Curl Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⡿⠇⠀⠀⣀⠤⣒⣫⣽⣛⡫⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡷⣤⣤⣶⢟⣻⠽⣚⠭⠤⣒⣲⣯⣓⣋⣉⣉⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣟⣝⠮⢗⣊⠥⣒⡯⠖⡪⢝⡯⢭⣷⣶⣿⣿⡿⢟⡷⡦⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣖⠫⠓⣒⠟⣉⠴⣋⣾⠵⠖⠛⠲⣮⣍⠲⡙⢆⠙⢮⣆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠛⠛⠋⠁⠀⠀⠀⠀⠀⠙⡆⢱⣹⠀⡇⠈⡟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⡏⡆⡇⢰⢣⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣶⢶⣶⣶⠶⣤⣤⣶⠶⠟⢋⣉⠿⠒⠚⣩⢞⡴⢣⢡⢡⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⢞⢕⣿⠟⣉⠭⣳⠶⣛⣿⡽⣟⣲⠶⠿⣛⡺⢵⣺⣵⣣⡮⣾⠇
⠀⠀⠀⠀⠀⠀⡴⢹⢁⠏⡎⣾⠃⡜⠁⠞⡱⡪⢻⢗⡩⢵⣶⠺⠯⣷⣯⣟⣯⡵⠾⠚⠁
⠀⠀⠀⠀⠀⠀⢧⢸⠈⡆⡇⡇⡄⠇⠸⢰⠱⣁⠁⣾⠀⡃⠸⢦⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣄⢱⠸⡹⡵⡘⣄⡟⡆⢻⣆⢏⢧⢣⠘⣄⠑⢿⡷⡜⡟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣽⠼⠞⠋⠉⠻⣌⣎⠻⣧⢇⠳⡈⢣⠈⡟⡿⡜⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢾⡈⢧⢸⡄⡇⢸⢇⠸⣧⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠎⣸⠁⡇⢸⢸⢀⠏⣆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣶⣗⠮⢖⡡⡫⢎⡼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⡫⢵⣿⣿⣩⣴⠭⠷⠾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡎⡞⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣵⡱⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣣⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠌⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢪⢫⢞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⠸⡈⢢⢏⢗⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢯⣦⣈⢂⢎⢎⠣⡈⢎⢛⠗⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠎⠌⡄⢱⠘⠀⠌⡄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⡤⢖⢏⠇⠄⡄⡄⢸⢀⠂⡶⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⢟⡰⡡⡪⢔⡡⢊⠌⣜⠜⡠⡣⢪⢊⢃⠎⡰⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⢕⢕⡩⡪⣊⢔⡡⢊⠥⣊⠕⡪⢒⡵⢵⠞⢁⢌⢼⣇
⠀⠀⠀⠀⠀⠀⠀⣼⢕⠕⡱⣪⡾⣗⠕⡪⢕⡨⢐⣭⡲⢝⣚⠥⡺⢛⢕⠏⣿⣷⣶⢶⣶⣦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡏⢎⢎⢜⣿⣪⡴⣛⣬⡳⢞⠿⢐⠨⠅⡲⠏⣊⠕⡡⡪⡟⡙⢜⡕⢝⢷⡑⢝⣄
⠀⠀⠀⠀⠀⠀⠀⣟⢈⣈⣾⣿⡫⡪⡪⠕⣊⠕⢊⡠⢂⠕⣊⠥⠒⢉⠔⣵⠃⡇⠈⡜⡈⢆⡌⢆⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠹⣼⣿⣿⣟⣰⠋⢠⠚⡡⣒⠅⣚⠕⣊⡠⠔⣊⠕⣪⢂⣔⠇⢠⠃⠀⠸⢰⠈⠘⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣟⠀⠇⡜⡜⡠⢊⠔⣋⠔⣒⠭⢒⡨⢔⠝⢁⠔⢃⠜⢀⢇⠆⡔⡰⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⡅⡏⠠⢁⡾⢒⠩⠔⢊⡡⠔⣁⠔⢁⠔⡡⢖⠕⡡⢊⠜⡰⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢴⣿⡾⢑⣨⣭⡴⢖⡿⢑⠨⠕⡪⢚⠕⣩⠖⠛⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡕⠱⢡⢊⠔⡵⢊⠕⡺⠗⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⢸⢸⠈⡄⢣⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠤⢱⣌⢢⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⣰⠂⠀⠃⡀⠀⠀⠀⠀⠉⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣤⣾⣁⡾⢁⡴⠁⢠⣀⣠⠀⠀⠀⠀⡈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣾⣅⢠⡾⣿⣿⣧⣴⣀⣀⡠⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣧⢖⡀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠙⠛⠛⠉⠉⠀⢻⣿⣿⣏⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡻⠃⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⣿⠈⠇⠀⠀⠀⠀⡀⠙⣄
⠀⠀⠀⠀⠀⢀⣀⣤⣤⡐⠒⠒⠒⠒⠦⣄⡀⠀⠀⠀⠐⢄⠐⢄⠀⠀⠀⠀⠆⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡰⠀⠈⢆
⠀⠀⢠⣤⠾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠐⢀⣁⣤⡤⠖⠒⠒⠒⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣠⣶⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢩⣿⣇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣤⣬⣿⣄⠀⠀⠀⠀⢀⣾⣿⣿⣧⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠠⢤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣧⣉⣽⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢰⣿⣿⣿⣿⣿⣿⣿⡿⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣍⣩⣭⡿⢿⣿⡿⠿⠟⠁⠀⣿⣿⣿⣿⣯⣼⣿⣯⡀⣼⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠋⢹⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠀⠀⠈⠁⠀⠀⢠⣧⣔⣙⣿⣿⣿⣿⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠟⠀⠀⠛⣻⣿⡿⠁⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣦⣄⣀⠀⢀⣀⣬⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠰⠛⠟⢹⣿⡟⠁⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡙⠛⠿⠿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡟⢶⡄⠘⣷⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣦⣌⠳⣾⣿⣦⣿⣷⣦⢸⡏⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠛⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣇⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠛⢠⣶⣿⣿⣿⣿⣿⣿⣷⣶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣉⣉⣉⣉⠙⠻⢿⣿⣿⡿⠟⠃⠀⠀⠻⢛⣩⣽⣿⣿⣿⣟⣋⣁⣠⣴⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⣿⣿⣿⣿⣿⣿⣦⣽⠿⠇⠀⠀⠀⠀⢰⣿⢟⣵⢾⣿⣿⣿⣿⣿⣿⠿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣉⣥⣴⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢡⣿⢋⣾⢻⣿⣿⣿⣿⣷⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣯⣴⣶⣿⠾⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢼⣿⣿⣯⣿⣷⣍⣉⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⡿⠟⠋⣁⣤⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⣴⣾⣿⣿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⡟⠟⢋⣉⣥⡽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣏⣴⣾⣻⣭⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠟⠛⢉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⢉⣤⣶⣾⣿⣏⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⣴⣿⣿⣿⠿⠟⢉⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⠹⡿⠃⣰⣟⣵⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⠁⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣿⢻⣿⣿⣿⣋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠇⢠⣴⠿⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋

⠀⠀⠐⠠⡆⠀⠀⠈⠉⠀⠈⠉⠁⠄⠠⢀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸
⠀⢀⡀⠀⠁⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠈⠳⠦⡙⢧⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠠⣄⣀⣀⡵⠔⠀⠉⠒⠀⠀⠀⣀⠴⡄⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠠⠂⠀⠀⠂⠀⠀⠀⠠
⠀⠀⢀⠀⠀⠀⠁⠑⠒⠚⠉⠁⠀⠀⠀⠀⠒⠒⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠸⢁⠀⠠
⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠈⠉
⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠇⠀⠀⠀⠀⠊⠀⠀⠐⠀⢀⡈⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⣃⠤⠀⠂⠀⠠⠤⠀⠀⠀⠉⠙⠎⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⢱⡀⠉⡀⢠⢀⢈⡀⡀⠀⠈⠀⠐⠀⠀⠀⠐⠀⠀⠀⠐⢄⣀⡀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠒⢦⠀⢈⠂⠉⠀⢀⠀⠡⠀⠂⢾⠠⠹⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠨⠂⠀⠀⠑⠁⢀
⠀⠀⡀⠀⠀⠀⠀⢀⠤⠆⠀⠀⠐⠁⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠸⡅⠀⣴⠛⠄⣀⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠁⠀⠀⢀⠊⢀⠔⡀⠀⠀⠀⠀⠈⠁⠀⠐⢠⡈⠀⠀⠀⠀⠀⢅⠫⠐⣡⡁⠀⠀⠀⠐⠈⠀⠈
⠀⠀⢄⣀⣀⠄⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⢈⠇⠀⣥⣄⠀⠒⡆⠀⠎⠡⠀⠀⠀⢰⠅⡀⠀⠀⠀⠈
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⡀⠄⠤⠈⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⢄⠀⠈
⠀⠀⠆⠤⠀⡅⠈⠀⠀⣀⠤⠆⠀⢂⣀⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠒⠀⠀⡂⠀⠀⠉
⠀⠓⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⡀⠈⠋⠀⡜⠁⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐
⠠⡠⡀⠀⠀⠀⠀⠀⠀⠏⠉⡧⠀⠀⡚⠀⠈⠀⠈⠠⡊⠀⣠⠦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠊⠳⠄⠀⠀⠀⠀⠀⢠⠇⠀⠄⠀⠀⠉⠆⠀⠀⠡⢰⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⢀⠀⠀⠀⠀⠠
