀⠈⢿⣇⡀⠀⠀⠀⠈⠐⠠⠌⠁⠀⠰⢾⠃⠀⠀⠀⠚⠀⡐⠎
⠀⠀⠠⣿⠀⠀⣿⠋⢧⣄⠀⠉⠻⠦⢤⣀⠀⠀⠀⣀⣤⣤⣦⣤⣄⣀⣀⣴⣴⣦⣄
⠀⠀⠀⢽⣆⠀⠘⠢⠄⠙⠓⠄⢷⡆⠀⠀⣀⣉⠉⠉⠉⠉⠡⠴⢚⣿⣿⠿⠃⠙⠍⠂
⠀⠀⠀⠀⠙⠷⣦⣀⣀⣤⣤⣿⣶⣦⣤⠄⡐⠶⠠⠶⠆⠴⠒⠚⠉⠉⠁⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠐⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢤⠤⠤⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⢸⣆⠀⠀⢸⠀⠀⢀⣼⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠓⢄⡀⠘⠟⡑⡶⢺⠳⡖⢋⠟⠁⢀⡠⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⠖⠋⢉⣷⣤⠤⠴⠗⠚⠓⠳⠤⠤⢶⣟⠉⠓⢦⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣀⢀⡼⠦⣼⠁⠀⠈⡿⢉⣄⣐⣂⣈⢹⡉⠀⠈⢱⡤⠼⣁⢀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢩⡏⠀⢠⠞⠒⠲⢶⡁⠀⠐⠒⠒⠂⠉⣳⠖⠒⠚⢦⠀⠘⡏⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢄⣠⠗⠲⡏⠀⠀⠀⣆⡈⠉⠉⠉⠉⠉⠉⣨⣄⠀⠀⣸⠖⠺⢅⣠⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⡇⠀⢠⠏⠛⠛⢙⣄⠀⠉⠉⠉⠉⠉⠉⢀⡌⠉⠉⠉⡆⠀⢸⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢹⠖⠛⣄⣠⡤⢮⠀⠉⠉⠁⠀⠀⠉⠉⠀⡸⠦⢤⣤⠟⠒⢺⠀⢙⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠙⣦⣤⣇⠀⢀⣮⠉⠁⠒⠒⠒⠒⠂⠉⠁⢸⣤⣀⣠⢧⣤⡞⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣿⠀⢨⡋⠁⢸⠑⠢⠤⠤⠤⠤⠤⠔⠒⢻⠀⠀⢹⠀⢀⣧⢴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣟⠙⢦⡠⠼⡦⢀⣀⣀⣀⣀⡀⠠⠤⢞⠲⢤⠞⠙⣏⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⣦⢼⠀⠀⣣⣀⡀⠀⠀⠀⠀⢀⣀⣜⠀⢠⠧⡼⢹⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣤⡟⠉⠙⣄⣈⡉⠉⠉⠉⣁⣀⡎⠉⣯⣠⢿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⠀⠀⠹⣇⠙⡶⠺⣇⠀⠈⠉⠉⠉⠁⠀⡵⢶⠃⣸⠎⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⣩⠥⠖⠋⠁⠀⠀⠀⠹⣿⢧⣠⣏⠉⠉⠒⠒⠒⠉⠉⣣⠿⣞⠏⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣤⡏⠉⠓⠒⠒⠒⠒⠉⢱⣤⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⢀⡴⠋⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣨⠗⠢⠤⠤⠤⠤⠤⠤⢾⣿⠛⠉⠛⠓⠒⠲⠤⠤⠤⠤⠤⠤⠖⠂⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⡞⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⠹⣾⣀⠀⠀⠀⠀⠀⠀⠀⣨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠦⣄⣀⣠⠤⠴⠚⠋⠁⠀⠀⠀⠀⠀⣇⠈⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠑⠲⠤⠤⠤⠤⠤⠖⠊⢱⠒⠒⠲⠶⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⠀⠀⠀⢀⣀⣀⣠⡤⠖⠚⠉⠈⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠙⠒⠒⠊⠉⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⣘⠀⡁⣄
⣤⡆⠀⠀⡄⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣫⣵⣤⣮⣳⣄⢀
⡷⠃⠀⠀⠰⠁⢾⡅⠀⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣶⡖⣶⣶⣶⣿⣆
⡐⠀⠂⠀⠳⣅⣾⣱⢿⡃⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⠉⠹⠛⣿⢿⡻⣿
⡍⠀⣙⡂⠀⣞⣛⠻⣾⡁⠠⠀⠻⢿⣿⣿⣯⣽⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣽⣯⡿⢀⠀⢛⣤⣿⡙⣿
⣷⠀⢉⢃⣈⠋⠉⠁⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣷⣷⣧⣽⣿⣿⣿⣻⣿
⣏⢀⣴⡇⠉⡀⣘⠂⠀⠀⠀⠀⣼⣿⣿⣿⠙⢿⣿⣿⣿⣿⣧⠀⠀⢠⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿
⣭⡶⠄⠀⠈⠄⠙⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⡀⣰⣎⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⠿⠉⡀
⡌⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⠟⠑⠛⣶⠏⠿⣿⣟⣷⣿⣿⣿⡿⢟⠛⣧⣀⢐⠈
⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠿⠛⠉⠉⠉⣁⢽⡍⢙⣿⣯⣌⣧⣟
⣿⠇⠀⠀⠀⠘⠀⣀⠀⠀⢸⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣀⣠⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠈⣟⡫⠀⣇⣬⣯⣿⣿
⣿⣿⣀⣾⣄⠀⠈⠋⠀⠀⢸⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠈⠗⠊⠛⢃⠄⢩⠿
⣿⣿⣿⣿⣿⣿⣦⡔⠀⢀⣸⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈
⠰⡿⢿⣿⣿⢾⣇⣤⣼⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣽⠾⠚⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠈⠉⠈⣠⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⡟⣽⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣮⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣶⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⣾⣿⣸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠤⠀⢈⣿⣿⣿⣿⣿⣿⡏⠀⣿⡆⠀⢠⣿⣿⣿⣿⣧⣄⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⣿⣿⡇⠈⠓
⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⢸⡆⢀⢸⣿⠙⢿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⠁
⠀⢀⣿⣿⣿⣿⣿⡏⣁⠄⠀⢸⣿⣼⣾⣿⡀⠀⠈⠙⠛⠻⠻⣿⣿⣿⣿⡿⠋⢸⣿⣿⣿⣿⣿⠀⣰⣿⡟⠁
⠀⢸⣿⣿⣿⣿⣿⣿⠉⠀⠀⢀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⠀⣸⣿⣿⣿⣿⡇⢰⡿⠋
⠁⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⣇⣠⣴⣿⣿⣿⣿⣿⠇⢻⡇
⣴⣄⣿⣿⣿⣿⣿⣟⠀⣀⡄⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⢿⣤⣀⣀⣀⣤⡶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉⠉⣉⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉⠛⠉⠁
