⢐⢢⡒⢥⢒⡒⠒⡌⢒⠰⢂⠱⢂⠒⣂⠓⡰⢊⠒⣂⠓⡰⠊⡔⢂⠃⠖⡘⡐⠆⡓⡐⢊⠔⣂⠃⠖⡘⢂⠖⡑⢂⠚⡔⢂⠓⡰⠊⡔⢂⠓⡰⠊⡔⠣⡘⠰⡈⢆⠱⡈⠜⢢⢉⠒⣉⠒⡡⢉⠒⡡⠚⢄⢃⠲⠑⡊⠔⡃⢆⠓⡰⢊⠒⢢⠑⡒⢌⠓⡌⢚⠰⡘⡐⢂⠆⠒⡌⢒⡐⢂⠆⢓⠰⢂⠒⠀⠀⠀⠀⠀⠀ ⢈⠆⡍⢆⠣⢌⡱⢈⢆⠱⡈⢆⡡⢊⠤⡘⢄⠢⡑⢄⡊⠤⡑⢄⠣⡘⠤⡑⢌⡰⢡⠘⣄⢊⢄⡊⡔⢡⢊⠰⡈⢆⠡⣂⢅⢊⠤⡑⢄⠣⡘⢠⡑⠤⡑⡈⢅⠒⡨⠐⡌⢢⢁⠢⡁⢆⡘⢄⠃⡜⣀⠣⢌⠂⡌⡑⢌⠂⡅⢢⠘⡄⢢⠉⡔⡨⢐⡌⢢⠘⡠⡁⢆⠱⣈⠰⢡⠘⡤⠘⡠⢊⡄⢣⠌⡘⠀⠀⠀⠀⠀⠀ ⢈⠦⠩⡌⢓⠬⡰⠩⣌⠲⠱⡌⢒⠥⢒⡑⣊⠱⣘⠢⣑⢊⡱⢊⢡⢃⡓⡘⢆⡑⢢⠍⡰⢌⠒⡌⡌⢥⠊⢥⡑⣊⠱⣐⠪⠜⣂⠍⣆⢣⡙⠴⡘⢆⠱⣩⠘⡬⢑⢩⠒⡥⢊⡕⢩⠒⡜⣌⠚⡤⢃⠞⣠⢋⠴⣉⠦⡙⢬⠡⡓⢬⢡⠋⠴⢡⢣⠘⡆⡙⠴⣉⠜⡢⢡⠃⠦⡙⣄⠣⡑⠦⡘⣡⠚⠰⠀⠀⠀⠀⠀⠀ ⠰⣈⠑⠌⢢⠑⣌⠓⡤⣉⠇⣌⢃⢎⡡⢚⠠⡓⢄⡓⢌⢢⢑⡊⡔⢣⡈⡕⡨⡘⠤⣉⠒⡌⡱⢘⡈⠦⡙⠤⡒⢡⢃⡔⡉⢆⡡⢎⡐⠢⢌⡱⢌⡘⡒⡄⢳⢠⢉⠢⢑⠨⢡⠘⢂⠍⡰⢌⡱⠢⢍⠢⢅⡊⠴⣁⠒⡩⢄⠓⡈⢆⠣⡘⢡⠃⢦⢙⡰⢉⡒⠌⣆⠑⢢⡉⢆⡱⢂⠱⣈⠒⣅⠢⢉⠒⠀⠀⠀⠀⠀⠀ ⠰⠠⢍⡘⢢⠑⣌⢚⡐⠦⢩⡐⢎⡰⠌⡥⢓⡘⠆⡜⡌⢆⠣⠜⡰⣁⠖⡡⢡⠣⡑⠬⡑⣘⠰⡁⢎⠱⡘⢰⡉⠖⡌⠴⡉⠦⡑⢢⠥⡙⢢⠔⣊⠴⠑⡌⢡⠂⡌⢢⠁⢎⠰⣬⣆⡘⠄⢢⠰⣉⠎⡔⢢⡑⡒⣌⠱⢒⡌⢢⠑⡌⢆⠱⠢⣉⠲⢌⡐⢣⢌⠣⣄⠫⢰⡈⢆⠲⢡⢒⠠⢋⠔⡂⢅⠚⠀⠀⠀⠀⠀⠀ ⢨⠑⣢⠘⡤⢃⡌⠦⡑⠎⣅⠲⢌⣂⠳⡈⠦⣡⠋⠴⡘⠢⢍⡚⠔⣢⠚⣄⠣⢒⡉⢆⡱⢈⡱⠘⣌⠱⢌⢣⠘⡜⡈⠖⣡⠣⡑⡃⠦⡙⢄⡋⡔⡊⠕⡈⢆⠡⣢⣥⣾⣿⡿⠿⢿⣷⡌⢂⠱⢌⡒⣉⠖⡰⢡⠜⣈⠇⡘⢆⠩⡐⠌⡒⢅⠢⡐⢌⡘⢅⡊⠖⠤⢋⠔⡸⢄⠫⡔⡈⠆⣍⠒⡡⠌⣘⠀⠀⠀⠀⠀⠀ ⢠⠃⢆⡩⢰⠡⡜⢢⡙⡸⢠⢃⠎⢤⠃⡕⢢⢡⠚⡔⣡⠓⠬⠰⣁⠦⡑⠬⡘⣡⠚⢤⢃⠦⡑⢣⠘⡆⠜⢢⡑⢢⡑⠬⡐⠦⢡⡑⢆⠱⢂⠦⡑⢩⠐⣡⣦⣿⠟⠋⢉⠁⠀⠄⠀⣿⣷⡈⢒⠨⠰⢡⠚⡄⢃⡒⢄⠊⡔⡈⠆⢡⠊⡔⢊⢷⣌⠤⢈⠆⣡⠋⡜⡡⢚⠰⡈⠖⡤⢉⠔⠬⡱⢀⠣⡐⠀⠀⠀⠀⠀⠀ ⠠⢍⠢⢅⣃⠣⣌⠱⡰⢡⢃⠎⡘⢆⡩⠒⣅⠪⢔⡡⢆⡉⢆⡓⠄⠦⡉⠔⡡⠄⢃⠢⠌⡐⢡⠂⡍⡘⠬⢡⠜⢢⠜⢢⢑⡊⠖⡨⢆⠩⢆⠢⡑⢢⠡⡘⣿⣧⡀⠚⠓⡈⠄⡈⠀⠌⠻⣿⣄⢃⡑⢂⡓⡌⢡⠂⡌⢒⣴⣼⢮⠳⠌⢀⢂⠀⢻⣎⠰⡈⢄⠳⡘⠤⣉⢆⢡⡙⢄⠣⡘⠴⣁⠎⠤⢑⠀⠀⠀⠀⠀⠀ ⠘⡄⡋⠔⢢⡑⠤⢣⡑⠣⡜⢨⠑⢎⡰⠩⢄⠓⣌⠰⢢⠉⢆⡘⡘⠤⢑⠨⣐⣌⣦⣡⣊⣔⡡⠒⡠⠑⢌⠂⡜⠠⢋⡐⠢⠑⠬⡑⢌⠚⡄⢣⡑⢆⠡⡐⠩⢿⣷⣌⠀⠰⠘⠠⠳⠎⠐⣹⣿⠄⢢⠁⡖⡈⠆⢱⣼⠟⢋⣄⡀⠂⠐⣨⢒⠈⡀⢿⣇⠌⡂⢅⠣⢆⡡⢎⠰⡘⢢⠑⢌⡒⡡⢌⠢⢡⠀⠀⠀⠀⠀⠀ ⠘⡄⡃⠎⢥⡘⢡⠣⠜⡱⢨⡑⢎⠢⢅⠫⢄⡋⢤⠓⣌⡑⢊⠔⡡⢊⠄⢣⣿⡿⠛⠛⠛⠻⠿⣿⣶⣯⣦⣜⣤⣑⠂⡔⢡⠉⡒⡈⠔⡨⢐⠡⡐⠌⡂⢅⠃⡌⠻⣿⣧⠐⢠⣐⣤⣶⣿⠿⠛⢌⢂⠱⣈⠱⢈⢺⣯⠀⢿⣿⣿⣦⡁⠀⠎⢀⠈⠈⠻⢷⡈⠆⡘⢄⠲⢌⠢⡙⢤⡉⠔⣨⠑⢢⠘⠤⠀⠀⠀⠀⠀⠀ ⠘⠤⣑⢊⠦⣘⢡⠣⣙⠰⢃⡜⠤⢋⠬⡑⠢⠜⢢⢍⡰⢈⡜⠢⢁⠆⣼⣹⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣷⣶⣷⣬⣦⣕⣨⣐⠌⡂⢅⠊⡔⢈⠥⠘⠻⢿⠿⠿⠛⡍⢢⠡⢉⠢⢌⢢⠱⡈⢆⠸⢿⣶⡀⠙⠋⢃⣿⣟⠆⡖⠮⠷⠇⣸⣷⡜⠐⡌⣘⠢⢡⢍⠢⡐⠡⢆⡹⢀⠎⡰⠀⠀⠀⠀⠀⠀ ⢨⠑⡄⣊⠴⠡⢆⡓⠬⣡⠣⢌⡒⠥⠚⡌⠥⣉⠆⠲⢄⠣⠰⡁⠎⠰⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⢿⣷⣾⣶⣬⣦⣆⣙⣘⡆⢎⠰⢁⠢⡁⢆⠡⢒⡈⠆⡱⢁⠊⡔⣈⠻⣿⣷⡀⠢⣿⡧⠀⢠⣴⣴⣾⣿⠟⣀⠣⢰⢨⡑⠆⡬⢡⢁⠃⡎⠴⡁⢢⠑⠀⠀⠀⠀⠀⠀ ⢠⠃⠖⡠⠣⢍⡒⠬⡱⢄⠳⣈⢒⡩⠱⣘⠰⢨⠌⡱⢌⠢⡑⠌⡌⢱⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣿⣦⣧⣴⣈⡆⢡⡐⢌⠰⡈⠒⡄⢂⠥⠙⣿⣷⠀⡛⢛⣰⣿⡿⢏⠩⣀⠒⡄⠎⡤⢃⠜⠤⢃⡱⠈⢆⡩⢆⠱⠠⣉⠀⠀⠀⠀⠀⠀ ⠠⠍⡆⢡⠓⣌⠰⡃⢖⣉⠲⢌⠢⡐⠣⢄⠣⢃⡜⢡⠎⡰⢁⠎⡐⢩⣿⣿⣶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣷⣾⣶⣥⣣⣌⣆⠢⡑⣼⣿⣿⣿⠿⠟⡩⢁⠆⣡⢂⡜⢨⠱⣠⢉⠎⡒⠥⢒⠩⡐⣂⠇⡌⢡⠰⠀⠀⠀⠀⠀⠀ ⢘⡡⠜⡠⠣⢌⠱⣉⠦⠌⢃⠆⢡⢂⠱⣈⠢⢡⠘⡄⢊⡁⢆⡘⠄⣻⣿⣿⣿⢿⣷⣯⣛⣻⣿⣿⢿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⢿⣷⣾⣽⣇⢆⡘⠤⠑⡈⠖⡤⢃⠜⢢⡑⡰⢌⠢⢅⢋⢆⠱⣀⠣⠜⡠⢃⡘⠀⠀⠀⠀⠀⠀ ⠰⢂⡕⢠⠓⣌⠃⡖⢌⡘⠄⡊⠖⢈⠳⣾⣶⣷⣷⣌⣆⠐⢢⠐⡌⣿⣿⣿⠇⢰⣶⣅⡉⠉⠙⠛⠿⢿⣶⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣷⣾⣦⡑⢌⡘⠤⢩⡘⠆⡴⢁⠎⡜⠨⡌⢆⠡⢂⠝⣘⠰⢠⠘⠀⠀⠀⠀⠀⠀ ⢘⠆⡘⢄⠚⣄⠣⡘⢄⠢⠑⡄⠂⢄⠠⢈⡉⣉⠉⢻⣿⠎⡐⢌⡐⣿⣿⣿⠀⣼⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣿⣿⣿⣶⣶⣦⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣾⣿⣿⣿⣷⣿⣿⣿⣧⠂⡔⡘⢰⡈⠖⠤⣃⢚⠰⢃⡜⡨⢑⠨⡜⢄⢃⠢⢉⠀⠀⠀⠀⠀⠀ ⢨⠆⡱⢈⠜⠤⢃⡱⢂⠡⢃⠜⠀⠂⣄⣾⠟⠁⢂⣼⣿⠡⡘⢠⠐⣻⣿⣿⣤⣼⣭⣿⣟⣂⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⣻⣿⣿⣿⣿⠿⣋⣥⣿⠇⡘⠠⢌⠥⡘⠬⡑⢤⢊⡑⠢⣌⠱⣈⠒⡌⠎⡄⠣⢌⠀⠀⠀⠀⠀⠀ ⠰⣁⠣⠌⡌⢓⠢⡐⠌⡒⢉⠠⣈⠾⠙⢣⡆⡈⢸⣿⡟⡁⢆⠡⢊⠄⡩⠻⣿⣏⠉⠉⠛⠛⠻⠿⠿⣿⣿⣶⣦⣤⣀⡀⠀⢀⣾⡿⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣠⣶⣿⣿⣿⣟⢰⣿⣿⣿⣛⣥⣾⠿⢋⠡⡘⠄⢣⡘⢢⠙⡰⢉⢆⡸⢄⠓⡤⠃⡔⢨⡘⠥⡘⠰⣈⠀⠀⠀⠀⠀⠀ ⠸⡄⢣⠘⡰⣉⠒⢌⡐⢩⡀⠄⡉⠄⠠⢈⠛⣀⣾⡿⢃⠌⡤⢃⠢⢘⠠⡑⡈⠿⣷⣦⣶⣤⣀⣀⠀⠀⣹⣿⣿⣿⣿⣿⣄⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠈⠉⠛⠛⠿⣿⣿⠻⣿⣿⣿⣿⢃⣾⣿⣿⣿⠟⣋⠩⡐⠌⢢⡑⢌⢣⠘⠤⢋⠔⣉⠆⡔⡊⠴⣈⠇⢌⠰⢌⡱⢈⠥⢐⠀⠀⠀⠀⠀⠀ ⠸⡄⡡⢊⠔⡬⢘⠠⠌⡄⠹⠿⢶⣶⣷⣶⣾⠿⠟⡡⢂⠜⣀⠣⢘⠠⡑⢤⡑⣬⣾⣿⣿⠏⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣷⢀⣿⣿⣿⣿⣸⣿⢿⠉⡔⠢⢄⡱⢠⡙⢢⠜⡌⠦⡙⢢⠍⡜⡐⢪⢐⡑⠢⡅⠎⡄⢃⠎⠴⡁⠒⡌⠀⠀⠀⠀⠀⠀ ⢸⠄⡱⢀⠚⡤⢃⠧⡘⢄⠃⡌⠰⡀⠆⠒⡌⢢⠑⡄⢃⠔⣠⢊⣤⣳⣾⣾⣿⠟⠉⢹⣿⣧⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⢀⣼⣿⠛⠻⢿⣿⣿⣿⣿⣿⠀⠣⢄⠓⡬⢰⡁⢲⡁⢎⠴⣁⠳⣈⠜⡤⠙⡔⢊⠔⡱⢘⠤⡉⠔⢪⡑⢌⠡⡘⠀⠀⠀⠀⠀⠀ ⢘⡆⢡⠊⠜⣄⢃⠲⣉⠜⡢⢌⠱⢠⢉⠒⡈⠔⡂⢜⣠⣿⣾⡿⠿⠿⠿⢿⣥⡀⠀⠈⠀⠈⠛⢷⣦⣀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢷⣶⣤⣤⣤⣤⣾⣿⣿⣿⣤⣄⣋⣁⣿⣿⠇⢌⠱⠈⢦⠑⢢⠉⡆⠜⡨⢔⡈⢦⢁⡚⢄⢫⠰⣉⠒⠤⢋⡔⠡⢊⠴⣈⠆⡑⢌⠀⠀⠀⠀⠀⠀ ⠸⡄⢃⡘⠌⢆⠌⡒⡌⠼⡐⠌⢢⢁⠢⢑⡈⢦⣵⣾⣿⡿⢿⣷⣆⡀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠈⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠃⡌⠢⢌⡑⢢⡙⠢⢍⡌⠱⣑⠊⡜⡄⠣⢜⡈⠦⡑⠤⡉⢆⢣⠘⠤⢃⠜⣄⠊⡔⢨⠀⠀⠀⠀⠀⠀ ⢸⡅⠢⢌⡘⠤⢃⡱⣈⠇⡱⠈⢆⢢⣹⣶⣿⣿⠟⠋⠁⠀⠀⠈⠙⠻⢿⣦⣄⣠⣟⢿⣦⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠁⠀⠀⠀⠀⢀⣶⣿⢀⣼⣿⡿⠿⠟⡋⢅⠒⡈⠅⢦⠈⢥⠒⡉⠦⢌⠱⣂⠭⠰⡌⠓⡬⢘⡡⢑⢪⠐⡌⢢⠍⡒⢌⠸⡠⢃⠔⡡⠀⠀⠀⠀⠀⠀ ⢸⡆⠱⠠⢌⢃⠣⠰⣁⠲⣤⣽⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣽⣿⣷⣄⠀⠀⠀⠀⠻⢧⡿⠛⠉⠉⠙⠛⠻⠿⠿⣿⣷⣶⣶⣤⣿⠿⠁⠀⠀⠀⣰⣿⣿⢏⣾⡿⢁⠆⡘⠤⡑⢨⢐⡡⢊⠤⢋⡄⢣⢉⠖⡨⡑⡔⡊⡕⢌⠣⠔⠣⡌⢃⠦⡑⠌⡥⢊⠔⡨⢡⠓⡌⠰⡐⠀⠀⠀⠀⠀⠀ ⢸⡇⠌⡡⢂⠌⣂⢳⣽⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⡙⠻⣿⣿⣄⠀⠀⠀⠸⠷⣶⣶⣶⣦⣄⣀⢀⡀⠁⠀⠉⠉⠉⠁⠀⠀⠀⣠⣼⣿⣿⣣⣿⡟⣀⠣⡐⢡⠆⡍⢆⢢⠱⢌⡘⢆⠬⡡⢎⡘⢤⡑⠴⢡⡘⠬⣌⠩⣒⠡⢋⠤⡑⡘⢤⠃⡜⢠⢃⠎⡔⢡⠘⠀⠀⠀⠀⠀⠀ ⢹⡆⡘⢄⠡⢺⣷⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡅⠓⠀⠙⢿⣷⡀⠀⠀⠀⣾⣯⣿⣟⣛⠻⠿⣿⣿⣾⣷⣦⣤⣀⠀⠀⣽⣿⡿⢟⣿⡿⣉⠰⢀⠆⣙⢂⠞⡈⠦⡘⢢⠌⡸⠄⢎⠱⣠⢉⢆⡘⠌⣆⠡⢣⠄⡓⠤⢋⡌⢢⠑⡌⠦⡑⢌⠢⠜⣨⠐⣂⠩⠀⠀⠀⠀⠀⠀ ⢸⠆⡡⠌⣲⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠀⠀⠀⠈⠻⣿⣆⠀⢰⣿⣿⣿⣿⣿⣧⣄⣀⡀⠹⣿⣻⣛⠻⢿⣿⣿⣃⣼⣿⠟⢡⠐⢌⡒⡘⠰⡌⢢⠱⣘⡐⢣⠌⡑⢎⠌⡱⢂⠎⢤⠉⠖⣨⢁⢣⡘⢌⡡⢣⡘⠤⡃⢜⡰⢉⠰⡈⡜⡄⠣⠄⢣⠀⠀⠀⠀⠀⠀ ⣺⡇⠰⣘⣿⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠈⢿⣧⣸⣿⣿⣿⣿⣿⡟⠸⣿⣿⡄⣿⡟⠻⣧⣀⠙⢿⣿⠿⠷⢈⠢⠜⠢⡜⢡⠓⡌⢡⠚⢤⠘⡆⠥⡙⠢⠜⡡⠎⡘⢢⠙⡌⠒⡌⡒⢌⠢⢅⢣⡘⢰⢉⠢⡔⡉⢆⡑⢰⡉⢆⠩⡐⠀⠀⠀⠀⠀⠀ ⣽⡇⢡⠐⢉⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣷⣿⣇⠀⠈⢿⣿⣄⠢⠘⡄⢃⠦⢩⡑⡘⢢⡘⠌⣅⠚⠤⢃⠜⡡⠜⡡⢣⠔⠣⠜⡂⢧⠘⣑⠢⢍⠢⢍⠢⡃⢜⡠⢃⠆⡱⢡⠂⠜⢢⠜⡠⢡⠘⠀⠀⠀⠀⠀⠀ ⣾⡇⢢⡁⢸⣿⡇⠀⠀⢀⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣯⣿⠇⠀⢸⣿⠋⠡⣿⠀⠀⠈⣿⣷⡌⢡⠘⡰⠨⢅⠢⢍⠢⢌⠱⡠⠍⢆⡉⠦⡑⣊⠴⠡⢌⡃⢣⠜⣠⢋⠤⠓⣌⠱⢌⡒⣉⠦⡐⠣⢌⡱⢡⠉⡜⢂⠞⡀⢆⠩⠀⠀⠀⠀⠀⠀ ⢾⡇⢢⣿⣿⣿⡇⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⢸⡟⠀⠀⣿⡇⠀⠀⢻⣿⣇⠢⠑⠤⢙⠢⡉⠦⡉⢆⠱⢂⢍⠢⡉⠔⡡⢂⢌⡑⢢⢉⢆⡚⢄⠎⡌⢓⡌⠸⡄⢣⠆⡒⢡⢃⠦⣘⠢⡑⢨⡑⣊⠔⣈⠒⠀⠀⠀⠀⠀⠀ ⣹⡇⢢⣿⣿⠘⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⢹⣿⣽⣧⠀⠀⣸⡧⠀⠀⣿⣯⠀⠀⢘⣿⣿⠠⢉⠒⡌⣒⠡⢣⠜⡠⢃⠃⢎⡐⢉⠆⡱⢁⠆⠎⡅⢎⠢⢜⡈⢖⡨⠥⢌⠣⢌⡡⢎⡑⢌⡂⢒⠤⠓⡌⠤⠱⡄⢊⠄⢚⠀⠀⠀⠀⠀⠀ ⢽⡇⢆⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣻⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠘⣿⡟⣿⡄⠀⣿⡇⠀⠀⣻⣧⠀⠀⠀⣿⣿⡀⠣⢌⠰⡄⢣⡁⠎⡰⠉⡜⠤⢘⢠⠊⠔⡡⠊⠜⡐⠨⡑⢢⠘⢆⡰⢃⢎⠸⣀⠒⣆⠘⢤⠉⢆⡙⢆⡘⢄⠳⡈⢆⡘⠰⠀⠀⠀⠀⠀⠀ ⣿⡇⣎⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⢿⣿⣿⣧⡀⣿⡇⠀⠀⣿⡷⠀⠀⠀⣿⣿⡆⡑⢂⠱⡘⠤⡘⠤⢁⠃⢆⡉⢆⠃⢎⠰⢁⠜⡠⣁⠣⡐⠡⢌⠢⡐⡉⢆⡱⢂⠍⡤⢋⢄⠫⡐⡜⠤⡘⢠⠓⡌⢂⠔⢩⠀⠀⠀⠀⠀⠀ ⢼⡧⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠘⣿⣿⣿⣧⣿⡇⠀⠀⣿⡏⠀⠀⠀⣿⣿⣧⠘⡄⠣⢑⠊⡱⢈⠌⡘⠤⠘⡄⢊⠤⣃⣬⣶⣷⠿⣷⣿⣶⣤⡁⢆⠡⢂⠒⡩⠘⡔⢡⠊⡴⢁⡚⠤⡉⠤⢋⠔⡡⠊⡔⠀⠀⠀⠀⠀⠀ ⢸⣗⣹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣸⣿⣿⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⣼⡟⠀⠀⠀⢘⣿⣿⣷⢃⠰⡁⠎⡐⠡⠌⡂⣅⢊⣥⣘⣦⣿⡿⠟⠋⠀⠀⠀⠀⠉⠻⢿⣦⣧⣌⠢⣑⠣⠜⣠⠙⠤⣃⠜⡰⠑⠬⣑⠊⡔⢡⠘⠀⠀⠀⠀⠀⠀ ⢸⡗⢾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢿⣿⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠈⣿⣿⣿⣿⠀⣰⣿⠇⠀⠀⠀⢸⣿⣿⠣⣍⠰⣀⢣⣌⣱⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣮⡑⠌⡄⢩⠒⡌⢒⠡⡚⠤⢡⠍⡐⢂⠭⠀⠀⠀⠀⠀⠀ ⢸⣏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢹⣿⣿⣏⢰⣿⣿⠀⠀⠀⠘⢻⣿⣿⣿⣦⣷⣾⣿⠿⠛⣿⣿⣿⠟⢻⣤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⣿⣷⡌⢄⠣⠘⢢⠱⢠⢃⢣⡘⢄⢃⠸⠀⠀⠀⠀⠀⠀ ⣽⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⠁⠈⢀⣾⣿⠏⠁⠀⠀⠙⠻⣿⡟⢻⣷⡆⣀⣀⣀⠀⠀⠀⢺⡄⠀⠀⠀⠸⣿⣿⣤⣇⡩⠐⢌⠂⡌⠒⣌⠢⠌⢒⠀⠀⠀⠀⠀⠀ ⣿⡏⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣽⣿⠏⠀⠀⠀⢰⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠁⣴⣿⣿⣿⠉⠛⣿⡗⠀⣼⡇⠀⠀⠀⢀⣿⣿⣿⠟⠓⢩⣄⠊⡔⠡⢂⠅⡊⢬⠀⠀⠀⠀⠀⠀ ⣻⡧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢣⣿⣿⡟⠲⣶⣦⣤⣤⣄⣀⣠⣾⣿⣿⣿⣿⣦⣤⣿⣷⠀⣺⣇⠀⠀⠀⠙⠛⠛⠉⠀⠀⣈⠻⠐⣄⡣⢌⠂⡅⢲⠀⠀⠀⠀⠀⠀ ⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣸⣿⣿⡧⠀⠈⠩⣭⣥⣽⡿⢿⠏⣿⡯⠩⣿⠿⣿⡿⠁⠘⠿⠧⣤⣴⣾⣦⣀⠀⠀⣴⡿⠿⣿⣿⣛⣛⣶⣷⡾⣿⡅⠀⠀⠀⠀⠀ ⣿⡏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠈⣿⣿⣷⣶⣀⣹⣧⡄⣠⣶⣿⠇⠀⠀⠀⢸⣿⠴⣿⣿⣿⣆⠀⠹⠇⠀⠹⣿⡿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣶⣼⣿⣷⣀⣹⡿⠿⣿⣿⣿⣿⣷⣤⣤⣄⣄⣠⣄⡀⢀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠁⠀⠀⠀⠀⠀ ⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠿⠧⠟⠛⠿⣷⣿⣤⣌⡉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⣀⠀ ⣻⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⣟⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠲⠶⠷⣿⣯⣤⣭⣤⣤⠷⠶⠶⠶⠶⣾⢶⡾⣿⣶⣿⣷⣶⣿⣿⣿⠟⠛⠁ ⣻⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣀⣤⣴⣿⣿⣟⣿⣿⡿⠿⠛⢁⣠⣿⠆⠀⠀⢀⠀⢀⣠⡀⣀⠀⣀⠀⣀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠏⠀⠀⠀ ⣽⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣷⣤⡀⠀⠀⢀⣿⣿⣿⠿⠟⣻⣿⣿⣿⡿⠛⡡⢐⣽⣿⣿⣿⣿⣶⣾⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀ ⣿⡇⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⠃⠀⠀⠉⠻⣿⣦⣄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣬⣿⣼⣿⣿⣿⣿⣤⣠⣼⣿⣧⣤⣿⣿⣿⡿⣿⣿⣿⣧⣴⣿⣿⣧⣿⣿⣿⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⣿⣇⢺⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⢿⣿⣦⣤⣠⣴⣾⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀ ⣿⡇⠎⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠉⠉⣿⣿⠟⠋⠁⠀⠀⠀⠈⠋⠛⠛⠻⢿⠿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⣀⣀⣀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⣿⡇⡍⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀ ⢿⡇⡘⢌⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢣⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⣿⡇⡒⢨⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣫⣵⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀ ⣿⡇⡑⢢⢹⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⢶⡶⠖⣿⣾⣿⣿⣿⡟⠉⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⠀⠀ ⣿⡗⡈⠔⡨⢙⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣇⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀ ⣿⡇⡘⠤⠑⡬⡐⢻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠘⣿⣿⣧⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⢛⣉⣉⣛⣩⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢘⠀⠀⠀⠀⠀⠀ ⢻⡇⠰⡁⠭⡐⢡⢓⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣴⣿⣿⣿⡀⠐⠿⢿⣷⣤⣤⣀⣀⣀⣀⣀⣀⣀⣼⣿⡛⠛⠻⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠆⠀⠀⠀⠀⠀⠀ ⣹⡇⢡⠘⡰⡁⠆⡌⠼⣿⣧⠉⠻⣷⣶⣤⣤⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣤⣠⣄⣤⣠⣤⣤⣴⣶⣤⣄⠀⠉⠛⠉⠁⠀⠻⣿⣄⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣤⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⢨⠀⠀⠀⠀⠀⠀ ⢰⡇⢂⠱⡐⡱⢈⠄⡃⢿⣿⣇⠀⠀⠈⠙⠻⢿⣿⣽⣿⣿⣿⣿⣿⡿⣿⠿⡿⣷⣿⣿⣶⣿⡷⣿⠿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⣿⣿⣮⣥⣤⣶⣶⣶⣶⣿⣻⣿⣛⣛⣀⣠⣡⣤⣤⣤⣬⣤⣤⣤⣭⣬⣽⣥⣤⣤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⣸⣿⣟⡈⢆⠀⠀⠀⠀⠀⠀ ⠸⡄⢃⠢⢡⡑⠌⡂⢥⣻⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣛⣽⣯⣿⣿⣿⡶⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⣷⣶⣶⣿⣮⣭⣭⣿⣿⣻⣿⣶⣤⣿⣉⣘⣼⣼⡆⠀⠀⠀⠀⠀ ⠸⡄⢃⡘⠰⢌⢂⠱⣘⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣶⣿⣿⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣦⣀⣀⣀⠀⠀ ⠸⡄⢃⠰⢉⠆⡌⠢⢄⢻⣿⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⠿⠿ ⠘⡄⠣⠘⡄⢊⠄⣃⢂⠚⣹⣿⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀ ⠸⣄⠣⡑⣨⠐⡌⣄⣢⣡⣏⣿⣧⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠉⠀⠈⠁⠉⠙⠋⢻⣷⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢫⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢃⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⣿⢁⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢃⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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