⡀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢁⣄⠀⠀⠐⠂⠀⠈⠀⠀⠰⠤⠀⠀⠀⠤⢆⠀⠀⠀⠀⠀⠀⢀⠠⠁⠬⠀⣀
⠀⠀⠀⠀⠀⠒⠀⣀⣨⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣄⣰⣇⣄⡐⡊⠽⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠹⠛⠈⠁⠀⠀⠀⠒⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⣄⠛⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠁⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⢺⠄⠤⠤⣄⡀
⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠰⣤⡄⠀⠀⠀⠀⠀⠀⠩⢛⣛⡲⡄
⠀⡀⠀⠀⡠⢶⣚⢀⠀⠀⠀⠀⠈⠉⠒⠶⣤⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⣠⠤⠧⡨⢆⢀⣰⣴⣶⣄⡀⠰⠟⣯⢧⣷
⡄⠹⡄⢠⣅⠈⠙⢦⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠐⠢⠄⠾⠶⠂⠀⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⢌⡉⢔⣚⠋⢈⠇
⠑⠀⠈⠓⠉⠐⠤⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁
⠀⠀⠀⠐⠒⠒⠒⠒⠛⠉⠉⠁⠀⠈⠉⠉⠉⠐⠒⠤⠥⢤⣀⣀⣤⡤⠀⣀⣀⡤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣽⣷⣶⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠉⠉⠉⠉⠉⠁⡀⢀⣀⣠⡇⠀⢀⡀⠀⢸⣄⣀⡀⢀⠈⠉⠉⠉⠉⠉⠛⠓⠒⠦⢄⣀
⠀⠀⠀⢀⠴⠊⠁⠀⠀⣀⣠⠴⠖⠂⢀⡤⠖⠊⡏⠉⠉⠹⡏⠳⣴⣦⠞⢹⠏⠉⠉⢹⠑⠲⢤⡀⠐⠲⠦⣤⣀⠀⠀⠈⠑⠦⡀
⠀⠀⠐⠁⠀⢀⠤⠒⠋⠁⠀⠀⣠⠴⣥⣤⡤⠞⠁⢀⣀⠀⢧⠴⢛⡟⠦⡼⠂⣀⡀⠈⠳⢤⣤⣬⠦⣄⠀⠀⠈⠙⠒⠤⡀⠀⠈⠢
⠀⠀⠀⠀⠊⠁⠀⠀⠀⠄⠒⠒⠛⠒⠒⢦⡀⠀⡼⠉⠀⢹⠘⠀⢸⡇⠀⠃⡏⠀⠉⢷⠀⢀⡴⠒⠒⠛⠒⠒⠠⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⡼⠃⠘⣇⠀⠀⠊⠐⠀⡸⢇⠀⠀⠑⠀⠀⢸⠃⠘⢧⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠦⣄⣀⡤⠞⠁⠈⠳⢤⣀⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⢀⠀⠀⠀⠀⠀⠀⡀⠠⢄⣀
⠀⠀⠀⠀⡠⠤⠄⣒⠀⠤⠤⠤⠤⠶⠒⠒⠛⠋⠀⢀⡴⠓⠒⠒⡲⢖⠒⠒⠚⢦⡂⠀⠙⠛⠒⠒⠶⠤⠤⠤⠤⠀⣒⠠⠤⢄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠉⠒⠤⣀⣀⣠⣄⣀⣀⣤⠔⠋⠀⠀⠀⠸⡅⢨⠇⠀⠀⠀⠙⠢⣤⣀⣀⣠⣄⣀⣀⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠛⠓⠒⠒⠛⠛⠒⠒⠚⠛⠉⠉⠉⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⡀⢠⠛⢄⠀⠀⠠⠻⡄⢀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⠀⠔⠁⠈⠒⠊⠀⠀⠑⠒⠁⠀⠢⠀⠠⠄⠒⠉⠁⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡡⢌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠒⠒⠒⠤⠶⠖⠒⠚⠉⠀⠀⠉⠑⠒⠲⠦⠤⠒⠒⠒⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣀⠀⠀⣀⡤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⢄⠃⠀⠀⡌⢣⡔⢡⠀⠀⠘⡠⢊⡇
⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⠙⡾⢄⡀⠀⠰⣜⣣⠎⠀⢀⡠⢷⡋⢀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣀⣀⣀⣀⠤⠚⠀⠀⠀⢀⣀⣠⠤⡾⢷⠤⢄⣀⡀⠀⠀⠀⠓⠤⣄⣀⣀⣀⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⣤⣤⣐⡂⠈⠉⠉⣠⠗⠀⠀⠀⠀⠀⠀⠺⣄⠉⠉⠁⠐⣂⣤⣤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠄⠠⡀⠙⣄
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠰⠂⠃⠀⡈⠆
⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⢢⡠⠁⢠⠃⠐
⠀⠀⠀⠀⠀⠀⠘⢄⢀⠠⠊⠀⠠⠃⢀⢿
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⢀⠊⡜
⠀⠀⠀⠀⢀⠜⠀⢀⠤⠂⠀⡠⠔⢁⠼⡈⠐⠤⡀
⠀⠀⠀⢠⠃⢀⠔⠁⠀⠀⣀⠔⠊⠣⢄⠈⠑⠀⠈⠒⡀
⠀⠀⠀⡆⢀⠊⠀⠀⡠⣊⠄⠴⢤⢄⡀⠉⠒⢄⠀⠀⠈⡄
⠀⠀⠀⡇⡌⠀⠀⢰⡰⠁⡠⢀⠀⠀⠱⠀⠀⠀⢱⠀⢡
⠀⠀⠀⢣⣁⠀⠀⠈⢇⣀⡡⠌⢀⠀⢰⠀⡎⠈⠖⢀⠌
⠀⠀⠀⠀⠙⢢⡀⠐⠤⠀⠠⠔⠁⣠⡃⠀⠈⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠒⢤⠀⢤⠒⠉⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠁⠐⠒⠂⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠑⢄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠂⢕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠐⠢⡀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠄⢀⣀⣀⣀⣀⡀⠠⠄⠐⠒⢀⣉⡐⢄⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⡜⡠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣀⠔⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠻⡹⡍⠉⠉⢙⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⡵⢟⠩⠿⣿⣶⢈⡇⠔⠠⠊⠙⠻⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢫⡞⠁⠁⣤⢸⡜⣾⢳⡘⡀⢸⣆⠈⠘⡎⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠄⣿⢀⠀⠂⠀⢺⣿⣟⣾⣷⣌⠘⢿⣿⣦⠃⣟⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢼⣿⠃⠀⠀⠀⠘⣿⢁⢡⠏⣿⣷⠀⠈⠈⣶⡿⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠘⣿⡀⠀⠀⠀⠀⠈⢿⣾⡂⠋⡟⢰⠀⡄⢸⣷⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠘⡿⡇⠀⣡⠎⣴⠁⢸⡇⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⡤⣽⣿⣧⠀⠀⠀⢠⡇⣿⣾⡿⢰⡏⢀⣾⢃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠛⠕⠛⡝⠀⠀⢀⣾⣇⡿⠋⢀⣾⣡⣾⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣀⠴⡶⠋⠀⠀⢀⠎⡼⣽⠁⠀⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⡘⠡⣴⡀⠀⠀⢀⡏⠀⢹⡇⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠵⣟⣵⣄⠀⠸⡇⠀⠙⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠻⠀⠀⢣⡀⠀⠀⠙⣂⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠙⠦⣐⣶⣮⣿⣿⣟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⡃⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣭⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡇

⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠳⠄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⢀⡀⠀⡀⠆
⠀⠀⠀⠀⢀⠂⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠀⠀⠀⠀⢀⡠⣄⣀⠔⠀⠀⠀⠀⢠⠊⠀⠀⡴⠁⠀⠀⠑⠂⠀⡀
⠀⠀⠀⢀⠆⠀⠀⣧⠀⠀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢰⠁⠀⢸⠀⡠⠄⠰⠁⠀⠀⠈⠁⠀⠀⠀⢴⠃⠀⠀⠠⠓⠒⠲⢶⡒⠒⠚
⠀⠀⠀⢸⠀⠀⢀⠟⠊⠁⠀⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⡆⠀⠀⠀⡏⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠘⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⣠⠋⢣⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠹⡇⠀⠀⠀⠀⠀⠀⠀⠧⣀⣀⣤⠤⠤⠒⠋⠙⡆⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⡠⠂⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠥⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⣐⠃
⠀⠀⠀⠀⡇⠐⡋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠁
⠀⠀⠀⠀⡇⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢆
⠀⠀⠀⢠⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⢠⠇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠘⠀⠀⠀⠆
⠀⠀⠀⠘⡀⠀⠀⢸⠤⠒⠒⠢⢴⠒⠒⠲⠂⠀⠀⠀⡰⠁⠀⠀⠀⠟⠉⠉⠉⠲⠉⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠰⠒⠉⠉⠒⠤⠔⠒⠤
⠀⠀⠀⠀⢇⡀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀
⠀⠀⠀⠀⠀⠈⠓⠢⠤⣀⣀⡀⢴⡉⢣⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠤⠤⠼⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣶⣄⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣤⣤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣴⡿⠟⠃⠀⠀⣀⡤⢖⣫⡥⣶⣺⡯⠥⠶⠖⢛⣩⡭⠿⣓⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣼⡿⣦⣤⣴⣶⡿⠷⣚⡩⠴⢊⣩⠤⠴⠒⣚⣫⠭⢒⣋⣉⣉⣉⠉⠙⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡹⡝⢮⣙⣫⡽⠖⢋⣡⠴⢞⣩⠴⢖⣫⠽⢟⣛⣉⣩⣥⣶⣶⣿⣿⠿⣶⣦⣈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢳⡙⠦⠤⠤⠖⣋⣩⣴⠞⠉⣠⠞⣫⠔⠋⣉⣴⠚⣒⣳⣟⡓⠲⣌⠙⠢⣝⢮⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢯⣛⠛⠛⣉⡥⠚⣁⡴⢚⣡⡾⠷⠞⠛⠉⠉⠙⢷⠶⢤⡉⢣⡈⠳⡀⠈⢧⢱⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠶⠿⠛⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠹⡄⣧⠀⢹⠀⠀⡇⢳⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢹⢸⡄⢸⠀⠀⡇⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣀⡴⢻⠀⢸⢸⡇⣸⠀⡼⢁⣯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢖⡶⠟⣻⣿⣿⠿⠶⣤⣤⣶⣞⡯⠽⠛⠉⣉⡽⠟⠛⠛⢉⡠⠏⣠⠞⣸⢃⠇⣼⢁⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⡴⢋⢔⡿⣻⠿⠓⢚⣩⣭⣤⡶⠶⢖⣒⣫⣭⠤⢶⣶⣒⣫⡭⢖⣋⡥⢞⣡⠞⣠⢇⡞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡝⢁⡜⢡⢏⣾⠟⠁⡤⠚⢉⡴⠊⣡⢖⡿⢟⡫⠵⠒⢋⣉⣉⠤⠖⣚⠭⢔⣚⠭⠒⣫⢗⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢸⠁⣼⠀⡏⢸⢻⠀⢸⠁⢠⠏⣠⢎⡴⢉⠖⢉⡴⢚⡟⣿⠉⠛⠲⠿⣷⣾⣭⡴⠶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⠀⢻⠀⣇⢸⢸⡀⢹⠀⢸⠀⡏⢸⢁⡏⢰⣿⠀⣾⠀⢹⢦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⡄⠈⣇⢸⡘⣎⢧⠘⣆⠘⡆⣇⠘⣿⡇⢹⠸⡄⢹⡀⢸⡀⠹⣍⢿⡻⣍⠻⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢸⠀⢳⡘⣎⢣⣘⣦⣧⣸⡄⠹⡿⣌⢧⡙⣆⢳⡀⠳⣄⠀⠻⡷⡜⣆⢳⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣽⠾⠟⠋⠁⠀⠙⠷⣄⣣⠈⠳⣽⡸⡄⠳⣄⠈⢧⠀⢹⡹⡞⣆⢳⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣼⡇⠙⣄⠈⣇⠈⡇⠀⣇⣇⠘⣞⡇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⠀⣿⠀⡇⠀⣿⢹⠀⢹⢹⡈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡰⠃⣠⠏⢠⠇⢀⡟⣸⠀⡼⢸⢇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⡷⣚⣩⠴⢋⡴⢋⠞⢁⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⣩⣴⣾⣿⠟⢋⡥⠖⣚⣭⣞⣡⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⡻⢋⠔⣫⠼⠟⠛⠓⠚⠛⠒⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡞⢁⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡙⣄⢷⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⡆⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠴⠋