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣤⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡋⡀⢀⡠⠄⠀⠀⢀⠀⠰⡤⢤
⣿⣿⣿⣿⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠛⠀⠁⣀⠀⠐⠒⡌⡁⠀⠘⠂
⣿⣿⣿⣿⣿⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠎⠖⠊⠑⠃⠀⠄⢲⡀⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣶⣷⣆⣐⢶⣐⣦⠎⠀⠀⠹⠅
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠁⠉⠀⠉
⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣤⣀⣈⣤⣤⡈⠑⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣿⣿⣇⣈⡋⠹⢟⣻⣧⣭⣶⣦⣬⡁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠁⠙⢦⣤⣥⣤⣭⠯⠽⠤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⢈⣷⣅⠂⠠⢈⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⢸⣿⠟⢻⣿⣿⣦⡙⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣿⣿⡿⡌⣿⠂⠘⣿⢿⣿⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢿⣿⡟⣧⠹⣆⠀⠘⢿⣵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢯⣿⣽⣧⡸⣶⡀⡠⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡗⣿⣿⣷⣌⢿⣤⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⡻⢷⡄⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣌⠻⣆⡀⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠹⡤⠚⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢿⣋⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠘⣧⠤⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡼⠶⢺⠀⣠⣔⡪⣭⣓⠀⡀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣤⠠⣤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠓⠂⣸⠧⢾⡽⣿⣻⡙⣧⣽⡈⢂
⠀⠀⠀⠀⠀⠆⠉⣋⡁⠶⢤⠻⢌⠱⠦⣷⢎⣹⡗⣶⠤⣄⣀⣀⣠⣤⣴⢞⡴⠏⠉⣹⣿⣓⣯⡽⣯⡉⡧⢚⠸⢻⣶⡅⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⣀
⠀⠀⠀⠀⠃⢈⠰⠅⢠⠒⠄⡛⢢⣍⡳⣯⡩⣍⢧⣨⣥⣱⣌⢻⡽⢟⣻⣟⠶⠶⢾⣿⠛⢛⡩⣽⢯⡜⣙⣧⠞⣡⣰⠇⠀⠀⠀⠀⣠⢀⡾⠋⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠘⣴⠺⡩⣧⣤⣤⣌⣗⡚⠷⠞⠦⡵⣌⠳⡌⢶⡷⢂⡷⢤⡐⢈⣉⡶⠿⣛⣶⣛⣾⣭⠧⣞⢙⣥⣿⣶⣶⣲⣴⣖⡿⠋
⠀⠀⠀⠀⠀⠀⠚⠈⠁⢏⡙⣭⡿⢿⡿⢿⣻⣿⣿⣿⣿⣭⣟⣦⡑⣶⣍⣡⣍⣲⠦⢼⣉⠱⠶⢿⠶⣗⡈⠔⠋⠙⠛⠛⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⣋⣉⣙⣷⣿⣿⣾⣿⡿⠿⠟⠛⠉⠉⠉⠛⠓⠓⠶⠿⠷⠶⠦⠛⠐⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠄⠂⠶⠖⠤⠄⠀⠤⠠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠋⠙⠠⠤⠂⠀⠠⠝⠰⣯⣤⣶⠀⠑⡆⠲⣬⣁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢏⡠⠓⠄⢀⡀⠸⡀⠀⠀⢀⡶⢣⡞⢾⠉⣘⣇⣾⡇⢨⣿⡝⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡛⠤⣔⠾⣀⡀⠀⠀⠙⡄⠀⠉⠻⠋⣴⣾⠀⢸⠁⣠⠉⣃⣀⠬⣤⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣤⡈⢫⠭⣉⠉⡁⢲⡞⢒⡲⠚⢒⡟⠉⢤⡍⠀⢉⣁⡀⠤⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣶⣶⠆⠉⢀⠄⡐⠋⠠⣤⣐⡶⠾⠋⣀⣰⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡙⠻⣿⠎⠙⠀⠀⠈⢤⡇⠉⣵⠾⡀⢁⡠⢦⣙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣾⢿⣿⡶⢒⣀⠈⢻⠟⠛⠂⠀⠀⣴⠿⠁⢀⡹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡶⠛⠛⢻⡉⠙⠷⠀⠑⠂⢀⣀⣼⠉⠀⠀⠀⠙⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣿⣧⣴⢖⢉⠉⠀⠀⠀⠀⠀⠐⣿⣿⢀⣀⠀⠂⠺⣞⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠿⢃⣠⣾⣿⣆⣀⡀⠀⠀⠀⠀⢿⡾⢸⣿⡦⢤⠀⡘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⡸⣿⣿⠏⠀⠈⠃⠀⠀⠒⠐⠈⠀⠈⣿⠇⢈⠁⠙⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠟⡤⢿⣿⡷⠒⠂⠠⠤⠀⠤⠀⠀⠀⠐⢋⠀⠈⢦⠤⣦⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣀⡞⠈⡹⠄⣀⣀⣂⢀⡀⠀⠀⠀⠀⠀⡈⣤⠀⣠⡀⠘⡷⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢣⡸⣤⣀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠘⣧⠀⠈⠛⠘⢧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢀⠁⠛⠛⠓⠶⠶⠦⠴⠶⠀⠂⠀⢀⣾⠈⠷⠀⢦⠀⠸⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡉⠰⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⠘⠀⡀⠈⠓⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⢇⡀⠀⠉⠁⠀⠉⠉⠉⠉⠉⠀⠀⡀⠾⠆⢙⡁⠀⢣⡀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡏⠀⠠⣄⣀⣠⣤⣤⣤⣤⠔⠊⠁⠀⣠⣾⣷⣄⣠⡉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠋⢹⡉⠉⢷⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠏⠙⠙⢶⣤⣤⣤⣶⣶⠚⠛⠁⠀⢀⣴⣿⣷⣄⣸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡴⠧⣄⠉⠉⠀⠈⠋⠀⣀⣠⡶⠛⠏⢈⡇⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣰⣿⠙⠒⠿⠿⠟⠛⠁⠀⠀⢀⣴⢿⣿⠷⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣿⠦⣀⣀⣀⣀⣀⣤⡤⠴⠛⠁⢈⣿⣧⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⢠⡈⠉⠉⠉⠉⠁⠀⠀⢀⣤⡿⠿⢣⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠷⢦⣤⣤⣤⣤⡴⠞⠋⠁⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⢶⠀⠀⠀⠉⠀⠀⠀⢀⣠⡴⠛⠋⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣼⣟⣿⠲⣶⣶⣶⣶⠚⠛⠁⠀⣠⡔⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣿⢠⣽⡟⠀⠁⠀⠀⠀⢀⣀⡴⠚⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠋⠉⠚⠟⠀⠊⠉⠉⠉⠁⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠤⠀⠠⠀⠀⡄⠄⠄⠀⠆⠄⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠂⠀⠀⠆⠠⠀⠆⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡭⠉⠉⡩⣉⡭⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠍⠅⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠄⠅⠀⠀⠀⠀⠐⠁
