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U.S. stocks meandered but finished mostly higher Tuesday as retailers and industrial companies rose, and a jump in metals prices helped mining and materials companies. Asian markets jumped after the North Korean government said it was open to talks with the U.S. about ending its nuclear program.

On Tuesday:

The Standard & Poor’s 500 index gained 7.18 points, or 0.3 percent, to 2,728.12.

The Dow Jones industrial average added 9.36 points to 24,884.12.

The Nasdaq composite advanced 41.30 points, or 0.6 percent, to 7,372.01.

The Russell 2000 index of smaller-company stocks surged 16.16 points, or 1 percent, to 1,562.20.

For the week:

The S&P 500 is up 36.87 points, or 1.4 percent.

The Dow is up 346.06 points, or 1.4 percent.

The Nasdaq is up 114.14 points, or 1.6 percent.

The Russell 2000 is up 29.03 points, or 1.9 percent.

For the year:

The S&P 500 is up 54.51 points, or 2 percent.

The Dow is up 164.90 points, or 0.7 percent.

The Nasdaq is up 468.62 points, or 6.8 percent.

The Russell 2000 is up 26.69 points, or 1.7 percent.