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⣶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡯⠖⠊⠉⠉⠉⠙⠲⢤⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣀⠤⠤⠤⣄⡀⠀⠀⠈⠢⡀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⢤⣀⣀⣀⠀⠀⠀⠀⠀⢰⠃⢀⡎⢀⡤⢄⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⢄⣈⠉⠓⠦⣄⡀⢸⡀⠈⢇⣸⡄⠀⢳⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠙⠪⣷⣄⡀⠀⢀⡠⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠉⠑⠒⠦⣄⡀⠀⠀⠀⠙⠆⠀⠀⠈⢢⡉⠉⠉⠀⠀⠀⢀⡼⠁⠀⠀⢠⠃⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⣀⣀⣹⣄⣀⣤⠤⠖⠋⠀⠀⠀⣠⠋⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⢈⡷⠖⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡼⢡⠇
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣰⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⣀⠀⠀⡠⠞⠁⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠋⠁⠀⠀⠀⣠⠞⠀⡞
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠀⠀⢠⠏⠀⠀⠀⢀⡴⠚⠉⠁⠈⣩⡿⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⢀⡜⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⢀⡏⠀⠀⠀⣠⠋⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⣀⣠⠤⠴⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⣰⠋⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠈⡇⠀⠀⢸⡄⠀⠀⠸⡇⠀⠀⢠⠇⠀⠀⠀⡴⠁⠀⠀⠀⣠⠴⡎⠉⠹⡁⠀⢸⠁⠀⢻
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢹⡀⠀⠀⢧⠀⠀⠀⢳⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⠀⡴⠃⠀⣳⠀⢠⠃⠀⡞⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢳⠀⠀⠈⣆⠀⠀⠈⢧⠀⢸⠀⠀⠀⠸⡀⠀⠀⠀⣇⣀⣠⠇⠀⠀⠀⡼⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⢣⠀⠀⠘⣆⠀⠀⠈⢧⠀⢧⠀⠀⠀⠱⣄⠀⠀⠀⠉⠀⠀⠀⣠⠞⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⢧⠀⠀⠘⢆⠀⠀⠈⢇⠈⠳⡀⠀⠀⠀⠙⠒⠲⠶⠖⠒⠋⠁⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⢧⠀⠀⠘⢇⠀⠀⠘⡆⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⣀⡀⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⣆⠀⠀⠈⣆⠀⠀⢳⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢹⡀⠀⠀⢸⡄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⢀⡴⠒⠲⣄⠀⠀⡼⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢸⠁
⠀⠀⠀⠀⡞⠀⠀⠀⣹⠀⡰⠃⠀⠀⠀⢠⠇⠀⠀⢠⡇⢀⡏
⠀⠀⠀⠀⣇⠀⠠⢴⡧⠞⠁⠀⠀⠀⢀⡞⠀⠀⠀⡜⢀⠞
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣾⠴⠋
⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⣴⡖⠋⠁⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⣉⣽⣿⠁⠈⠳⢦⣀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠞⠟⠙⠁⠀⠀⠀⠀⠈⠳⣦⣀⢄⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⣠⡶⢋⡽⠛⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣧⠀⠀⠘⢆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣴⠞⠁⣠⡟⠀⠀⠈⠛⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠈⡄
⠀⡄⢀⣠⠴⠒⠒⠛⠒⠂⠀⠤⣾⣿⡿⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⢁⣿⠁⠀⠀⠀⣴⣶⡿⠛⠛⠉⠁⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⢻⡄⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⣷⣧⣤⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠳⣄⠀⠀⠀⠀⢀⣸⡗⠀⢀⣤⣠⣀⣀⣀⣴⠶⠊⠁
⠀⠀⡐⠋⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⠀⠀⠀⢀⣠⠆⠀⠀⠀⠈⣧⠀⠀⠀⢠⣿⡴⠞⠛⠛⠛⠉⠉⠁
⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡳⣝⣦⡀⠀⠈⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢸⠏
⠀⡇⠀⠀⠀⠀⠀⠀⣀⠴⠟⠛⠛⠛⠛⠿⠷⣶⣄⣀⣀⣀⡄⠄⠀⠀⠀⢀⠞
⠀⢹⡀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣤⣤⣄⣤⣥⣾
⠀⠀⢧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣿⠹⡄
⠀⠀⡜⠀⠀⠀⠀⠀⠀⣠⠤⠠⠤⠤⠤⠤⣀⣀⣀⣀⣀⠀⠀⣀⣠⡞⠁⠀⠇
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⣿⣿⣿⠿⠛⠀⢀⣼
⠀⡇⠀⠀⠂⠀⠀⠀⠀⠀⢀⣠⣶⠶⠚⠛⠉⠋⠉⣩⣽⠏⠀⠀⠀⡠⠜⠁
⠸⡇⡄⠀⠀⠀⠀⠀⠠⠴⠛⠋⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⢠⠎
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠄⠋
⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⣀⡤⠴⠒⠊⠉⠁
⠀⠀⠱⡀⢠⠀⠀⠀⠀⢀⣾⠟⢻⡏
⠀⠀⠀⢘⡞⠀⠀⠀⠀⡞⠀⠀⠘⣷⣰⠆⠂
⠀⠀⠀⠈⠁⠀⠀⠀⢰⠁⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢰⠁
⠀⢰⣀⠀⢀⣤⠴⠊⣀⠀⠀⠀⡎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣔⠶⠞⠻⢿⡲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⠙⢈⡥⣶⣍⠳⣦⠀⠀⢉⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢡⣥⢰⡥⠙⣷⠌⡆⡾⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢀⡔⠀⢀⢜⣼⡷⣣⠞⠀⠈⣇⣣⣿⣧⣞⠡⢘⡝⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠠⢈⠜⡟⣨⡷⡀⢩⣿⣿⣿⣿⣠⡄⡞⠤⢋⠟⡟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⢠⡞⢱⡀⠄⠀⢈⢸⣷⣿⣥⠚⣿⣿⣿⡿⣡⣿⠘⠁⠄⠋⠐⠁⢸⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡹⣷⡦⠤⣤⣾⠏⣡⠈⡅⣧⠀⣀⣿⠿⠿⠀⣼⣿⣿⠛⡸⣿⢇⡌⠁⠐⠀⠁⠀⠞⣠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣭⠈⢻⣗⡩⢎⠠⣃⠐⢆⣧⡶⠟⠁⠀⠀⢹⣿⣿⠇⠈⣰⣿⠀⣰⠃⡀⠈⠀⡤⣱⡿⣟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠾⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢸⡿⠃⠁⠀⣸⡟⣰⢇⣜⡴⡈⣰⡾⡋⠈⠠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣿⣇⢿⣾⣿⣿⠾⠋⠀⠐⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡐⠀⠀⠜⣹⣿⣹⣿⡿⠋⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠒⣌⠀⢼⣿⣿⣿⠅⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⡟⢀⠈⠃⢿⢻⣧⢀⡋⠀⡠⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠻⡨⢄⣂⡀⣽⣿⣮⡃⣘⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡩⢛⣦⠣⠌⠻⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡉⢳⣦⣙⠲⠶⠿⢿⡿⣿⣿⡿⣛⡓⣶⣤⣤⣤⣤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣷⣬⣍⣿⣭⣿⠾⠿⠛⠛⠣⢍⠂⢂⠀⠀⡈⠁⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣦⣤⣭⣝⣛⡄⠀⠈⠺⣔⠡⢄⣸⣇⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠯⠻⠍⠉⡻⢷⡀⣶⢙⢰⣮⣿⢏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠞⢀⡎⠠⣡⣾⢅⣛⡾⣾⡿⢋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠇⣈⣧⢾⢏⣥⣾⣿⡿⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣾⣿⣯⣷⣾⣿⡿⣟⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⡿⢿⢛⣿⣾⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠋⣑⣬⡷⢟⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣁⣴⣿⡿⢋⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡹⢋⠋⢠⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⣄⣀⣆⡻⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠃
⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠩⡉⠁⠤⠄⠀⠄⠁⠉⠉⠛⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⢀⡀⠀⠀⢀⠀⠉⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠡⠀⡀⡀⢀⠀⢀⠀⠀⠀⠠⠀⠤⠤⣀⣥⣂⣤⡑⣬⣌⢂⢈⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⡐⠐⠀⠀⠀⠡⠈⠀⠀⢀⠬⣷⡶⠿⠟⠛⠛⠛⠻⠿⣿⣿⣧⢞⡀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⡆⢡⢀⠀⠀⠀⠠⠀⠀⠐⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡇⡇⢸⠘⠀⠀⠀⠀⠀⠀⣬⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣸⢁⠁⠂⠆⠀⠀⠀⠀⠈⠔⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⡼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢡⢆⠀⠀⠊⢀⠀⠂⠀⢬⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢣⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠡⠊⠀⠀⢀⠀⠀⠐⢄⠪⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠈⠇⣿⠟⠷⣦⣤⣤⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠸⣆⠀⠘⠡⠉⢒⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠊⢀⠀⠀⠢⡀⠀⠀⠁⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣁⠣⠁⢀⣈⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠱⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⢀⠀⠄⠁⠀⠀⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣐⠄⠂⠀⠐⠀⠀⢀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣮⡱⠶⠀⠒⠨⠀⠁⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣟⠛⠠⠄⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠛⠉⠉⠉⠉⠁⠠⠬⠭⠀⢒⣨⡿⠟⠁
⠀⠀⠀⠀⣠⡶⡛⠍⠀⢒⠐⢠⣴⣶⣶⠶⠶⠟⠛⠛⠛⠋⠁
⠀⠀⠀⣸⠏⠈⠐⠀⢐⢦⣿⣿⠟⠉
⠀⠀⠀⣿⠠⠊⠀⠀⠁⢸⣿⠃
⠀⠀⠀⠹⣆⠀⡠⠠⠀⣸⡇
⠀⠀⠀⠀⠈⠳⢦⣁⢀⢿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡥⣀⢤⣍⠑⠤⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣸⣷⡇⠀⠈⠑⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡔⡾⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⠀⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢻⠘⡀⣡⢟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠛⠋⠈⠉⡻⣦⡀⠀⠀⠀⣰⠁⠸⣔⢍⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢴⣿⣆⠈⠘⠃⠀⠀⠀⢡⠀⠃⢛⣻⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠀⢸⣿⡆⠰⣄⣂⣤⠄⠢⠃⠈⠀⢧⢃⢷⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⢄⡻⣿⡦⢿⣿⠄⡌⡋⠁⠀⠈⠀⠀⠀⢺⡎⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠻⢿⠀⠀⢹⣆⠀⠀⠀⠈⠀⢀⠂⠀⣸⡇⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡘⣇⠀⠸⣿⡳⢄⠠⠀⠈⠁⠀⠀⢾⡇⢠⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣾⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⣾⠃⠠⣸⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣦⣀⢄⢀⣤⣀⠀⠀⠀⢀⣾⣇⠈⢿⡄⠀⠙⢦⣀⠀⠀⠀⠀⠟⢃⣤⡿⠃
⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠈⠙⢿⢿⣿⣿⠿⡋⢸⡇⣧⠈⢇⠀⠀⠀⠉⠛⠲⠤⠶⠿⠛⠉
⠀⠀⠀⠀⠀⠐⠇⠐⠀⠀⠀⠈⠓⠟⢝⣷⣄⠐⠹⢠⡏⠀⡚
⠀⠀⠀⠀⠀⠀⢆⠀⢀⣌⠛⠶⣤⡘⢢⡙⠋⣯⣴⠞⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠱⣿⡆⠂⠀⠉⠙⠛⠒⠬⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢀⢄⡜
⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⢄⠀⠀⣀⠴⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠦⣄⠀⠀⡠⠤⠤⡀
⠀⠀⣠⠄⠠⠤⣀⠀⢸⢸⣉⣮⠀⡴⠁⡖⣭⠉⡆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢰⠉⣭⠳⡈⢣⠀⣥⣋⡁⡷⠀⣀⠤⠄⠠⢄
⠀⢸⠁⠐⠛⣍⠢⡕⢌⢆⠀⢁⠀⡇⠘⡀⠀⣬⠤⠚⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠑⠤⣥⠀⠀⡇⢸⠀⢈⠁⡰⡣⢊⠕⢩⠛⠒⠀⡇
⠀⠈⠣⠄⠠⢎⡤⠤⠬⢤⣑⢌⣢⡹⣄⠑⠤⠄⠀⠬⠬⠤⠬⠌⣉⠲⢄⠀⠀⠀⡠⠔⣊⡩⠥⠤⠬⠥⠀⠠⠤⠊⣠⢎⣴⡣⣊⡤⠥⠤⠤⣐⠄⠠⠔⠁
⠀⠀⠀⢀⡜⢁⠴⠒⠒⠢⢌⡑⠮⣑⡈⠙⠒⠒⡒⠒⠚⠛⠑⠒⠦⣍⠢⡑⠀⢊⠔⣫⠤⠒⠚⠛⠑⠒⢒⡒⠒⠊⢁⣊⠭⢊⡡⠄⠒⠒⠢⡈⢳⡀
⠀⠀⠀⢸⠀⡇⠠⠒⠛⠓⢦⠈⣒⠢⠭⠭⢉⡩⠖⢒⣊⣉⣓⠒⠤⣀⠑⣌⠀⣡⠎⣁⠤⠒⣚⣋⣑⡒⠲⢭⡉⠭⠭⠤⣒⠉⡠⠒⠛⠒⠄⢸⡄⡇
⠀⠀⠀⠘⡄⠣⡀⠀⠈⡃⠈⡇⢀⡩⠭⢡⠋⡴⠊⣁⠠⠶⠤⠬⣑⢬⡑⠌⠂⠁⠞⡥⣒⠭⠴⠦⠦⣀⠙⢢⡙⣎⠭⠭⡁⢸⡁⢰⠁⠀⢀⡜⢠⠇
⠀⠀⠀⠀⠈⠢⢌⣉⣉⡠⠞⢰⠃⠤⡄⣏⢸⠀⡭⡀⡙⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠋⢀⠭⠀⡇⢸⢀⠤⠈⡆⠳⢤⣉⣉⡡⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⢦⣛⠝⡘⢌⡓⠭⠜⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠳⠭⢔⡡⢇⠻⣛⡤⣣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠘⠒⠤⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠛⠶⢤⣤⣀⣀⡀⠀⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠶⠖⢋⣽⣿⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠷⣤⣄⡀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⠁⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣜
⠀⠀⠀⠀⠀⠀⠀⢀⠚⠉⡟⠀⠀⠀⠀⠀⣠⣴⡟⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣴⠋⣼⠀⠀⠙⠉⠙⠂⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣆⠀⣼⠃⠐⣯⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠀⠀⠀⠀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣠⣶⠶⠋⠁
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⣐⣯⠿⠋⠀⠀⠀⠀⠀⠉⠲⣦⣄⣀⠀⠀⠀⠀⢹⣇⡞⠋
⠀⠀⠀⠁⣠⠎⠁⠀⢠⣾⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣿
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠈⠀⠀⠀⡁
⠀⠀⠀⠀⠈⠑⣦⣀⡴⠖⠂⠀⠀⠀⠒⠲⣤⣀⠀⠀⠀⠀⠀⢀⡤⠂⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⢀⣀⣬⡽⠿⠛⠛⠛⠛⠛⠛⠒⠚⠛⠉
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠣⡀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⡖⢫⣭⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡸⠁⢰⡟⠺⢋⣳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣴⠃⣰⠟⢠⡞⠉⠛⠇⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣾⢧⣰⣇⣴⠋⠀⣀⣆⣴⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣶⣽⣿⣿⣧⣻⣟⣻⣍⣷⣶⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣧⣇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⡒⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣾⡭⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⢀⣠⣴⡾⠟⠛⠛⠛⠛⠻⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣦⣀⣠⠤⠶⠚⠛⠛⠛⠛⠶⢦⣄⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⢾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⡀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡛⢅⠀⠀⠀⠀⠀⠀⢀⣴⠀⢀⠀⡌⠻⡿⣿⣷⣄⠀⠀⣀⣤⣬⣶⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠠⠴⣿⣿⢖⡠⠀⠀⠀⠀⠀⠉⠓⠄⠀⠹⢿⣿⣿⣧⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠨⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⣀⣠⣄⡂⢀⣤⣺⣗⡀⠀⢙⣿⡭⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⢛⠿⣿⣏⣉⣃⣀⡀⠠⠈⠻⢿⠛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣭⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡟⠀⢀⡼⠋⠉⠉⠉⠉⠉⠛⠛⠛⠲⠷⠾⢶⣶⣶⣶⣶⡶⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠈⢡⠾⠍⣉⡛⠛⠶⠶⢶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⡆⠀⡀⠉⠉⠰⠢⠀⠀⠀⠉⠙⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣾⠃⢠⡏⠀⡤⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⡏⠀⣾⠁⢸⠇⠀⢰⣿⣄⣀⣰⠆⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⣻⣿⣷⣤⣿⡀⠀⠘⣹⡟⢻⠋⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠙⠛⣿⡋⠀⠈⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠈⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣿⠃
⠀⠀⠀⠀⠀⢸⡏⠀⠈⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣶⣶⡾⠿⠛⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣤⣤⣤⣤⣤⣶⣾⡿⠟⠛⠋⠉⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣲⣶⡄⠀⠀⠀⠀⣀⣠⠴⢶⣲⠶⠶⢶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣯⣾⠛⠉⠀⣀⣠⣶⡫⠵⣒⠿⠿⠒⢚⣋⣩⠵⣒⡫⠭⠑⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⢿⡻⠿⠿⢟⣫⠵⠒⣋⠥⢖⣛⡭⢭⣶⡾⠭⠴⢶⣶⣤⣤⣈⡉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢏⢧⡙⠒⣚⣩⠴⢒⣫⠵⠚⣩⢔⣫⠭⢖⣒⡿⠿⠿⢿⣛⠫⢝⡻⣗⠾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣗⠮⠭⠵⢒⣻⠟⢁⡤⢊⣱⣯⡤⠶⠛⠲⢾⣋⣉⠲⣌⠳⡄⠙⢮⢳⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣯⠴⠾⠷⠖⠋⠁⠀⠀⠀⠀⠀⠘⢷⡈⢳⡘⡆⠘⡆⠀⣧⢣⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢧⢳⠀⡇⠀⣿⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⣀⡴⢻⠀⢸⢸⢠⡇⣰⠃⣯⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢖⡿⢛⣻⣿⣿⣛⣲⣶⡶⠿⠭⠛⣉⣀⡭⠟⠉⢉⣉⡴⣋⡴⢃⡞⡼⢰⠃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣰⢋⢞⣿⡿⠋⣉⡭⢔⡶⠞⣛⣫⣭⠽⢖⣲⡾⠿⠭⣒⣫⠥⣒⡩⢞⣡⣏⢜⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠇⡸⢡⠏⣾⡏⢠⠞⢁⡴⢋⡴⣫⢟⡭⢒⣫⣭⣤⣶⣖⣫⣵⣚⡭⠗⣋⣥⣾⡵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡁⣼⠀⡇⢸⠀⠟⡇⢸⠀⢸⢠⠏⡜⢡⠋⣴⠋⡸⠙⣧⡀⠈⠉⠙⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣹⠀⢹⡘⡆⣇⢇⠸⡄⢸⢸⡀⢧⣏⢰⡿⡀⢧⠀⡏⠹⣗⢶⣶⡶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⡀⣇⠹⡘⣎⢦⡱⣌⣇⢧⠘⡿⣌⢧⠱⡜⣆⠘⢆⠈⠳⣷⡙⡄⢧⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣤⣽⣼⠶⠛⠉⠉⠻⢦⣹⡈⠳⣷⣹⡈⢦⡀⠳⡄⠹⡽⡜⡌⢇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣼⡇⠳⡄⢹⡄⢷⠀⣧⣇⠸⣾⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⢀⡇⢠⡇⢸⠀⢸⢸⠀⠏⢳⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠞⢀⡞⣀⠞⢀⠏⡸⢠⠆⡼⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣡⣶⣿⡭⠴⣚⡥⢞⡵⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢞⡭⢖⣿⣿⣏⣡⣖⡭⠴⠾⠷⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⡔⢡⠋⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⢧⠸⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠥⠞⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢠⠀⠀⠀⠀⢀⠠⡜⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢼⢷⣤⡀⠀⡞⢰⠇⠋⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠂⢀⠞⠉⠀⣰⠁⢨⠀⡃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠠⢀⣶⠊⠀⠀⠀⠈⠻⠩