⠀⠀⠀⢀⠐⡷⠈⠀⠠⠀⡠⠂
⠀⠀⠄⠀⠀⠘⠠⠀⠄⠊⠀⠀⠀⠀⢀⣀⣠⣄⡀
⡄⠑⠀⠀⠀⢎⡀⠃⠀⠀⠀⠀⠀⣶⣿⣿⢿⡟⠃
⡇⠀⠀⢂⠀⠊⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⢸⡇
⡇⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣍⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠒⠒⠛⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⣺⠋⠀⣹⠀⣠⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣤⣤⣤⣤⣤⣤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣄⠀⠀⢠⠟⢠⠀⡇⢀⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡏⠁⠉⣼⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⡄⠀⣹⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⡉⣹⣭⡭⠽⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡖⠂⢰⠀⠀⢢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡁⠐⡷⢄⢸⢄⡴⡿⠀⢙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣥⠒⣘⠦⣤⠔⠚⠒⠢⠀⠶⡁⠲⡼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⢤⠊⢺⣄⣀⡜⠐⠒⠐⠺⢄⣀⠸⡊⢣⠔⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⡵⠰⡇⠀⢠⠁⡀⠒⠒⣂⢹⣀⣀⡳⠲⣅⠤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠺⣀⢸⠉⠉⡑⠠⠀⠀⠀⠤⠐⣅⠀⢸⢀⡜⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⢧⣨⡏⢉⡅⠂⠀⠀⠀⠐⠊⣅⣉⡡⣀⠗⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡾⣄⡌⠀⣈⠐⠒⠒⠒⠒⠈⣇⠀⣇⡰⢶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⣼⡋⢹⣁⠉⠉⠉⠈⣉⡆⢹⣀⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣣⢟⠉⡧⠌⠉⠉⠡⠤⡉⡡⣜⠏
⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⡲⠞⠂⠀⠹⣬⣍⡕⠀⠤⠤⠤⠰⣹⣤⠏⣀⠠⠔⠒⠂⠀⠐⠒⠤⣀
⠀⠀⠀⠀⠀⡤⢊⡵⠊⠁⠀⠀⠀⠀⠀⢱⡮⡏⠁⠒⠒⠒⠉⣧⣟⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢠⠊⠀⡎⠀⠀⠀⠀⠀⠀⢀⡠⠴⢷⡋⠉⠉⠉⠉⠉⣻⠁⠀⠈⠉⠉⠁⠀⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⢎⠀⠀⠑⠤⠀⠤⠤⠒⠉⠁⠀⠀⢸⡉⠁⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢾⠈⠁⠐⠒⠂⠉⢈⠉⠉⠉⠐⠒⠒⠠⠤⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠂⠉⠉⠁⠀⠀⢸⠉⠐⠒⠂⠒⠒⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⡀⠤⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠞⣲⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠛⠉⠀⢠⣾⡟⣟⣻⣤⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣧⣀⣀⣰⣿⣿⡿⠏⠉⠉⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣩⣻⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣖⣿⡿⢿⣿⣿⡇⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⠍⠽⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣿⣿⠉⠽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠳⣻⣄⠀⣚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⣿⠀⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠶⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠄⠀⢀⠀⠀⠀⠀⢣⢿⡇⣐⡓⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠄⠠⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠔⢄⢂⣴⠾⠢⠹⠧⠥⣆⡄⢔⡹⢏⠷⣅⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣇⠈⢽
⠀⠀⠀⠀⠀⠀⠀⠀⡚⠋⠀⢬⠏⠁⠁⠀⠀⠀⠀⠀⠉⠛⢾⣙⣺⢰⢿⣇⣻⣵⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⢻⣿⠭⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠕⠈⡭⢸⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⣥⡿⡏⣴⣮⣴⣦⣤⠄⠤⢲⡽⢠⣼⣺⡟⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢂⠲⡕⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡞⠛⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⠀⠀⠁⢺⠓⢦⣄⡀⠀⠀⠀⣀⣀⡀⠠⣀⠚⠁⠀⠀⠐⠀⠰⠂⠀⢀⣀⣁⠐⠪⡀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⣀⠂⠀⠀⠐⠴⠈⠡⡈⠄⡠⠀⡀⠀⢐⣤⠴⢦⣤⣷⠿⠾⠞⠛⠋⠈⠉⠛⠷⣶⣦⣤⣦⣔⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣀⠀⠁⢖⣂⠈⢑⠢⠐⠃⡠⠤⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⣯⣤⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂⣤⡈⠀⠀⢁⠒⣠⠀⡖⠶⠶⠶⠰⠆⣤⣎⠄⡋⠀⠀⠃⠀⠂⠀⠀⠀⢀⠀⠂⡀⠀⢀⠄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⡠⡀⢊⣡⠮⠉⠒⠓⠚⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⡀⠅⠂⠄⢀⠀⠀⠠⢀⠠⡀⠂⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠓⠃⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠴⠲⠳⠲⠴⠇⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠉⢡⡄⠀⠀⣀⣀⢀⠀⣤⣠⣤⠶⠶⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠵⣴⢠⠦⡁⠮⠴⠖⠘⠙⠙⠀⠈⠉⠑⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⢀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣟⣿⣿⣿⣿⣯⣿⡿⠿⠭⢵⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠙⠿⣿⣟⡁⢸⣿⡟⠛⠓⠀⣀⠀⢀⡉⠛⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⢿⣿⣇⠛⢿⣿⣿⠀⠉⠉⢻⣤⠂⠀⠀⠐⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠻⠻⡄⠀⢻⣿⡿⠉⠈⢙⣿⣇⠀⠀⠀⢩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⣿⣏⠀⠀⢉⣿⣷⠠⡀⠐⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⢲⣿⣏⠀⢈⣹⣿⠛⢀⣼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⣿⣿⣁⣀⣩⣿⣵⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡿⠿⠥⣤⣾⣽⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⢤⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠂⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠀⣠⣿⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠧⢀⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠠⢰⣿⣿⠏⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠢⠀⣼⣿⣿⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⡆⠀⣾⣿⣿⠀⢀⣠⣾⣧⣴⡶⣶⡶⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢿⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⡿⡟⠿⣿⣿⣿⣱⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠹⢿⣿⣿⣿⣿⣿⣷⣿⡧⢥⣤⡿⣟⢛⠵⢋⡸⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢧⣼⣼⣹⣿⣿⣿⣿⣿⣟⣹⣴⡶⡴⣰⣼⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠚⠓⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⠄⢀⡴⠋⢁⠔⠁⠀⣸⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣰⢟⣤⣶⡦⠀⠀⣤⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠐⠀⠈⠀⠈⠁⠀⠄⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣼⣿⡿⠇⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⢈⣥⠶⠚⠛⠉⠉⠛⠲⢤⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠘⠋⠁⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠂⠒⠄⣠⠟⠋⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⡀⠀⡄⠀⠰⢷⣤⡶⠟⠉⠀⠀⠀⠀⠀⠐⠂⠀⢠⡞⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠠⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⡙
⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⠞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⢨⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠊⠁⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣧⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠂⠀⢀⡤⠒⠀⢀⣠⠔⢡⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⣸⠁⠀⠀⠀⠀⠀⣠⠟⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡡⠀⠀⠉⡠⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡍⠀⠀⢀⠀⠀⡴⠋⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠁⠀⢀⣤⠶⠉⣰⡏⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⡐⠝⠀⠀⠀⠀⢰⠞⠑⠂⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⠁⠀⢀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠜⠀⠀⠀⢀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠆⠀⠀⣠⠖⠁⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠠⡣⠃⢀⣴⣞⣁⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠄⢊⠅⠀⠀⠀⠀⠀⠀⠀⣴⢖⡡⠞⡽⠋⠉⠑⠉⠑⠤⣀⢀⠔⠁⠀⢀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠋⢠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢣⠈
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⣏⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠄⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⢠⠃⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡎
