Set

You are given two sets of integers: A and B. You need to output the sum of elements in the set C = \{x | x = a ⊕ b, a ∈ A, b ∈ B} modulo 998244353, where ⊕ denotes the bitwise XOR operation. Each number should be counted only once.

For example, if A = {2, 3} and B = {2, 3} you should count integer 1 only once, despite the fact that you can get it as 3 ⊕ 2 and as 2 ⊕ 3. So the answer for this case is equal to 1 + 0 = 1.

Let's call a segment [l; r] a set of integers \{l, l+1, ..., r}.

The set A is given as a union of n_A segments, the set B is given as a union of n_B segments.

Input

The first line contains a single integer n_A (1 ≤ n_A ≤ 100).

The i-th of the next n_A lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ 10^{18}), describing a segment of values of set A.

The next line contains a single integer n_B (1 ≤ n_B ≤ 100).

The i-th of the next n_B lines contains two integers l_j and r_j (1 ≤ l_j ≤ r_j ≤ 10^{18}), describing a segment of values of set B.

Note that segments in both sets may intersect.

Output

Print one integer — the sum of all elements in set C = \{x | x = a ⊕ b, a ∈ A, b ∈ B} modulo 998244353.

Examples

Input

2 3 5 5 8 3 1 2 1 9 2 9

Output

112

Input

1 1 9 2 2 4 2 10

Output

120

Note

In the second example, we can discover that the set C = {0,1,...,15}, which means that all numbers between 0 and 15 can be represented as a ⊕ b.

inputFormat

outputFormat

output the sum of elements in the set C = \{x | x = a ⊕ b, a ∈ A, b ∈ B} modulo 998244353, where ⊕ denotes the bitwise XOR operation. Each number should be counted only once.

For example, if A = {2, 3} and B = {2, 3} you should count integer 1 only once, despite the fact that you can get it as 3 ⊕ 2 and as 2 ⊕ 3. So the answer for this case is equal to 1 + 0 = 1.

Let's call a segment [l; r] a set of integers \{l, l+1, ..., r}.

The set A is given as a union of n_A segments, the set B is given as a union of n_B segments.

Input

The first line contains a single integer n_A (1 ≤ n_A ≤ 100).

The i-th of the next n_A lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ 10^{18}), describing a segment of values of set A.

The next line contains a single integer n_B (1 ≤ n_B ≤ 100).

The i-th of the next n_B lines contains two integers l_j and r_j (1 ≤ l_j ≤ r_j ≤ 10^{18}), describing a segment of values of set B.

Note that segments in both sets may intersect.

Output

Print one integer — the sum of all elements in set C = \{x | x = a ⊕ b, a ∈ A, b ∈ B} modulo 998244353.

Examples

Input

2 3 5 5 8 3 1 2 1 9 2 9

Output

112

Input

1 1 9 2 2 4 2 10

Output

120

Note

In the second example, we can discover that the set C = {0,1,...,15}, which means that all numbers between 0 and 15 can be represented as a ⊕ b.

样例

1
1 9
2
2 4
2 10

120

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