⢠⢻⣿⡿⣟⡛⠻⢿⣿⣿⡿⠿⠟⠻⢿⣿⣇⠄
⢀⣺⣿⡟⠋⡉⢉⠚⢿⣿⠗⢊⠙⡛⢿⣿⡌⠄
⠈⣝⣿⣿⣿⣧⣤⣤⣿⣿⣶⣤⣼⣿⣿⣿⡇⠄
⠄⠙⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⡟⠄⠄
⠄⠄⣿⣿⣿⠛⣋⣩⣬⣥⣤⡍⢙⣿⣿⡇⠄⠄
⠄⠄⠘⣿⣿⣴⣭⣿⣿⣿⣿⣵⣾⣿⠏⠄⠄⠄
⠄⠄⠄⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⠄

⠀⣿⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⡏⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⡰⠋⢙⣿⣦⡀ ⠀⠀⠀⠀⠀
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣦⣮⣤⡀⣸⣿⣿⣿⣆⠀⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⢟⣫⠟⠋⠀⠀⠀⠀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣷⣿⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣧⣿⣿⣆⠙⢆⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣤⣿⣿⣿⡟⠹⣿⣿⣿⣿⣷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⠏⢧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢳⡀

⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡄ ⠀⠈⣙⡟⢿⢋⡉⠀⠀ ⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢧⣤⢶⢛⣉⣅⢉⣩⡘⡳⣦⣴⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⢵⢌⣮⣶⣾⣶⣶⣥⡋⡠⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠖⣱⢿⣿⣿⣿⠲⠪⢝⡚⣦⢒⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡐⡒⣿⣗⠿⢟⣛⠤⠨⢐⡂⢿⡏⠬⠨⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⢿⠉⠁⣿⣿⡕⠅⡢⠭⡍⠕⣂⠍⠣⢭⣴⠑⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⡀⠀⠐⣯⠚⢘⢿⣷⣱⣾⣩⣒⣭⡶⢋⣄⣲⠟⠀⢀⣴⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡂⠀⠘⢷⣍⠠⠈⢉⡛⢛⢻⡍⠰⣀⣴⠋⠀⠐⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠹⣷⣄⡴⠋⠈⠻⠶⡤⡌⣠⣤⠷⠚⠋⠈⠳⣤⣾⠟⠙⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡼⢿⣷⣤⣀⠀⠀⣀⣷⣽⣀⠀⠀⣀⣤⣾⡿⠻⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡄ ⠀⠈⣙⡟⢿⢋⡉⠀⠀ ⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢧⣤⢶⢛⣉⣅⢉⣩⡘⡳⣦⣴⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⢵⢌⣮⣶⣾⣶⣶⣥⡋⡠⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠖⣱⢿⣿⣿⣿⠲⠪⢝⡚⣦⢒⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡐⡒⣿⣗⠿⢟⣛⠤⠨⢐⡂⢿⡏⠬⠨⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⢿⠉⠁⣿⣿⡕⠅⡢⠭⡍⠕⣂⠍⠣⢭⣴⠑⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⡀⠀⠐⣯⠚⢘⢿⣷⣱⣾⣩⣒⣭⡶⢋⣄⣲⠟⠀⢀⣴⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡂⠀⠘⢷⣍⠠⠈⢉⡛⢛⢻⡍⠰⣀⣴⠋⠀⠐⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠹⣷⣄⡴⠋⠈⠻⠶⡤⡌⣠⣤⠷⠚⠋⠈⠳⣤⣾⠟⠙⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡼⢿⣷⣤⣀⠀⠀⣀⣷⣽⣀⠀⠀⣀⣤⣾⡿⠻⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡄ ⠀⠈⣙⡟⢿⢋⡉⠀⠀ ⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢧⣤⢶⢛⣉⣅⢉⣩⡘⡳⣦⣴⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⢵⢌⣮⣶⣾⣶⣶⣥⡋⡠⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠖⣱⢿⣿⣿⣿⠲⠪⢝⡚⣦⢒⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡐⡒⣿⣗⠿⢟⣛⠤⠨⢐⡂⢿⡏⠬⠨⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⢿⠉⠁⣿⣿⡕⠅⡢⠭⡍⠕⣂⠍⠣⢭⣴⠑⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⡀⠀⠐⣯⠚⢘⢿⣷⣱⣾⣩⣒⣭⡶⢋⣄⣲⠟⠀⢀⣴⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡂⠀⠘⢷⣍⠠⠈⢉⡛⢛⢻⡍⠰⣀⣴⠋⠀⠐⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠹⣷⣄⡴⠋⠈⠻⠶⡤⡌⣠⣤⠷⠚⠋⠈⠳⣤⣾⠟⠙⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡼⢿⣷⣤⣀⠀⠀⣀⣷⣽⣀⠀⠀⣀⣤⣾⡿⠻⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡄ ⠀⠈⣙⡟⢿⢋⡉⠀⠀ ⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢧⣤⢶⢛⣉⣅⢉⣩⡘⡳⣦⣴⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⢵⢌⣮⣶⣾⣶⣶⣥⡋⡠⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠖⣱⢿⣿⣿⣿⠲⠪⢝⡚⣦⢒⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡐⡒⣿⣗⠿⢟⣛⠤⠨⢐⡂⢿⡏⠬⠨⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⢿⠉⠁⣿⣿⡕⠅⡢⠭⡍⠕⣂⠍⠣⢭⣴⠑⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⡀⠀⠐⣯⠚⢘⢿⣷⣱⣾⣩⣒⣭⡶⢋⣄⣲⠟⠀⢀⣴⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡂⠀⠘⢷⣍⠠⠈⢉⡛⢛⢻⡍⠰⣀⣴⠋⠀⠐⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠹⣷⣄⡴⠋⠈⠻⠶⡤⡌⣠⣤⠷⠚⠋⠈⠳⣤⣾⠟⠙⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡼⢿⣷⣤⣀⠀⠀⣀⣷⣽⣀⠀⠀⣀⣤⣾⡿⠻⣄⠀⠀⠀⠀⠀⠀