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⡀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡇⠀⠠⠀⠤⢀⠀⢘⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡅⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠑⠆⠀⠀⢀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠁⠀⢀⡀⠊⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⣀⣀⣀⣀⣀⣀⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣍⢡⠈⣛⣯⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠠⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣗⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⣛⣟⣿⣿⣿⣿⣻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⢿⡋⢡⣾⠟⠛⠉⠉⠛⢿⣿⣷⣿⡿⣿⣿⣿⣦⣄⡀⠀⠀⠀⢀⣼⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣿⣦⢠⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡿⢿⡿⢿⣿⣿⣿⣿⣾⣿⡿⢿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣟⣏⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣋⠝⣛⣿⣿⣭⣿⣷⣾⣿⣷⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣄⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡟⣿⣿⠍⣽⣿⣿⣿⣟⣛⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣷⣾⣯⣻⣤⣀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣷⣶⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣯⣜⣛⣿⣿⣿⣿⣿⣿⣿⣶⣜⣽⣿⠿⣿⣶⣦⣤⣤⣤⣴⣾⢿⣿⢿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⣰⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⣭⣟⣻⡿⣾⣿⣋⣿⡿⣿⣿⢹⣿⣦⣤⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⣿⣿⣿⣯⣿⣿⣽⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠹⣿⣿⣷⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉⠉⠙⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⠤⣤⠤⠤⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⢦⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡈⡦⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣉⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠈⠓⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⠀⠤⠀⠤⠀⡀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠛⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠔⢀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡄⠲⠊⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢢⡌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⢆⣀⠀⢀⣀⠂⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡒⣒⣒⣒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠻⠗⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢉⠱⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠸⠈⠉⠭⣆⣀⠤⢀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡉⡣⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠁⢠⣿⣁⠫⣤⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⣡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⡕⡩⢵⠀⢼⠃⠠⢬⠋⠙⣆⠰⠀⠀⠀⠀⠀⠀⠀⠶⠴⠬⠭⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡄⢡⡄⠠⢨⣎⠁⠀⡈⡏⡉⢻⣦⡂⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡄⠒⠢⠊⠀⢀⠞⠠⠄⣸⠁⠀⠠⠎⢹⡆⠀⠀⠀⠀⠀⠀⠉⢀⠛⠣⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡿⠀⢄⡄⢢⣠⠏⣈⠐⢲⠃⠘⠀⡖⠀⢸⠁⠀⠀⠀⠀⠀⠀⡴⢁⠘⢢⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢣⠉⠐⠡⡰⣁⠂⠠⢬⠃⠤⣈⠢⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠙⢄⠑⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡓⢤⡞⠃⠀⠀⡰⠃⢰⠂⠜⣰⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠷⠧⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢈⡻⠀⢁⠐⡰⠷⣁⣀⣐⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠮⢁⠐⠂⡼⠁⠐⠲⠒⠉⠀⠀⢀⡀⠀⠀⠀⢰⠀⠀⠀⠀⠿⢉⠿⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡞⠁⠀⠆⡜⠁⠄⠉⢄⠀⠀⠀⠀⠀⡅⠀⡄⠀⠀⡄⠀⡄⠀⣠⠊⠤⡈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣠⠀⠀⣾⠀⢀⠀⣼⠴⠁⠀⠀⠾⠀⠀⡆⠀⢠⡃⠀⢣⠀⠀⠃⠀⠃⠀⢧⡈⢠⠁⡠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡀⠀⠍⠀⠂⣼⠃⠀⡆⠀⠀⣄⠀⢰⠁⠀⠘⣇⠀⠸⠀⢸⠀⢸⠀⠀⠀⠙⣆⡔⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠨⠀⠀⢠⣟⠀⢀⣔⠀⠀⢍⠀⠀⡆⠀⠀⡇⠀⡏⠀⠀⡄⠀⡆⠀⠛⠃⠈⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢈⡤⣾⠀⠀⠘⣇⠀⠀⠉⠑⣤⠼⠂⠈⠛⠁⠐⠷⠀⢸⠀⠀⠀⢠⠁⠀⣶⠴⣤⠴⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⢙⡀⣀⡀⠙⠟⡶⠊⠀⠀⠀⠀⠀⠀⣀⣀⠀⠘⣇⠀⠀⡄⠀⡄⠀⠀⡴⢉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠃⠀⠀⠱⣄⠐⠊⡰⢡⠃⢀⡀⠄⠂⠉⠉⠀⠀⠈⠉⠛⠄⢀⡇⠀⡏⠀⣾⠀⡈⠱⢀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⣼⠀⠸⣧⡀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⣀⠤⠒⠈⠉⠉⢹⡶⢦⣌⢣⡠⣤⠀⠀⠑⢌⣡⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠠⠤⠀⠒⠂⠉⠁⠂⠀⠀⠒⠀⠁⠀⠀⠀⠙⠧⠀⠀⣟⠉⠛⠛⠓⢺⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠀⠙⠉⠀⠀⠀⠋⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠐⠐⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠂⣈⠴⣯⡆⠀⠀⣼⣵⢈⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠔⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠄⠀⠀⠂⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠁⠈⢦⢠⣤⠰⠁⠀⡀⠀⠀⠀⢂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠈⠁⠀⠀⠋⠂⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠛⡀⠀⡄⠀⠀⠀⡐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢐⠂⠀⠀⠀⠀⠀⠄⠔⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⡀⠀⠀⠀⠀⠀⠠⢂⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠑⣀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠈⢄⠀⠀⠀⠀⠈⠧⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠀⠀⠀⢀⡀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⡀⠒⠀⠄⠀⣀⢀⣁⡀⡀⠤⠐⠀⠀⠀⠀⡂
