#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
const long long INF = numeric_limits<long long>::max();
const long long NEGINF = numeric_limits<long long>::min();
template <typename T>
void print(T t) {
  cout << t << " ";
}
template <typename T, typename... Args>
void print(T t, Args... args) {
  cout << t << " ";
  print(args...);
}
template <class T>
void print(vector<T> &list) {
  for (auto &x : list) cout << x << " ";
}
template <class T>
void read(vector<T> &list, long long n) {
  list.clear(), list.resize(n);
  for (auto &x : list) cin >> x;
}
long long len_of_number(long long n) {
  long long len(0);
  while (n != 0) {
    ++len;
    n /= 10;
  }
  return len;
}
long long sum_of_digits(long long n) {
  long long sod = 0;
  while (n != 0) {
    sod += (n % 10);
    n /= 10;
  }
  return sod;
}
bool isPalindrome(string str) {
  long long n = str.length();
  for (long long i = (0); i <= (n / 2); i++)
    if (str[i] != str[n - i - 1]) return false;
  return true;
}
long long fast_exp(long long x, long long i) {
  long long ans = 1;
  while (i > 0) {
    if (i & 1) ans = (ans * x);
    i >>= 1;
    x = (x * x);
  }
  return ans;
}
long long fast_exp(long long x, long long i, long long mod) {
  long long ans = 1;
  while (i > 0) {
    if (i & 1) ans = (ans * x) % mod;
    i >>= 1;
    x = (x * x) % mod;
  }
  return ans;
}
long long modInverse(long long x, long long mod) {
  return fast_exp(x, mod - 2, mod);
}
long long egcd_x, egcd_y, egcd_d;
void egcd(long long a, long long b) {
  if (b == 0) {
    egcd_x = 1, egcd_y = 0;
    egcd_d = a;
    return;
  }
  egcd(b, a % b);
  long long temp = egcd_x;
  egcd_x = egcd_y;
  egcd_y = temp - (a / b) * egcd_y;
}
long long extended_gcd(long long a, long long b) {
  if (a >= b) {
    egcd(a, b);
    return ((egcd_x % b) + b) % b;
  } else {
    egcd(b, a);
    return ((egcd_y % b) + b) % b;
  }
}
long long gcd(long long x, long long y) {
  long long t;
  while (y != 0) {
    t = x % y;
    x = y;
    y = t;
  }
  return x;
}
vector<long long> lp, pr;
void genPrimes(long long n) {
  lp.resize(n + 1, 0);
  long long size = 0;
  for (long long i = (2); i <= (n); i++) {
    if (!lp[i]) {
      lp[i] = i;
      pr.push_back(i);
      ++size;
    }
    for (long long j = 0; j < size && pr[j] <= lp[i] && (i * pr[j]) <= n; ++j)
      lp[i * pr[j]] = pr[j];
  }
}
bool isPrime(long long n) {
  long long root = sqrt(n);
  for (long long i = (2); i <= (root); i++)
    if (n % i == 0) return 0;
  return 1;
}
vector<long long> fact, invFact;
void genFact(long long n, long long M) {
  fact.resize(n + 1), invFact.resize(n + 1);
  fact[0] = fact[1] = invFact[0] = invFact[1] = 1;
  for (long long i = (2); i <= (n); i++) {
    fact[i] = (fact[i - 1] * i) % M;
    invFact[i] = modInverse(fact[i], M);
  }
}
long long ncr(long long n, long long r, long long M) {
  return (((fact[n] * invFact[n - r]) % M) * invFact[r] % M);
}
long long nc2(long long a) { return (a * (a - 1)) / 2; }
vector<long long> cnt;
string groupAndCnt(string str) {
  string a = "";
  long long prev_count = 0;
  char prev_char = '~';
  for (auto &c : str) {
    if (c != prev_char) {
      if (prev_count) {
        a += prev_char;
        cnt.push_back(prev_count);
      }
      prev_count = 1;
      prev_char = c;
    } else
      ++prev_count;
  }
  cnt.push_back(prev_count);
  a += prev_char;
  return a;
}
long long firstValEG(vector<long long>::iterator a,
                     vector<long long>::iterator b, long long c) {
  auto it = lower_bound(a, b, c);
  if (it == b) return -1;
  return it - a;
}
long long lastValEL(vector<long long>::iterator a,
                    vector<long long>::iterator b, long long c) {
  long long lo = 0, hi = distance(a, b) - 1, m;
  while (lo < hi) {
    m = (lo) + ((hi) - (lo) + 1) / 2;
    if (*(a + m) > c)
      hi = m - 1;
    else
      lo = m;
  }
  return ((*(a + lo)) <= c) ? lo : -1;
}
long long countInRange(vector<long long>::iterator a,
                       vector<long long>::iterator b, long long c,
                       long long d) {
  long long e = firstValEG(a, b, c);
  if (e == -1) return 0;
  return (e == -1) ? 0 : (lastValEL(a, b, d) - e + 1);
}
vector<long long> pset, pset_size;
void initSet(long long _size) {
  pset.resize(_size);
  pset_size.resize(_size);
  for (long long i = (0); i <= (_size - 1); i++) pset[i] = i, pset_size[i] = 1;
}
long long findSet(long long i) {
  return (pset[i] == i) ? i : (pset[i] = findSet(pset[i]));
}
void unionSet(long long i, long long j) {
  long long p1 = findSet(i);
  long long p2 = findSet(j);
  pset[p1] = p2;
  if (p1 != p2) {
    pset_size[p2] += pset_size[p1];
  }
}
bool isSameSet(long long i, long long j) { return findSet(i) == findSet(j); }
vector<vector<long long> > adjList;
void getEdges(long long n, long long m) {
  long long a, b;
  adjList.clear();
  adjList.resize(n + 1);
  for (long long i = (1); i <= (m); i++) {
    cin >> a >> b;
    adjList[a].push_back(b), adjList[b].push_back(a);
  }
}
void printGraph(long long a, long long b, vector<vector<long long> > &graph) {
  for (long long i = (a); i <= (b); i++) {
    print(i, ": ");
    for (auto &x : graph[i]) {
      print(x, ",");
    }
    cout << "\n";
  }
}
long double areaTriangle(long double a, long double b, long double c) {
  long double s = (a + b + c) / 2.0;
  return sqrt(s * (s - a) * (s - b) * (s - c));
}
long double areaTriangle(long double a, long double b) {
  return a * b * 0.5 * sqrt(3) * 0.5;
}
long double thirdSide(long double a, long double b) {
  return sqrt(a * a + b * b + a * b);
}
inline void solve(long long _T) {
  long long a, b, c, d, e, f;
  cin >> a >> b >> c >> d >> e >> f;
  long double numerator =
      areaTriangle(a, b) + areaTriangle(c, d) + areaTriangle(e, f) +
      areaTriangle(thirdSide(a, b), thirdSide(c, d), thirdSide(e, f));
  long double denominator = sqrt(3) / 4;
  long double ans = numerator / denominator;
  long long ANS;
  if (abs(ans - ceil(ans)) <= abs(ans - floor(ans))) {
    ANS = ceil(ans);
  } else {
    ANS = floor(ans);
  }
  cout << ANS;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long test_cases;
  test_cases = 1;
  for (long long T = (0); T <= (test_cases - 1); T++) {
    solve(T);
  }
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

