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Merge sort is one of the classic sorting algorithms. It divides the input
array into two halves, recursively sorts each half, then merges the two sorted
halves.
In this problem merge sort is used to sort an array of integers in ascending
order. The exact behavior is given by the following pseudo-code:
function merge_sort(arr):
n = arr.length()
if n <= 1:
return arr
// arr is indexed 0 through n-1, inclusive
mid = floor(n/2)
first_half = merge_sort(arr[0..mid-1])
second_half = merge_sort(arr[mid..n-1])
return merge(first_half, second_half)
function merge(arr1, arr2):
result = []
while arr1.length() > 0 and arr2.length() > 0:
if arr1[0] < arr2[0]:
print '1' // for debugging
result.append(arr1[0])
arr1.remove_first()
else:
print '2' // for debugging
result.append(arr2[0])
arr2.remove_first()
result.append(arr1)
result.append(arr2)
return result
A very important permutation of the integers 1 through **N** was lost to a
hard drive failure. Luckily, that sequence had been sorted by the above
algorithm and the debug sequence of 1s and 2s was recorded on a different
disk. You will be given the length **N** of the original sequence, and the
debug sequence. Recover the original sequence of integers.
### Input
The first line of the input file contains an integer **T**. This is followed
by **T** test cases, each of which has two lines. The first line of each test
case contains the length of the original sequence, **N**. The second line
contains a string of 1s and 2s, the debug sequence produced by merge sort
while sorting the original sequence. Lines are separated using Unix-style
("\n") line endings.
### Output
To avoid having to upload the entire original sequence, output an integer
checksum of the original sequence, calculated by the following algorithm:
function checksum(arr):
result = 1
for i=0 to arr.length()-1:
result = (31 * result + arr[i]) mod 1000003
return result
### Constraints
5 ≤ **T** ≤ 20
2 ≤ N ≤ 10,000
### Examples
In the first example, N is 2 and the debug sequence is `1`. The original
sequence was 1 2 or 2 1. The debug sequence tells us that the first number was
smaller than the second so we know the sequence was 1 2. The checksum is 994.
In the second example, N is 2 and the debug sequence is `2`. This time the
original sequence is 2 1.
In the third example, N is 4 and the debug sequence is `12212`. The original
sequence is 2 4 3 1.
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