⠁⠁⡀⠄⠀⠀⠠⠂⣠⠔⠊⠃⠀⠀⢶⡀⡠⢀⡈⠉⠉⠉⠓⠒⠒⠒⠀⠀⠀⠀⠐⠒⠁⠈⠉⠀⠀⠀⠀⠀⢀⠠⡸⠃⠠⢀
⠀⠀⠀⠁⠒⠖⠒⠊⠉⠀⠀⠀⠀⠀⠛⠈⠁⠈⠀⠤⠤⠴⠤⠀⠀⣠⠀⠀⠀⡄⠀⠀⡄⠀⠀⢀⡒⠂⠠⠌⠴⠊⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⠤⠀⠀⢠⡄⠀⠀⠆⠀⠐⠆⠀⠉⠸⠀⠠⠤⠭⠀⠀⠉⠁⠀⠀⢐⢀⣀⣒⣒⡒⠂⠲⠄⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⠶⣶⣒⣖⣂⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣟⣿⣿⣟⠛⣿⣶⣬⡹⢟⣿⣷⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⠿⣿⠿⠟⡛⠛⠛⣻⠻⢦⡁⢾⡟⣻⣤⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⡄⠀⣾⠁⠀⠀⣿⠀⠀⣹⣧⣼⣷⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⢉⣀⣀⣼⣧⣤⣾⡷⣶⣬⣿⡏⢡⣴⣿⣿⣿⣽⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠟⢿⡿⡏⠀⠚⠛⠿⣿⣿⣿⣯⣡⣬⣤⣶⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣀⠈⣨⠇⣸⡇⠙⠓⢿⣤⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⣿⡽⠋⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠾⠆⠸⠇⢈⡀⠠⠙⠻⣤⣾⠟⢿⣿⣿⡿⠟⠋⠬⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⢿⡿⠛⡿⠷⣧⣶⠖⠀⣤⠀⠁⠀⠄⠛⠷⣤⣿⣤⡄⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣘⣱⣦⢡⡄⣿⡉⢻⣶⣯⣑⣶⡆⣀⡀⠀⠸⠋⠀⣸⡿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣿⡿⠿⠿⠿⠾⢿⣿⣿⣶⡿⠦⢀⣑⠠⠟⠀⠘⢻⡏⣿⠲⣤
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠉⠙⠛⠻⠶⣶⣦⣤⣀⣤⣼⣥⣯⣜⡛⠻⣆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣽⣿⡿⢻⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⣿⠉⣹⣶⡟⢋⠁⠽⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⡧⢾⣿⣀⣿⠛⢡⣾⠟⠃⣰⣮⣙⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠘⣿⣿⡿⣿⣷⣼⣿⠋⠉⢡⣬⣧⠘⠁⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠿⢀⣿⡟⠿⣿⣷⠀⠈⣿⡇⠘⠛⠋⠀⠙⡶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣤⣾⣿⣷⣄⣿⣿⡄⣻⣦⡄⢀⣠⡄⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣉⣿⣿⠉⠓⣿⣿⣄⠀⢀⡈⢩⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣷⣾⣿⣿⡍⣀⣾⡿⠻⢟⣻⢛⡉⠐⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⠛⠏⠁⢀⣼⡿⠻⣷⠀⠀⠸⠛⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣤⣾⣿⣏⠁⠀⣠⣾⣤⡄⠻⠦⠴⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⣴⡇⠸⡜⠻⣴⠃⠀⠀⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡓⠀⢠⡴⢿⣆⠀⠄⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⡈⠀⠀⠀⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣽⣯⡅⠀⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⣿⣿⣿⣿⡟⢿⠀⠈⢠⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣿⣧⡶⠂⢠⡀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣹⣿⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡗⢀⡀⠠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡰⣋⣠⣤⡀⠈⠉⠉⠛⠶⠶⠶⠶⢶⠶⠛⠛⠙⠛⠶⠦⣄
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣦⣄⢰⠋⠑⠲⠀⠄⠤⠀⠠⠖⠊⠙⡆⢰⣎⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣄⠈⢻⡏⢓⣶⠀⠀⠀⠀⠀⠀⢀⣶⠋⢹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠈⠉⢁⠢⠄⢻⢆⠀⠀⠀⠐⠟⠠⢞⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠒⠀⠀⠬⢷⣦⡀⠈⠀⠀⠀⠁⢠⣴⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠙⣿⣄⣀⠀⠀⠀⢹⣿⢰⣶⣤⣶⡎⣿⣯⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢿⣷⡀⠀⠀⠀⠈⡀⣿⣯⢉⣽⣿⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠙⢿⣖⠒⠉⠀⠘⠢⠍⠬⠭⠄⢸⡏⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⠿⢷⣄⣀⡀⡼⠠⠀⠀⠒⠊⢧⡆
⠀⠀⠀⠀⠀⠀⣀⣀⡠⣤⡾⠁⠈⠳⣄⠹⣿⣄⠸⠀⠀⠀⠀⠀⣈⣇⣀⣀⣠⡤⢤⣤⣤⣤⣀⣀
⠀⠀⣀⠔⢚⣯⡽⠶⠛⠋⠀⠀⠀⠀⠈⠑⣄⠹⣷⡒⠙⠉⠉⠉⠁⠈⢀⣀⢀⣴⣀⡤⢀⠉⢹⣯⠙⢦⡀
⠀⢰⣿⠀⠈⠳⠤⣤⣤⣤⣶⠶⠶⠶⠿⠛⠛⢷⡙⢻⣦⡠⣄⣲⡋⠉⠉⠿⠛⢛⣻⡿⢋⣰⠞⠁⠐⣿⡗
⠀⠘⠿⣿⣶⣧⣶⣤⣦⣴⣦⣶⣴⣤⣴⣶⣾⣾⣷⡸⢿⣷⡘⣄⢉⣁⠂⠼⢯⡤⠴⠚⠉⣤⣄⣹⣿⡿⠁
⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣉⡭⠵⠖⢛⣛⣉⣭⡭⢷⡠⣿⣿⡉⠂⠀⠀⠀⢀⣦⣤⣿⣶⡿⠿⠟⠋
⠀⠀⠀⠀⠀⢀⡤⠒⠋⢉⣤⠶⠚⠛⠉⣉⣀⣦⣠⣶⣷⠈⣹⣿⡖⠒⠀⠉⠀⢻⠉⠁
⠀⠀⠀⠀⣴⣏⠀⠀⠀⢺⡅⠰⣦⣿⣿⠟⢛⣟⣩⣽⠿⡇⢉⣿⣷⡀⠠⠄⠐⠒
⠀⠀⠀⠀⢿⣇⣠⡤⠀⠀⠙⢤⡙⢷⡚⠋⠉⠁⠀⠀⠀⢹⠈⠻⣿⡇⠀⠀⢀⣠