Gerald got a very curious hexagon for his birthday. The boy found out that all the angles of the hexagon are equal to <image>. Then he measured the length of its sides, and found that each of them is equal to an integer number of centimeters. There the properties of the hexagon ended and Gerald decided to draw on it.

He painted a few lines, parallel to the sides of the hexagon. The lines split the hexagon into regular triangles with sides of 1 centimeter. Now Gerald wonders how many triangles he has got. But there were so many of them that Gerald lost the track of his counting. Help the boy count the triangles.

Input

The first and the single line of the input contains 6 space-separated integers a1, a2, a3, a4, a5 and a6 (1 ≤ ai ≤ 1000) — the lengths of the sides of the hexagons in centimeters in the clockwise order. It is guaranteed that the hexagon with the indicated properties and the exactly such sides exists.

Output

Print a single integer — the number of triangles with the sides of one 1 centimeter, into which the hexagon is split.

Examples

Input

1 1 1 1 1 1


Output

6


Input

1 2 1 2 1 2


Output

13

Note

This is what Gerald's hexagon looks like in the first sample:

<image>

And that's what it looks like in the second sample:

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
const long long INF = numeric_limits<long long>::max();
const long long NEGINF = numeric_limits<long long>::min();
template <typename T>
void print(T t) {
  cout << t << " ";
}
template <typename T, typename... Args>
void print(T t, Args... args) {
  cout << t << " ";
  print(args...);
}
template <class T>
void print(vector<T> &list) {
  for (auto &x : list) cout << x << " ";
}
template <class T>
void read(vector<T> &list, long long n) {
  list.clear(), list.resize(n);
  for (auto &x : list) cin >> x;
}
long long len_of_number(long long n) {
  long long len(0);
  while (n != 0) {
    ++len;
    n /= 10;
  }
  return len;
}
long long sum_of_digits(long long n) {
  long long sod = 0;
  while (n != 0) {
    sod += (n % 10);
    n /= 10;
  }
  return sod;
}
bool isPalindrome(string str) {
  long long n = str.length();
  for (long long i = (0); i <= (n / 2); i++)
    if (str[i] != str[n - i - 1]) return false;
  return true;
}
long long fast_exp(long long x, long long i) {
  long long ans = 1;
  while (i > 0) {
    if (i & 1) ans = (ans * x);
    i >>= 1;
    x = (x * x);
  }
  return ans;
}
long long fast_exp(long long x, long long i, long long mod) {
  long long ans = 1;
  while (i > 0) {
    if (i & 1) ans = (ans * x) % mod;
    i >>= 1;
    x = (x * x) % mod;
  }
  return ans;
}
long long modInverse(long long x, long long mod) {
  return fast_exp(x, mod - 2, mod);
}
long long egcd_x, egcd_y, egcd_d;
void egcd(long long a, long long b) {
  if (b == 0) {
    egcd_x = 1, egcd_y = 0;
    egcd_d = a;
    return;
  }
  egcd(b, a % b);
  long long temp = egcd_x;
  egcd_x = egcd_y;
  egcd_y = temp - (a / b) * egcd_y;
}
long long extended_gcd(long long a, long long b) {
  if (a >= b) {
    egcd(a, b);
    return ((egcd_x % b) + b) % b;
  } else {
    egcd(b, a);
    return ((egcd_y % b) + b) % b;
  }
}
long long gcd(long long x, long long y) {
  long long t;
  while (y != 0) {
    t = x % y;
    x = y;
    y = t;
  }
  return x;
}
vector<long long> lp, pr;
void genPrimes(long long n) {
  lp.resize(n + 1, 0);
  long long size = 0;
  for (long long i = (2); i <= (n); i++) {
    if (!lp[i]) {
      lp[i] = i;
      pr.push_back(i);
      ++size;
    }