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⣠⡴⢻⡟⡄
⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠰⠉⠀⢰⣾⡇⡆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⢀⡴⠃⢀⡤⢨⡿⡑⡠⠊⠁⠀⠀⠀⠉⠢⣤⠂⠉⠀⠀⠈⠁⠐⠠⡀
⠀⠀⠀⠀⠀⣼⢤⣀⠀⠀⢠⠞⣱⣿⡾⠁⡍⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⢠⠉⠀⠀⢘⣆⠭⢛⣡⠋⢀⡤⢧⡀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣦
⠀⠀⠀⠀⠘⢷⣄⡈⠉⠒⠛⣫⣴⠖⢋⣀⣈⡛⢿⣿⣿⣿⡿⢿⣛⣉⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⣤⣭⡭⠶⠛⠉⠁⠀⠀⠀⠉⠁⠛⠒⠒⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢟⠿⣥⣄⣀⣀⣠⣤⣴⣶⣶⣿⣿⣶⣶⣶⣦⣶⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠛⠿⢛⣿⠿⠿⠟⣛⣛⠻⠿⣿⣿⡿⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠈⠑⠦⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂

⠀⢀⠀⡤⣰⢆⡴⣀⡀⠀⠀⠀⠀⠀⣀⢰⡆⣴⢂⡴⢀⡀⠀⠀⠀⠀⢀⣰⡦⡳⡞⡶⣦⡄⠀⠀⠀⠀⠀⢀⣴⡆⣶⡶⣠⣦⡀⠀⠀⠀⠀⠀⡀⢤⡄⢶⡄⢀
⢠⡸⣇⣇⣯⣯⣞⡭⠶⠦⠀⠀⠀⢶⡹⡌⠇⢧⢏⢖⣫⣥⡄⠀⠀⣰⣾⡒⠝⠘⠈⠀⢃⢏⢧⡄⠀⠀⣼⣦⣛⢷⣝⣇⣿⢫⣶⣦⠀⠀⢠⣌⢿⣼⠱⠫⢴⣛⣣
⢦⣛⢼⣾⠕⣁⣓⣿⠭⣝⡃⠀⠚⠦⣝⡪⠊⠈⠉⢍⣒⡲⠶⠀⠠⣟⡢⠆⠀⠀⠀⠀⠀⠩⣪⣖⠀⢰⣬⣭⣽⡟⠈⠉⢫⣟⣥⣶⡄⠀⣭⣙⢞⠀⠀⠀⠀⡻⣭
⠲⠯⠽⣗⣦⣠⣾⡿⡝⣮⠃⠀⢙⣛⣛⡬⡀⣤⢰⢏⠪⣝⠷⠀⠐⣻⣪⢄⠀⠀⠀⠀⠀⣚⣲⡏⠀⠈⣉⣭⡾⣵⣤⣔⡾⢯⣭⣍⠁⠀⢡⣭⣧⡀⠀⠀⣀⡞⣦
⠈⠛⣯⡵⣫⢏⡏⣷⠻⠈⠀⠀⠈⠩⡶⢚⡼⣹⢹⡎⣧⠙⠀⠀⠀⠉⠧⣧⡇⡆⡠⡐⢵⣲⠛⠀⠀⠀⠙⢋⣴⡿⢹⣮⢻⣷⡙⠋⠀⠀⠈⠰⡞⣫⡵⣱⡇⠿⠎
⣀⣀⣀⣘⣁⣚⣁⣁⣀⣀⣀⣀⣀⣀⣀⣉⣐⣛⣘⣃⣀⣀⣀⣀⣀⣀⣀⣁⣛⣱⣟⣎⣙⣀⣀⣀⣀⣀⣀⣀⣉⣁⣛⣛⣈⣉⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣉⣀⣀
⣿⣿⡟⠉⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠒⠶⢦⡀
⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠁⠀⠀⠀⠀⡀⠈⣧
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠠⡀⠀⡄⢰⢠⡟
⠀⠀⠀⠀⣸⠇⠀⠄⣤⡼⠇⠀⢻⣄⣷⣾⡟⠁
⠀⠀⠀⢠⡏⠀⠀⠀⠀⢙⡖⠒⠚⠛⠯⠞
⠀⠀⠀⣾⠀⠀⠀⠀⠀⡾⡆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠃⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⣀⣠⣤⣤⣀⣀⠀⠀⠀⣠⠴⠛⠉⠉⠉⠀⠉⠙⠷⣦⡴⠞⠋
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣠⠴⠋⠉⠀⠐⠒⠀⠩⠽⠳⢾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣆
⠀⠀⢸⣷⠀⠀⢧⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠘⣗⠃⠀⣿⠀⠀⠀⢀⣠⠋⣿⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⢿⡄⢘⡏⠀⠐⠚⠋⠀⠀⠁⣀⠈⠻⢷⣄⣀⣀⣤⠶⠛⠉⠳⣄⠀⠀⠈
⠀⠀⠀⠈⠳⢾⣄⣀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠓⠒⠒⠛⠛⢆⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢯⣭⣭⣥⣤⣤⣤⣤⡤⠶⠶⠖⠲⠶⠄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠶⠤⠴⠶⣆⠂⠀⠁⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠠⢄⢤⣤⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠉⢛⣳⣄⡀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠈⠉⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤

⠀⠀⠀⠀⡇⠀⠉⠓⠒⠂⠤⠤⠤⢼⣷⣄⣼⠋⠀⠉⠁⠀⣠⠞⠁
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣤⠀⢀⡴⠋⠉⠉⠉⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢙⣲⠖⠚⡛⠉⠉⠉⢻⡆⠀⡿⠀⠀⠀⠀⠀⠀⣐⡬⠦⢤⣸⠃
⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⢇⡴⠓⢦⣤⣤⡤⠖⠋⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⣿⡶⠟⠛⠛⠲⠶⢴⡴⠶⣿⢿⡄⠀⣰⣥⠤⣤⣤⣄⣤⡦⣾⠏
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠠⠀⢠⠖⣹⠁⢀⣼⣧⣿⣯⣀⠀⠀⠀⠀⠠⢔⡾⠃
⠀⠀⠀⠀⠀⠀⠘⣆⣠⣤⡶⠿⠶⠗⠛⣿⣃⣀⠀⠈⠉⠛⢦⡄⢀⣼⠟
⠀⠀⠀⠀⠀⣠⣴⣋⡉⠀⠀⠀⠀⠀⢸⡏⠁⠈⢳⡄⠀⠀⠀⠙⣏
⠀⠀⠀⢠⠾⠛⠉⠉⠛⠷⢄⡀⠀⠀⠀⢳⡀⠠⠘⡇⠀⠀⠀⠀⢸
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡏⠙⠳⣤⣀⣀⡽⣆⠈⢿⡐⠀⠀⠀⠸⠐⢟⠋⠙⠛⢦
⠀⠀⠀⢧⠀⠀⠀⢀⠠⢴⣿⢀⣼⠀⠀⠀⢠⠛⣦⠈⢷⣦⠀⠀⣾⠀⡸⠀⠀⠀⠈⡇
⠀⠀⠀⠈⠳⢤⣤⣵⡿⢟⡵⢟⡏⠀⠀⣠⣏⣠⡿⢧⣇⣏⠳⣧⣹⣏⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠐⣧⣆⣴⣏⣁⣼⠃⠀⠈⠉⠓⠒⢯⡙⠛⠶⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢈⡿⠋⠉⠉⢻⡷⣦⡀⠀⠀⠀⠁⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢸⣇⢀⢀⣴⣶⡇⠀⠙⣦⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢀⡤⠖⠒⠲⠾⢦⣄⠀⠙⢿⣾⣇⠟⠁⠀⠀⠜⣧⠀⢠⡞
⠀⠀⠀⢀⡟⡠⠈⠁⠀⠀⠀⠈⠳⣄⢀⡼⠋⠀⠀⠀⠀⠀⣽⠚⠛⠒⠦⣄
⠀⠀⠀⠈⣿⠟⠳⣄⠀⠀⠀⠀⠀⠘⣾⠑⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣀⣙⣇
⠀⠀⠀⠀⠘⣆⠀⠈⢷⡁⠀⠀⠀⢐⡟⠀⠀⠀⠀⠀⢀⡼⠁⢀⡴⠋⠉⠈⢻
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠙⠦⣄⣀⠀⣷⠀⠀⠀⠀⡰⠋⠀⢠⡏⠀⠀⠀⢀⡏
⠀⠀⠀⠀⢠⡾⠉⠉⠙⢆⡀⠀⠉⠉⠙⣦⠀⠀⡼⠁⠀⠄⣼⠁⠀⠀⣠⠋
⣀⣀⣀⣀⣟⣙⣀⣖⣶⣟⣈⣙⣲⣄⣀⣈⣳⣦⣿⣤⣶⣞⣁⣀⣠⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡾⠋⠐⠚⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠘⢷⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢷⣤⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠵⠒⠒⠢⠴⠊⠉⠉⠙⠒⠻⠄⠀⡀⠀⠸⠖⠊⠉⠁⠐⠦⠔⠒⠒⢼⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⣀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣤⣤⠀⠈⠉⠀⣀⣼⣿⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⣯⣀⠀⠈⠉⠀⣀⣤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠙⣇⢀⡝⠲⠦⣴⣶⡁⠀⢹⣶⣶⠶⠚⢁⢈⡟⠉⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣠⣆⠜⠋⠀⠀⠀⠀⠀⠙⢆⢢⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠸⠶⠀⠀⠀⠀⠀⢾⢆⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⣦⡄⠀⠀⠀⢠⣤⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣩⡀⠀⠀⠀⢀⣁⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢹⣿⣿⣶⣷⣾⣿⣿⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡀⠀⢸⡿⣿⣿⡿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⠃⠘⡏⠀⣿⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠈⠀⠀⡇⠀⠘⠀⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡆⠀⠀⠀⡸⢳⡀⠀⠀⢀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢹⡀⠀⢸⠃⠀⣷⠀⠀⡿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠁⠀⡾⠀⠀⢸⡀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡤⢀⣿⠀⠀⢸⡇⢠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⢸⣧⠀⠀⢸⣿⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⠀⠀⣿⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠸⠀⠀⢹⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣤⠃⠀⠀⠈⢧⡀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⠀⠀⠀⠈⠇

⣿⢿⣿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠁⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠈⠉⠛⠻⢶⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⢀⣠⠴⠚⠉⠀⠀⠘⢦⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢀⡴⠃⠀⠀⠉⠓⠦⣄⡀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⣴⠟⠁⠀⣠⡶⠛⠁⠀⣠⠔⠀⠀⠡⡀⠉⠓⣲⠤⠤⠄⠓⠤⠀⠀⠴⠚⠠⠤⠴⣖⠚⠋⣀⠌⠀⠀⠢⣄⠀⠈⠛⢷⣄⠀⠈⠻⣦
⠀⠀⠀⠀⣼⠃⠀⢀⣼⠏⠀⠀⣴⠟⠁⠀⣀⠄⠀⠈⠑⠂⠬⠉⠙⠓⠲⡄⠢⡔⣠⠖⠚⠋⠉⠥⠔⠊⠁⠀⠠⣀⠀⠈⠳⣦⡀⠀⠹⣷⡀⠀⠘⣧
⠀⠀⠀⢸⠃⠀⢠⡿⠁⠀⢠⣾⠃⠀⢠⡾⠁⢠⡴⠋⢀⠔⢀⠄⣀⠀⠐⢃⡀⢀⡘⠂⠀⣀⠠⡀⠢⡀⠙⢦⡄⠈⢳⡄⠀⠘⣷⡄⠀⠘⢿⡄⠀⠘⡇
⠀⠀⠀⠈⠀⢀⣿⠁⠀⢠⣿⠁⠀⢠⡟⠀⢰⠏⠀⢰⠋⢰⠏⡼⢡⠀⢂⠃⠀⠀⠘⡐⠀⡌⢧⠹⡆⠙⡆⠀⠹⣆⠀⢻⡄⠀⠈⣿⡄⠀⠈⢿⡀⠀⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠇⠀⠀⣿⠀⠀⣿⠀⠀⠸⠀⠘⠀⠃⠈⠈⠈⠂⡀⢀⠐⠁⠁⠁⠘⠀⠃⠀⠇⠀⠀⢿⠀⠀⣿⠀⠀⠸⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⠃⠀⠀⣿⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠸⡅⢨⠇⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢸⠀⠀⠀⣿⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⡔⠀⢧⡼⠀⢢⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣠⡟⢀⡄⠘⠃⢠⡀⠻⣄⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣾⠁⡄⢠⠈⣷⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⠃⢸⠃⠸⡇⠘⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⣿⠀⠀⣿⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡿

