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