⠀⠀⠀⠀⠘⢿⣿⣅⣠⡄⠀⠀⠙⠳⢭⣒⡦⢄⣀⣀⣠⡾⠀⠻⢿⣿⠈⠁⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣴⣆⠀⠀⠀⠈⠉⠙⠛⠒⠚⠁⠀⢰⣾⡿⠐⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣿⣄⣠⣄⠀⢀⣄⠀⢰⣤⣶⣿⠁⠀⠠⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⡋⠀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣯⣁⣈⠥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣴⣤⣬⣥⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠟⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠚⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣦⣄⣀⠀⠀⠀⢀⣠⣾⣏⠻⠿⡇
⠀⠀⠀⠀⣼⣿⠾⠀⣫⠿⠛⠋⠉⠙⠛⠿⣿⣿⣹⣿⢞⣻⣿⣿⣿⣻⣭⣥⣤⣄⣀⣀
⠀⠀⠀⢸⣿⡾⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⣪⣵⣾⣿⣿⣿⠷⣘⣿⣿⣾⣿⣿⣦⣄
⠀⠀⠀⢸⣿⡿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⣿⣼⣿⡿⠿⠿⠿⢿⣿⣿⣾⣿⣦
⠀⠀⠀⠸⣿⣶⣯⡄⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣻⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣷⣿⢿⣷⣦⣴⣶⣿⣿⣿⣟⣽⣿⡿⣋⣁⣀⣀⣀⡀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣻⣿⣿⣿⣿⡿⡿⣫⣻⣿⣿⣿⣿⣟⢿⣏⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣉⣻⣿⣿⡯⠙⠧⡏⠹⠘⠟⠛⠛⠛⠁⠀⠰⠿⠽⠽⣿⣿⡿⠶⠟⠋
⠀⠀⠀⠀⠀⣴⡾⡿⣿⣷⠾⠋⠃
⠀⠀⠀⠀⣸⡿⠙
⠀⠀⠀⠀⢹⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⠛⠉⠉⠙⠒
⠀⠀⠀⠀⠀⠻⢷⣧⣰⣤⣶⣶⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⢀⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⠀⠈⠻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⣀⠀⢻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠙⠻⢿⣿⣿⠿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡙⢿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣦⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣄⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⣠⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠙⠛⠂⣀⣤⣈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣶⣿⣧⣾⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠛⠛⢛⣿⣿⣿⣧⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠃⠀⠟⣿⣿⣿⡟⠀⠀⣸⣿⡿⠛⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠐⠻⣶⣯⡇⠀⠀⣯⡏⠀⠄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠈⢀⢺⣿⣟⡃⠀⠀⣿⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⢈⣿⣟⡇⠀⠀⣷⡀⠀⠂⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠌⢻⣟⡇⠀⠀⣽⡅⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⣿⡇⠀⠀⢸⣇⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠻⣿⣛⠀⠀⢸⣝⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⢽⣿⠀⠀⠈⣿⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠐⠃⠀⢀⢸⡏⠀⠀⠰⡛⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⣾⣿⠃⡾⠃⠀⢀⣿⠿⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⢀⡉⡡⠎⠁⠀⣠⢶⡏⡀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣤⣤⣤⣶⡞⠿⠿⠿⢷⣤⣨⣀⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⡿⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⠀⠈⠛⠋⠀⠀⢠⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣶⣥⠀⠀⠀⠀⠀⠀⣬⣶⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣴⣌⠃⠀⠀⠀⠀⠸⣱⣦⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣇⢿⣿⡄⠀⠀⠀⠀⢰⣿⡿⣸⡿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠻⣎⢿⡇⠀⠀⠀⠀⢸⡟⣱⡟⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢎⠁⠀⠀⠀⠀⠘⢰⢋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⣼⣄⠁⡀⠐⠀⠀⠄⠄⠀⠀⠀⠀⠠⠡⠀⠀⠄⢀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⣮⣤⣤⣦⣐⣀⣀⣂⣐⣀⣠⣥⣤⣴⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢀⣞⢈⠂⠩⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠛⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⢸⣿⣷⣶⣥⣐⣀⢄⠈⠀⡁⢀⠀⡀⢀⠀⡀⠈⠀⠄⡀⣀⣢⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀
⠀⠀⠀⣠⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⡾⣸
⠀⠀⠀⢿⣷⣦⣄⣈⠉⠙⠛⠛⠿⠿⠿⠿⡿⣿⢿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣵⠋
⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⡿⠿⠿⠿⠿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⡽⣛⣋⣭⣭⣀⣩⣭⣿⣿⣿⣿⣿⣯⣽⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⣀⣠⣤⣭⣿⣿⣿⡿⢿⣿⣿⠋⠉⠛⢻⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠉⠀⢀⣠⣼⣿⣿⣧⠴⠾⣝⢿⡍⢢⣀⢉⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠈⠉⠀⣠⠿⣿⣿⣠⡶⠛⠳⣝⡂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣳⣦⣀⡀⠀⠟⠻⣿⣦⣴⡟⠁⣙⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣮⣽⣳⠶⣤⣌⣛⠿⢿⣶⣯⡀⢠⡽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣮⣍⣛⠿⢶⣯⣽⣿⣦⣤⡾⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣽⣿⣿⣿⣷⣦⡞⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⣫⣴⣶⣶⣶⣶⣶⣦⣭⣟⣲⣦⣄⡀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣟⣽⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡳⡄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣾⣿⣿⣷⢻