⠀⠀⠀⠀⠀⠀⣀⡈⣁⡀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠤⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⠿⠟⠊⠀⠀⠀⠀⠀⠀⢸⣦⡄⠀⠀⠁⠀⠀⠀⠀⠈⠙⠲⠦⠟⠳⣶
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣄⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡜⠀⠘⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀
⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⢞⠁⠀⠀⠀⠀⠦⠀⠀⡏⠀⠒⠉⠀⠀⠀⠀⡀⠀⠀⠀⠠⢤⣼⡆⢀⣴
⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⢈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⣀⡀⠀⠀⠉⠻⣿⣿⣧
⠀⠀⢛⣆⢀⣀⣀⣤⣤⣴⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣾⣿⣿⠿⠟⠛⠁
⠀⠀⠉⠛⠛⠛⠛⠋⠉⠉⠉⠈⣎⢿⣷⣄⠀⠀⠀⠀⢀⣀⣀⣤⢾⠛⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡽⢿⣿⣿⡿⠆⠸⢽⣿⣿⠿⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⣌⡳⣦⣄⠀⠀⠈⣠⣤⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡙⠃⠀⠴⣒⡲⣦⣤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⠧⠀⠈⠉⠉⠛⠿⡋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠂⠀⠀⠶⣾⣿⣷⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠀⠀⠀⠈⠉⠉⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⡀
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠸⣷⠀⡇⠀⠀⠀⠀⠀⢀⡤⠶⠾⢿⣟⠿⣿⡷⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣄⡆⣠⠴⠒⠲⣄
⠀⠀⠀⠈⠉⠉⠉⠛⡿⡲⣖⠒⠋⢰⣞⢲⡄⠀⠈⠁⠀⠀⢠⠀⢄⢳⡌⢻⡌⢻⣷⠀⠀⣀⣀⣤⣾⣿⣿⠯⠶⠚⠛⠛⡻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡟⣸⠈⠑⠦⣬⣿⠞⠁⠀⠀⠀⠀⠀⠳⣄⣋⡼⠃⣼⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠁⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠤⠒⣚⣯⣭⣭⡭⣟⠻⢿⣦⡀⠀⠀⣠⠖⣋⡭⢽⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠔⠐⣦⡀⣇⣘⣣⡤⣖⣚⣛⣒⢦
⠀⠀⠀⠀⢠⡾⢋⡭⠒⡀⠉⠊⢧⠀⣿⣿⠀⠐⣇⡜⢡⠖⠉⢉⠛⠭⣓⠤⣀⣀⡤⠀⠈⢦⣀⣉⣁⡠⢴⣺⡿⠟⠋⠉⠉⠋⠃
⠀⠀⠀⠀⠉⠀⣾⠁⢸⡀⠀⢀⠞⠠⣿⠿⠀⠀⠈⠑⠸⣄⣀⡼⠂⠀⠀⠁⠀⠀⠀⠀⠐⠿⣷⣾⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠨⠉⠉⠲⠤⣀⣀⠤⠒⠉⢉⡵⠀⠀⢠⣿⡽⠿⠶⣯⣿⣄⣠⢰⠏⠀⣀⠀⠀⢸⡀⠚⠂⠀⠀⢀⣠⣤⡤⣤⣤⡀
⠀⠀⡴⠒⠁⠀⣀⠶⠒⠏⣈⠉⠉⠉⠠⣦⠀⠀⠸⣟⠀⠀⠀⠀⠙⣿⣿⣜⢆⠀⠀⣹⠀⠀⣙⠒⣲⣶⠶⣟⣛⣻⣿⣿⣟⠿⣆
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠐⠂⠂⠀⠀⠀⠙⠲⠤⠔⠁⠀⠀⠉⠛⠳⠶⠚⠁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠈⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠌⠀⠀⠰⡏⣳⠀⠀⠾⡏⣿⣼⠀⢀⣖⣻⣿⣶⣦⣄⣤⠶⣠⠄⣀⢠⣄⠀⠀⢞⣩⣭⣉⡻⣦⣀⢀⣠⡾⣣⡾⣠⡶
⠀⠀⠀⠀⠘⢆⣀⣀⡹⢧⣀⣀⣠⡼⣻⠟⠀⠘⣿⠁⠀⠉⠛⠻⠿⣿⣶⣿⣿⡾⠟⠀⠀⠿⠁⠀⠈⠙⢮⣛⢷⣴⣛⣯⣶⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠋⠁⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠒⠤⣀⠀⠀⠀⠀⣀⡤⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⣀⠀⠀⠀⠀⣀⠤⠒⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢢⠀⠀⡼⠃⠀⠀⢠⣬⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⡄⠀⠀⠘⢧⠀⠀⡴⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡇⠀⢀⣤⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⡀⠀⢸⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢧⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⡼⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠙⠢⣜⡌⢳⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡼⢡⢣⠔⠋⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠰⡿⢷⡀⠈⠺⣦⣍⡳⢿⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⡿⣞⣩⣴⡗⠁⢀⡾⢿⠆⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣀⡼⠃⠘⠛⣿⣿⣿⡿⢛⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⢿⣿⣿⣿⠛⠃⠘⢧⣀⣀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠵⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⠦⠉⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⠿⢿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡿⢿⣶⣷⣤
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣄⠀⠀⣼⣿⠵⠶⣦⡀⠀⠙⣦⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣴⠋⠁⢀⣴⠶⠮⣿⣧⠀⠀⣠⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢾⡶⠀⠀⠙⢧⣰⡟⠁⠀⠀⠛⠃⠀⠀⢸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⠈⠛⠀⠀⠈⢻⣇⡼⠋⠀⠀⢶⡿
⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⢻⡅⡴⠻⠂⠀⠀⣶⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣶⠀⠀⠐⠟⢦⢨⡟⠀⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⡴⠉⠀⠀⢀⣀⣉⣓⣤⡀⠀⢳⡇⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⢸⡞⠀⢀⣤⣚⣉⣁⡀⠀⠀⠉⢢
⠀⠀⢧⣰⣶⠐⣧⠀⠀⠀⠉⠛⠲⣄⠹⣄⠀⠀⠀⢯⡀⠀⢰⠆⠀⣠⠖⣶⠄⠀⠀⠠⣶⠲⣄⠀⠠⡆⠀⢀⡽⠀⠀⠀⣠⠏⣠⠶⠛⠉⠀⠀⠀⣼⠂⣶⣆⡼
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠰⠇⠈⠉⠙⠛⠮⣕⢦⣀⠀⠙⠢⣌⣦⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣴⣣⠔⠋⠀⣀⡴⣊⠵⠛⠃⠉⠁⠸⠆⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣒⣿⣾⣷⣦⣍⣉⠙⠛⠾⣦⡀⠀⠀⠀⠀⢀⣴⠷⠛⠉⣉⣩⣴⣾⣿⣿⣒⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠀⠀⠀⠉⣉⣓⣲⢬⣙⢦⡀⢀⡴⣋⣥⣔⣊⣉⠉⠀⠀⠀⠀⠀⠈⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣤⠀⠀⠀⠀⠀⠀⣾⡉⠀⠉⠙⠿⣧⣧⣼⣼⡿⠋⠉⠀⢉⣳⠀⠀⠀⠀⠀⠀⣤⣄⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⠃⠘⠏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⡀⠁⠀⠀⡀⢀⠈⠙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠂⣠⠀⣿⠉⠲⠟⠒⠊⠀⠈⡺⠖⠤⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠌⢹⠀⠞⠃⠀⠻⡀⠀⡀⠀⠀⠀⠀⢠⠀⢀⣼⡀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⡠⠒⡄⠀⡀⠆⢸⠀⠘⢀⠀⠅⠀⠀⠈⠙⠀⠀⠢⠀⠀⢁⡥⠌⠉⠣⠰⡂⠄⠀⢢
⠀⠀⠀⠀⠊⠀⠀⢖⡺⢽⣧⠘⠧⣀⢼⢧⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢒⠞⠁⠘⠁⠀⢀⡀
⠀⠀⠀⠀⠀⢠⠖⠀⠈⢀⠌⠀⠀⠀⠀⠁⢈⡭⠆⠀⢄⠀⠀⠀⠀⠀⢀⣰⠊⠀⣀⣀⠀⠁⠈⠈⠂⠀⠤⢠⣄
⠀⠀⠐⣀⡠⠎⠉⢢⢠⠎⠀⢴⡄⠀⢀⡔⠁⠀⠀⠃⠀⠀⠀⠀⠐⠋⠁⠓⠖⠀⠄⠉⠂⠄⠀⠀⠀⢠⠀⠀⢹⡑⡀
⠀⠐⠙⠉⠀⠀⠀⠈⠀⠀⠀⠈⠤⠴⠟⠀⣆⠲⣦⠁⠀⠀⠀⠀⠠⠀⠀⠀⣄⠀⠀⠀⠀⡀⠀⠀⠠⠋⠀⢀⠀⠁⡀
⠀⠀⠠⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⣄⠀⠀⠀⣰⡀⢠⠀⠀⠈⢣⡀⠀⢱⠀⠀⠀⢀⠀⢄⠃⡠
⠀⠂⠀⠀⠀⠂⠑⠀⠄⠁⠠⠒⠀⠀⢤⠖⠀⠂⠀⣾⠇⠀⢰⢏⡵⠃⢠⠀⠀⠀⠝⠓⠎⠀⠀⠂⠈⠀⠀⠀⠀⡠⠔
⠀⣆⠀⡄⠀⠀⡇⠀⠀⡄⠀⠀⠰⠀⢀⢰⠒⠆⡰⠃⠀⠀⢀⡝⠁⠀⠀⠀⡀⠡⠀⢠⣶⠀⠀⠀⠀⡀⢠⡟⡋
⠀⣨⠂⠉⠄⠀⢱⢤⣀⢻⡦⠴⠤⠀⠘⠄⠟⠉⠀⠀⠀⠀⠘⢄⡀⠀⢠⠀⠀⠀⠀⠈⢷⡀⠀⢀⣴⠃
⠀⢏⠀⠀⢀⠀⢺⠓⠬⠍⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⡏⠘⠀⢀
⠀⠀⠠⠀⠘⣇⢘⣇⡀⣀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠠⠀⠁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁


⠀⠄
⠀⠄
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡉⠉⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢁⡞⠀⡘⠀⡄⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠾⢧⣸⣁⡐⠁⡄⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠛⠓⢶⡟⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣶⠀⠀⣀⠀⠀⠀⢹⡄⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣿⠀⢠⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢚⡛⠛⠛⠷⣶⣤⣀⠈⠳⡄⠀⠁⠀⠀⠀⠈⠀⠠⠊⠀⣿⠀⠀⠀⠀⠀⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⢤⡉⠻⣷⣄⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠘⢆⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠛⠉⠁⠀⠀⠀⠈⠉⠻⣦⣘⣿⠀⠀⠀⠀⠀⠀⠸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣄⡀⠀⠀⠀⠀⠀⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣦⣄⣀⣀⣀⣀⣤⡴⠚⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠂⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠈⠉⠉⠉⠉⠉⠀⠴⠶⠶⠶⠶⠞⠛⠋⠉⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠏⠙⠻⢷⣶⣤⣤⣀⣀⣠⣤⣴⣶⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢠⣰⣹⡆⠀⠀⠀⠀⠀⠀⢰⣿⠁⠁⠀⠈⠉⣿⡇⠀⠀⠀⠀⠀⠠⡀⡀⡀⡀⠀⣠⡎⢂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⠟⣀⡀⠀⢀⣀⢹⣧⠀⠀⠀⠀⠀⠐⠷⠧⠇⠛⠁⠸⡄⠘⠷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠓⠉⠀⠟⠋⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠩⣽⣄
