Can Make Arrays Equal

Given two arrays a and b of length \(n\), determine if it is possible to transform array a into array b by repeatedly performing the following operation:

Select an arbitrary subarray of any length and add \(1\) to every element within that subarray.

In other words, if we define \(d_i = b_i - a_i\) for \(1 \leq i \leq n\), you need to check whether:

• \(d_i \ge 0\) for all \(i\), and
• The sequence \(d_1, d_2, \ldots, d_n\) is non-decreasing, i.e. \(d_i \le d_{i+1}\) for all \(1 \leq i < n\).

If both conditions hold, output YES; otherwise, output NO.

inputFormat

The input consists of three lines:

• The first line contains an integer \(n\) representing the number of elements in each array.
• The second line contains \(n\) space-separated integers, representing the array a.
• The third line contains \(n\) space-separated integers, representing the array b.

outputFormat

Print a single line containing YES if array a can be transformed into array b using the allowed operations; otherwise, print NO.

## sample

5
1 2 3 4 5
2 3 4 5 6

YES

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