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class Solution {
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  public int maxSizeSlices(int[] slices) {
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    int n = slices.length;
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    return Math.max(helper(slices, n / 3, 0, n - 2), helper(slices, n / 3, 1, n - 1));
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  }
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  private int helper(int[] slices, int rounds, int start, int end) {
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    int n = end - start + 1, max = 0;
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    int[][][] dp = new int[n][rounds + 1][2];
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    dp[0][1][1] = slices[start];
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    for (int i = start + 1; i <= end; i++) {
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      int x = i - start;
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      for (int j = 1; j <= rounds; j++) {
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        dp[x][j][0] = Math.max(dp[x - 1][j][0], dp[x - 1][j][1]);
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        dp[x][j][1] = dp[x - 1][j - 1][0] + slices[i];
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        if (j == rounds) {
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          max = Math.max(max, Math.max(dp[x][j][0], dp[x][j][1]));
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        }
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      }
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    }
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    return max;
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  }
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}