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