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣣⣬⣿⣿⣿⣿⣷⣶⣿⣿⣿⣭⣭⣤⣤⣾⣿⣿⡟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠁⢰⣿⣿⣿⡋⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠛⠛⠛⠛⠓⠲⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣖⠀⣰⣿⣿⢇⣶⣠⢽⣾⣿⡓⢰⣾⣾⢷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠛⠚⠻⢛⠿⡿⢁⣠⣿⣿⣯⣴⠤⡠⢌⢠⡟⣿⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠂⠈⠁⠀⠐⢈⠙⢋⣱⣫⣿⣶⣖⠔⠆⠃⠀⠀⠀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡱⢋⡜⣹⠟⣩⡟⠀⠀⠐⠢⠆⠀⠠⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠏⣤⣭⡍⠀⠀⠁⡠⠀⠀⠠⠀⢠⣄⢰⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣏⡾⢳⠎⡀⠀⠀⡀⢀⠐⡈⠆⣰⣧⡿⣿⢻⣭⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣬⢛⠞⠠⠀⠀⠀⢀⠈⣴⣇⢸⣯⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⠀⠀⠰⠀⠀⣌⡔⢻⣿⣺⣿⣿⣿⣯⣾⣿⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠂⠀⠀⠦⠀⠸⣧⢛⡹⣇⣿⣿⣿⣿⣹⡟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠐⠄⠰⠀⠀⢰⣿⣼⣟⡿⣷⣯⡿⠉⣻⣷⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠙⠂⠃⠄⠐⢸⣿⣿⣿⣾⣾⡻⣿⢛⣿⢿⢳⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠃⠠⠀⡄⣊⡉⠛⣿⣽⣿⣿⣠⣿⣿⢞⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠐⠆⢴⣾⡏⠀⠁⠝⠹⢿⡿⣹⣿⣿⡮⣣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⣃⣸⣬⡟⠡⠀⠀⡀⠀⠈⠈⠋⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣼⣿⣿⣦⡈⡀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⣭⣿⣽⡏⣹⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣛⢷⣾⣿⣿⣿⢿⣿⢿⣾⣦⣴⣾⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣽⢯⣬⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣻⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⡻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠛⢛⡋⠛⣿⡿⠟⠾⠙⠻⣻⠟⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠏⠛⠧⣿⣿⠀⠀⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠀⣿⣿⠄⢰⣤⡿⣹⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⣤⣦⣬⠛⠁⠠⢅⠧⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠓⣀⣿⣿⡒⠶⠾⣁⡳⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⡏⢹⣿⣧⢤⢤⣈⣱⡜⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⡀⣄⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣥⠈⣿⠟⣿⣌⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡥⠶⠾⣶⡿⠓⠄⠟⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⣄⡀⢠⡿⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⣿⣿⣿⡟⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡭⠁⠸⢿⣿⣿⢇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸⡗⠀⠀⠀⠀⠀⠘⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣄⣀⡀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠇⠉⠛⠛⠓⢤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⢀⣤⡶⠊⠉⠀⠀⠀⠀⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⢀⣴⣾⠟⠛⠛⠛⠙⠛⠻⠛⠷⢶⣤⣀⣀⠀⢀⣀⣴⡿⢡⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠮⢋⣁⣵⣶⣶⣿⣷⣦⣤⡀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⢠⣿⠟⢠⣤⣶⠿⠿⠿⠿⢷⣷⣶⣤⣬⣿⣿⣿⣿⣿⣛⡱⠃⠀⠁⠋⣉⣤⣶⠖⠉⣁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣷
⠀⠀⠀⢠⣿⡯⠀⣿⣿⣏⠦⠶⠶⠶⣦⣭⣍⣉⣍⣉⣭⣽⠾⠟⠍⠐⢠⣤⡾⠛⢉⣀⣤⣶⣿⣿⣿⣿⣟⢙⡽⠛⠛⠻⠿⣿⣿⡿⠀⠀⣴⣿⣷⡿⠁
⠀⠀⠀⣸⣿⣯⢰⣿⣿⠖⢻⡿⣿⣿⣷⣶⣟⣍⣋⣋⣱⣌⣤⡜⢂⣴⢟⣡⣄⣽⣿⣿⣿⡿⠟⠛⠁⡨⠈⠀⠀⠀⠀⠀⣀⣻⠿⢀⣀⣾⣿⣿⡟⠅
⠀⠀⠀⣿⣿⣷⣸⣿⣿⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣴⡿⣥⣾⣿⣿⣿⠿⢛⣭⠶⠚⠉⠀⠀⠀⠀⣀⣤⡴⠟⢋⣁⣴⣾⣿⡿⠟⠁
⠀⠀⢠⣿⣿⣿⣿⣷⣽⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⢿⣿⣿⣿⣿⢟⣩⠶⠋⠁⠀⠀⢀⣠⣴⠾⠟⣛⣡⣶⣿⣿⣿⢿⣋⠽
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣍⡉⠳⡲⣤⣤⣄⣤⡴⠻⣋⣴⣿⣿⣿⢟⣡⠞⠁⠀⠀⣠⣴⡾⢟⣉⣤⣶⣿⣿⡿⢿⡻⠿⠛⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣬⣭⣽⣷⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀⣠⣾⡿⠃⢠⣾⣿⢿⠟⠛⠉⠁
⠀⠀⠈⣹⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⢀⣴⣿⣿⣇⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠉⣼⡿⠻⠟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣠⣭⣶⣿⣿⣿⣿⣦⡈⠛⠷⣶⣤⣤⠶⠶⢚⣛⣋⣭⣼⣿⣭⣬⣍⣱⢦⡄
⠀⠀⠀⠀⠀⠐⠐⠿⠟⠛⠻⠿⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣵⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣧⡙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢞⡀⢿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣚⣯⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠚⠋⠁