H. Hard Cut
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a binary string $s$. You have to cut it into any number of non-intersecting substrings, so that the sum of binary integers denoted by these substrings is a power of 2. Each element of $s$ should be in exactly one substring.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). Description of the test cases follows.

Each test case contains a binary string $s$ ($1 \le |s| \le 10^6$).

It is guaranteed that the sum of $|s|$ over all test cases does not exceed $10^6$.

Output

For each test case output the answer to the problem as follows:

• If the answer does not exist, output $-1$.
• If the answer exists, firstly output an integer $k$ — the number of substrings in the answer. After that output $k$ non-intersecting substrings, for $i$-th substring output two integers $l_i, r_i$ ($1 \le l_i, r_i \le |s|$) — the description of $i$-th substring.

If there are multiple valid solutions, you can output any of them.

Example
Input
4
00000
01101
0111011001011
000111100111110

Output
-1

3
1 3
4 4
5 5

8
1 2
3 3
4 4
5 6
7 7
8 10
11 12
13 13

5
1 5
6 7
8 11
12 14
15 15

Note

In the first test case it is impossible to cut the string into substrings, so that the sum is a power of 2.

In the second test case such cut is valid:

• $011_2 = 3_{10}$,
• $0_2 = 0_{10}$,
• $1_2 = 1_{10}$.
$3 + 0 + 1 = 4$, $4$ is a power of 2.