Problem:
Score : 300 points

Problem Statement

You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N.
Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.

Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:

Add 2 to a_i.

Add 1 to b_j.

Constraints

1 ≤ N ≤ 10 000

0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N
b_1 b_2 .. b_N

Output

If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes; otherwise, print No.

Sample Input 1

3
1 2 3
5 2 2

Sample Output 1

Yes

For example, we can perform three operations as follows to do our job:

First operation: i=1 and j=2. Now we have a = \{3,2,3\}, b = \{5,3,2\}.

Second operation: i=1 and j=2. Now we have a = \{5,2,3\}, b = \{5,4,2\}.

Third operation: i=2 and j=3. Now we have a = \{5,4,3\}, b = \{5,4,3\}.

Sample Input 2

5
3 1 4 1 5
2 7 1 8 2

Sample Output 2

No

Sample Input 3

5
2 7 1 8 2
3 1 4 1 5

Sample Output 3

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

struct init_ { init_(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); } } init_;

template<class C> using iodef_rng_t = typename enable_if<decltype(declval<C>().begin(), true_type{})::value && !is_same<C, string>::value>::type;
template<class C, class = iodef_rng_t<C>> istream& operator>>(istream& in, C& c) { for (auto& v : c) { in >> v; } return in; }
template<class C, class = iodef_rng_t<C>> ostream& operator<<(ostream& out, const C& c) { int i = 0; for (const auto& v : c) { if (i++) { out << ' '; } out << v; } return out; }
template<size_t N, class T, class R> using when_last = typename enable_if<N == tuple_size<remove_reference_t<T>>::value - 1, R>::type;
template<size_t N, class T, class R> using when_init = typename enable_if<N != tuple_size<remove_reference_t<T>>::value - 1, R>::type;
template<size_t N = 0, class T> auto operator>>(istream& in, T&& t) -> when_last<N, T, istream&> { return in >> get<N>(t); }
template<size_t N = 0, class T> auto operator>>(istream& in, T&& t) -> when_init<N, T, istream&> { return operator>><N + 1>(in >> get<N>(t), forward<T>(t)); }
template<size_t N = 0, class T> auto operator<<(ostream& out, const T& t) -> when_last<N, T, ostream&> { return out << get<N>(t); }
template<size_t N = 0, class T> auto operator<<(ostream& out, const T& t) -> when_init<N, T, ostream&> { return operator<<<N + 1>(out << get<N>(t) << ' ', t); }

#ifdef LOCAL
template<class T> void trace_(const char* s, const T& v) { cerr << s << "=" << v; }
template<class T, class... Ts> void trace_(const char* s, const T& v, const Ts&... vs) { for (; *s != ','; ++s) { cerr << *s; } cerr << "=" << v << ","; trace_(++s, vs...); }
#define TRACE(...) (cerr << "\033[2m\033[33m", trace_(#__VA_ARGS__, __VA_ARGS__), cerr << "\033[0m\n")
#else
#define TRACE(...)
#endif

int main() {
    int n;
    cin >> n;
    vector<int> a(n), b(n);
    cin >> a >> b;
    int an = 0, bn = 0;
    for (int i = 0; i < n; i++) {
        if (a[i] > b[i]) bn += a[i] - b[i];
        if (a[i] < b[i]) an += (b[i] - a[i]) / 2;
    }
    if (bn <= an) puts("Yes");
    else puts("No");
}