⠀⠀⠀⠀⠀⠀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠒⡀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠹⡆
⠀⠀⠀⠀⠀⢀⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠁⠄⠉⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⡀⠀⣤⣾⡿⠟⠛⠋⠒⠠⣀⡤⠔⠒⠒⠲⢤⣀⠀⠀⠀⠈⢿⣦⣤⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣸⡃⠀⠀⠚⣇
⠀⠀⣬⣿⣿⣆⠰⣄⠀⠀⠀⠀⠈⢷⡁⠀⠀⠀⠀⠈⠳⣄⡔⠋⠀⠙⠯⠉⡉⢳⣤⣠⠴⠚⠉⠉⠀⠉⠑⠖⠁⠀⠀⠀⠉⠛⠿⣿⣿⡟
⠀⠀⠀⠉⠙⢿⡁⠈⠑⢦⣤⣀⣤⣼⣿⣆⠀⠀⠀⠀⠀⠈⠉⠀⢤⣀⠉⠀⠐⡛⠋⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⢶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⢽⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡏⠻⣷⣄⡀⠀⠀⢀⡀⢀⠀⠀⠀⣀⣴⣿⢟⡟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣧⠀⠀⠿⠿⠿⠟⠛⢷⡈⠛⠻⣿⠛⠛⢃⢿⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡉⠁⠠⠀⠀⠀⠀⠀⢨⠁⠀⠀⢡⠀⠀⢠⠎⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠰⢚⡀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣸⣄⡀⠠⡾⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠉⠉⠉⠡⡄⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀⣀⠀⠀⡀⣀⣀⣠⣃⣠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⡿⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠀⠉⠁⠀⠀⠈
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣄
⣿⣿⣿⣿⣿⡿⢫⣶⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣽⣿⣿⣿⣦
⣿⣿⣿⣿⡟⣴⣿⣿⣿⢏⣽⠿⠟⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡿⢫⣿⠿⠯⠿⣥⡀
⣿⣿⣿⣿⡇⢹⣿⡟⣷⣷⣭⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⠟⠋⠉⠉⠉⠁
⣿⣿⣿⡿⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠁⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠀⣤⣿⡟
⣿⣿⠉⠀⣸⣿⣇⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⣿⣿⣇⡀
⣿⠃⣼⣷⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⡟⠉⠑⢚⣿⣿⣿⣿⣿⣿⣿⠀⢀⣾⣷⣿⣿⣿⣿⠀⠀⠀⣠⣤⣤⣦⣤⣄⡀⠀⠒⣻⣿⣿⣷⣦⡀
⡟⢸⣿⣿⣿⣿⣿⡏⣘⡭⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣽⣻⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣍⣀⡄⢀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⣽⣻⣿⣿⣿⡆
⣷⠘⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⣛⣻⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣤⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷
⣿⣧⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣋⠉⢁⡘⢿⣿⣿⣿⣿⠘⣆⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⠉⣁⡹⣿⣿⣿⡿
⣿⣾⣍⣛⣛⣛⠋⠟⢛⡩⠼⣿⣿⣿⣿⣿⡿⢿⣶⣘⣧⡸⣿⣦⣙⣻⣿⣿⠀⠙⠝⠛⣛⡛⠹⠟⣛⠩⠾⣿⣿⣿⣿⣿⡿⠷⠶⢹⣦⣻⣿⣮⠙⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⡀⠀⠀⠀⢦⣀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⣠⣿⣿⡇⠀⢠⣔⠈⠙⢿⣶⣶⣶⣾⣿⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠴⠞⣿⣿⡿⠀⠀⢀⠛⢿⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣴⠶⠟⠛⠉⠀⠀⠀⠈⠳⣶⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⢺⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠛⠛⠉

⠀⠀⠀⢀⣠⡶⠾⠛⠛⢛⣿⣿⣤⡀⠀⠀⠀⠀⢀⣤⠶⠶⢶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣉⣙⣳⣾⣶⣴⣦⣀
⠀⢀⣴⠟⠁⣠⣶⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠁⠄⢚⣿⠿⠿⠿⣿⣿⣿⣧⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠚⠁⠀⣾⣿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠦⠀⠀⠐⢁⡤⠾⠟⠛⠿⠷⣿⣿⡿⠀⠀⠛⠋⠭⠹⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⢻⠋⠅⢴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⢄⣠⣤⢿⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⣶⣀⠀⣶⣶⡶⢿⣄
⠀⠀⠀⠀⢀⡾⠋⠉⠉⠉⠁⠀⠀⠀⠀⢲⠀⠀⠀⠀⢠⣽⠋⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠀⠀⢻⣆
⠀⠀⠀⣠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡤⠤⠶⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢻⣷
⠀⠀⠀⠀⣼⡇⠀⠀⠀⣀⠀⠀⠀⠀⠲⠂⠀⠁⠀⠰⢆⡿⡏⠀⠰⢄⡀⠀⠐⠤⣄⠀⠀⠠⣤⠀⠀⠀⣿
⠀⠸⠿⢿⡿⣿⣄⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⠃⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣰⠉⢙⠦⢴⣿
⠠⠤⣤⣬⣴⠛⠛⠳⠶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠁⠘⠋⠈⠀⠀⠀⠀⠀⣷⠆⣀⣴⠶⠿⠿⢶⣤⣤⣤⠼
⠀⠀⠀⠀⠉⠛⠲⠶⠶⠾⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠶⠶⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⢀⣀⣀⣠⣾⡀⠀⠀⢀⣠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢐⡂⠀⠉⠀⠙⠋⠀⠀⠉⣓⡫⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⣠⡆⠀⣰⣆⡀⢠⡀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠃⠀⢘⡃⠀⢸⠏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⠀⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢠⣄⠀⠰⠀⠁⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠋⠁⠀⠈⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣤⣇⣢⣼⠀⠀⠀⠀⠀⣰⡟⠛⠛⠉⠙⣷
⠀⠀⠀⠀⠀⡀⣠⠞⠉⠉⠉⠁⠀⠀⠀⠀⠀⢿⠡⣤⠀⣤⡀⢿
⠀⠀⠀⢀⠜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠉⠀⠈⠁⡾
⠀⠀⠀⡞⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⡀⠀⠀⢳⡀⠂⠈⡠⢧
⠀⠀⢸⣇⣀⡤⢿⡿⠋⠀⠀⠈⢻⠁⠀⠈⠳⢤⢾⣿⠶⠖⠁⠈⠓⠒⠢⢄⣀⣀
⠀⠀⠘⢿⣷⣤⣦⣄⠀⠀⠀⢀⣈⣷⡀⠀⠀⠈⠉⠙⠂⠚⠚⠋⠁⢠⣤⡄⠀⠀⠙⣦
⠀⠀⠀⠀⠈⠉⠲⢌⣳⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠰⡄⠀⠀⠰⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣯⠹⣿⣧⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⣿⣿⡏⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⣸⣷⣦⣤⠎⣥⣀⣀⣀⣤⣾⣿⣿⣿⣷⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢀⢉⡈⠀⠠⣄⠉⠉⠁⠀⠈⠉⣩⠋⠈⢹⠟⠋⣡⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⠷⠉⠀⢠⣄⠀⠀⠀⠀⢠⠎⠀⠀⡠⠋⠀⢈⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⣤⡀⢠⣄⡀⠀⠀⡠⢇⣀⠴⢊⣠⣴⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⢷⣄⠀⠀⠈⡀⣠⣾⡁⠀⣠⠴⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣄⣀⣀⣈⣸⣿⣿⣿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⣓⣿⠭⠭⠅⠀⠀⠀⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⢀⡠⠌⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣀⡄⠀⢲⡏⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣁⠒⠋⡠⠔⠚⠉⢳⡀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠉⠀⠀⠀⠀⠀⢇⠀⠀⢈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣀⡀⠀⢹⣴⢿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣄⠀⠀⠀⠈⣷⣤⣤⠀⠴⣾⣭⠄⠀⠀⠀⠤⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢹⣆⣷⡀⠀⢸⡏⠉⠀⠰⠉⠀⠀⠀⡼⠃⢷⠀⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠘⣧⠀⠀⡿⢻⡇⠀⠈⠳⣄⡦⣠⠖⢀⠠⡌⠀⢀⡾⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠹⡆⠹⠀⠀⠁⢸⠁⣰⡆⠀⠘⢧⠸⢭⠉⠀⣀⡴⠋⠀⢀⣀⣀⠄⠀⠘⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣁⣀⣀⣀⡀⠀⠙⢻⡇⠀⠀⠘⣧⣤⣤⠶⠋⠀⢠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣼⠋⠀⠈⠉⠉⠙⣧⠀⣧⠀⣠⠞⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⠏⠀⠀⠀⣶⣛⡰⠋⢳⣿⡴⠋⣠⠂⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⡿⠀⠀⠀⠀⠚⠉⠀⣠⢟⣿⠁⣸⠃⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡴⠡⠞⢻⣌⡇⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠉⢻⡅⠀⠀⠀⠈⣿⣇⠠⣄⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠻⣄⠀⠀⠀⢸⡘⠦⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠈⠓⢦⣄⠘⣧⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⢀⡀⣀⡴⠞⠁⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠋⠀⠀⠀⠁⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣄⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣬⡉⢀⣀⣀⣀⣀⣀⣀⣀⣠⠄⠐⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠈⠀⠂⠀⠈⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⠤⠤⠤⡀⢸⡟⢉⣁⠀⢀⣈⢻⡇⠀⣠⠤⠤⢤⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠉⢀⠀⠀⢀⡀⢳⣷⣼⡇⠐⢊⡇⠩⠎⢙⣷⢠⣷⠃⢀⠀⠀⢀⠈⠙⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⣀⡴⠋⠙⠶⣿⣭⢤⠟⠰⣿⠀⠘⠦⠂⠀⢸⡵⠈⢷⢤⣽⡿⠞⠋⠳⣄⡀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⣀⣤⣾⣏⡀⠀⠀⠀⠀⠈⠉⠀⠀⢹⣼⡀⠙⠁⣄⣾⠀⠀⠀⠉⠀⠀⠀⠀⠀⣈⣿⣶⣄⣀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣄⠉⠉⣉⡀⠀⠀⠙⠳⠿⠟⠉⠛⠳⣦⣀⣼⡟⢻⡷⢾⠟⣿⣀⣠⡴⠚⠋⠉⢙⡷⠚⠁⠀⠀⣈⡉⠉⢁⣼⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣬⣻⣿⣶⣄⣀⣤⣦⡀⠀⠀⠀⠙⢯⡙⢆⠣⠆⠜⡩⠟⠉⠀⠀⠀⢀⣿⣄⣀⣤⣾⣿⣫⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢰⡏⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⣛⠀⠀⠀⣀⢠⣄⡀⠀⢀⣘⣻⠟⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⠁⢠⠉⠉⠉⠉⢩⡴⢊⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠀⠀⠀⣸⣿⠷⠂⠀⠀⠒⣫⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⣠⣴⣾⣿⣿⣷⣦⣤⣠⣾⣵⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡶⣿⣙⣿⣹⡷⢶⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡆⠀⣿⣿⣿⢿⡷⠾⠿⢧⣿⢳⡾⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡄⢀⠼⠃⠀⠙⠇⠀⠀⠀⠀⠀⠈⢿⣟⣷⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⡷⣦⡀⠞⡻⣥⡀⠠⣿⡿⣿⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠇⠀⠀⠉⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠰⠀⠀⠀⠀⠀⢼⣉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡋⠁⠀⠀⢀⡴⣿⡟⢻⣷⢄
⠀⠀⠀⠠⠃⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣶⡾⠋⠀⢸⣰⣷⣟⣿
⠀⠀⠀⣄⠀⠀⢀⠀⠧⠤⠴⠖⠒⠒⠲⠦⣤⡤⢤⡶⠛⠒⣦⣤⣴⣟⠉⠀⠀⠀⠀⠻⣷⣿⠃
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⢆⠀⠀⢳⣼⡿⠿⣷⡄⠀⠀⠀⢀⡿⠙⣦⡀
⠀⠀⠀⠙⠲⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⣼⠀⠀⠀⠈⠁⢀⣤⣹⡄⣠⠴⠋⠀⡼⠁⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⣤⣤⣀⣀⣻⣿⡟⢑⠃⣤⠀⠀⠘⠛⠉⢸⣧⣿⠗⠒⣆⢸⡇⠀⣀⠀⠈⠉⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣠⡟⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠺⢣⠞⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⡟⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡤⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠠⠀⠈⣿⠀⢀⣀⣠⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠐⣼⠛⠿⠯⠷⠶⠬⣁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡄⢻⡀⠀⠀⠀⠀⠀⠀⣼⠃⣦⣤⠶⠶⢶⣭⡒⢄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⠢⡀⠹⡈⡇⠀⠀⠀⠀⠀⢘⡷⠞⠋⠀⠀⠀⠀⠀⠙⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⢀⡈⠢⠙⢣⠀⠀⠀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⢙⣂⣀⡨⠤⠒⠉⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠁⠀⠀⠀⣀⠠⠤⠴⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡊⠀⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂

⣿⣿⡿⠻⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⣉⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠿⠿⠿⠛⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣠⣶⣤⡀⢠⣴⡶⠌⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⡠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠉⠉⠙⡇⠀⠉⠉⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡼⣿⡿⢀⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠐⢧⡴⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⢽⣧⣾⠷⣦⡀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠓⠲⣤⠴⠒⠂⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⣆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀⠉⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡴⠟⠃⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⣿⠈⠙⠋⠀⠀⠀⢈⡏⠉⠓⠦⣄⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠞⠁⠀⠀⠃⠈⠀⠀⠀⠀⢀⣶⣿⣶⣤⠶⠚⠉⠁⠀⠀⠀⠀⣤⣦⣄⡀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠛⠋⠀⠀⠉⠳⣾⡇⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⡀⠀⠀⠀⠀⠀⠀⣤⣿⣟⡇⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣄⣠⣄⣀⣀⣿⣿⣿⣿⣿⣶⣦⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⢀⡼⣯⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣾⢿⣿⣷⡆⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⣼⠏⠈⣿⣿⣿⣶⣤⣀⣀⣀⣠⡴⠃⢙⠳⠷⠶⠴⠶⠟⠋⡝⣿⠁
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠘⢿⠀⠙⠉⠉⠉⠉⠁⢀⡠⠄⡀⠀⢀⡀⠀⠀⢠⢻⡏
⠀⠀⠀⣦⡀⠀⠀⣀⣬⣽⡟⠁⠀⠀⠀⠀⠈⣧⣸⣶⡤⠄⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⢀⠀⡿
⠀⠀⠸⣿⢷⡀⠛⠋⠉⠀⠈⠢⡀⠀⠀⠀⠀⢸⡇⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡇
⠀⠀⠀⠘⠳⣇⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⢸⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠉⢷⣿⠀⠀⠘⠣⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢦⣴⣶⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣤⣶⣤⢤⣤⣤⣤⣀⣠⣤⣤⣤⣤⣶⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣼⣿⣿⠸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣛⣸⣿⣟⣁⣹⣟⣋⣀⣛⣋⣉⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢈⣿⣿⣿⣿⣿⣿⡿⠛⠋⢉⣩⣿⣿⣿⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣼⣿⣿⣿⡿⠟⠉⠀⠀⢠⣿⣿⣿⣏⣩⣽⣿⣍⡻⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡉⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠀⠀⠀⣠⣾⣿⣿⡿⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣦⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⣠⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿⠄⢠⣼⣿⣿⣿⠟⠋⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⣼⣿⣿⡿⠁⠀⠀⠀⠈⠉⠉⠙⠷⣄⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢁⢤⡉⠛⠉⠀⠀⠀⠀⠀⢰⣶⣶⢦⡄⠀⠀⠀⢀⠶⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠈⠀⠀⠠⣾⠶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣹⣿⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⡇⣿⠇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢤⣤⣬⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⣠⠟⠀⠸⣇⣻⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⡌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠣⠀⠶⠞⠃⠀⠀⢠⡾⡟⠀⠀⠀⠀⠀⠈⠙⣷⣦⣄⡀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣯⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡟⣋⣀⣦⣄⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣛⣿⣶⣤⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠈⣟⣹⣷⣿⢿⣟⠙⢷⣄⡀⠀⠀⠀⠀⢀⣿⣹⣿⣷⣾⣿⣶⣿⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⡿⣿⣿⣄⣽⣷⣿⠿⣷⠀⣀⠀⠀⣸⢿⣧⣼⣿⣦⣿⡷⠀⣰⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⢉⡋⠉⠀⠘⠋⠀⢸⣆⣸⣷⣿⣏⠹⣷⣀⣽⣿⣿⠀⣰⣧⠀⢿⡏⢹⡿⠁⣄⣸⠟⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⣿⡿⠿⢷⣶⣿⣶⣿⡿⠟⠛⠯⠙⣷⢿⣿⠋⢙⣿⣠⣿⣨⣧⣼⣦⣾⠀⠀⠙⠁⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⢀⡼⠛⢉⠀⢸⢀⠀⠀⠉⠻⠀⢈⡷⠀⢀⣿⣶⡿⢿⣿⡿⠿⢿⣯⠈⣿⡏⣿⠁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⣸⣧⣴⣿⣶⣿⡿⠿⣷⣶⣿⣷⣾⣿⡷⢿⠛⠋⣅⠀⣿⣧⣤⣼⣿⣶⣼⡿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠃
⠀⠀⠀⠀⠀⣿⡿⠛⡋⠁⣨⣤⣤⣀⣭⣴⣄⣀⣽⣷⣶⣧⣴⣿⡿⠟⠛⡁⠉⢻⡇⢸⣧⣶⣶⡆⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠹⣿⣤⣾⣿⣿⣿⠉⠛⠋⣙⠙⠛⠋⠙⢇⣿⠉⢋⣠⣴⣿⣷⣶⣿⣶⣾⣿⠻⠋⠀⠀⠀⠀⠀⢀⣼⠏⢻⣧
⠀⠀⠀⠀⠀⠀⣿⠟⣿⡟⠉⣠⣶⠶⠻⡿⣿⣿⡿⠿⢿⣿⣶⣿⡿⠋⢹⣧⣄⣽⣀⠸⠟⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⠋⢠⡾⠋⠁⣀⣴⠿⠋⠁⠀⠀⠸⣿⡇⣴⣿⣶⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣠⣞⣹⣧⣼⠃⠸⣿
⠀⠀⠀⠀⠀⢀⣿⠁⢰⣿⠁⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⢻⣿⣯⣾⣿⡾⠟⠁⠀⠀⠀⠀⠀⠀⢀⡼⢻⣿⠟⢿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠸⣿⣧⡾⢃⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣾⣿⣀⣸⣿⡇⢠⡎
⠀⠀⠀⠀⠀⠀⠹⣿⡇⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣩⣁⣹⣟⡛⢿⡿⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠛⠻⠟⠛⠻⣿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⣴⠟

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⣿⡿⢿⠿⡿⢿⡏⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠿⠟⠟⢿⣿⡟⠿⠿⠿⠿⠿⢿
⣿⣶⣷⣶⣶⣶⣷⣾⣿⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