    for (long long j = 0; j < size && pr[j] <= lp[i] && (i * pr[j]) <= n; ++j)
      lp[i * pr[j]] = pr[j];
  }
}
bool isPrime(long long n) {
  long long root = sqrt(n);
  for (long long i = (2); i <= (root); i++)
    if (n % i == 0) return 0;
  return 1;
}
vector<long long> fact, invFact;
void genFact(long long n, long long M) {
  fact.resize(n + 1), invFact.resize(n + 1);
  fact[0] = fact[1] = invFact[0] = invFact[1] = 1;
  for (long long i = (2); i <= (n); i++) {
    fact[i] = (fact[i - 1] * i) % M;
    invFact[i] = modInverse(fact[i], M);
  }
}
long long ncr(long long n, long long r, long long M) {
  return (((fact[n] * invFact[n - r]) % M) * invFact[r] % M);
}
long long nc2(long long a) { return (a * (a - 1)) / 2; }
vector<long long> cnt;
string groupAndCnt(string str) {
  string a = "";
  long long prev_count = 0;
  char prev_char = '~';
  for (auto &c : str) {
    if (c != prev_char) {
      if (prev_count) {
        a += prev_char;
        cnt.push_back(prev_count);
      }
      prev_count = 1;
      prev_char = c;
    } else
      ++prev_count;
  }
  cnt.push_back(prev_count);
  a += prev_char;
  return a;
}
long long firstValEG(vector<long long>::iterator a,
                     vector<long long>::iterator b, long long c) {
  auto it = lower_bound(a, b, c);
  if (it == b) return -1;
  return it - a;
}
long long lastValEL(vector<long long>::iterator a,
                    vector<long long>::iterator b, long long c) {
  long long lo = 0, hi = distance(a, b) - 1, m;
  while (lo < hi) {
    m = (lo) + ((hi) - (lo) + 1) / 2;
    if (*(a + m) > c)
      hi = m - 1;
    else
      lo = m;
  }
  return ((*(a + lo)) <= c) ? lo : -1;
}
long long countInRange(vector<long long>::iterator a,
                       vector<long long>::iterator b, long long c,
                       long long d) {
  long long e = firstValEG(a, b, c);
  if (e == -1) return 0;
  return (e == -1) ? 0 : (lastValEL(a, b, d) - e + 1);
}
vector<long long> pset, pset_size;
void initSet(long long _size) {
  pset.resize(_size);
  pset_size.resize(_size);
  for (long long i = (0); i <= (_size - 1); i++) pset[i] = i, pset_size[i] = 1;
}
long long findSet(long long i) {
  return (pset[i] == i) ? i : (pset[i] = findSet(pset[i]));
}
void unionSet(long long i, long long j) {
  long long p1 = findSet(i);
  long long p2 = findSet(j);
  pset[p1] = p2;
  if (p1 != p2) {
    pset_size[p2] += pset_size[p1];
  }
}
bool isSameSet(long long i, long long j) { return findSet(i) == findSet(j); }
vector<vector<long long> > adjList;
void getEdges(long long n, long long m) {
  long long a, b;
  adjList.clear();
  adjList.resize(n + 1);
  for (long long i = (1); i <= (m); i++) {
    cin >> a >> b;
    adjList[a].push_back(b), adjList[b].push_back(a);
  }
}
void printGraph(long long a, long long b, vector<vector<long long> > &graph) {
  for (long long i = (a); i <= (b); i++) {
    print(i, ": ");
    for (auto &x : graph[i]) {
      print(x, ",");
    }
    cout << "\n";
  }
}
long double areaTriangle(long double a, long double b, long double c) {
  long double s = (a + b + c) / 2.0;
  return sqrt(s * (s - a) * (s - b) * (s - c));
}
long double areaTriangle(long double a, long double b) {
  return a * b * 0.5 * sqrt(3) * 0.5;
}
long double thirdSide(long double a, long double b) {
  return sqrt(a * a + b * b + a * b);
}
inline void solve(long long _T) {
  long long a, b, c, d, e, f;
  cin >> a >> b >> c >> d >> e >> f;
  long double numerator =
      areaTriangle(a, b) + areaTriangle(c, d) + areaTriangle(e, f) +
      areaTriangle(thirdSide(a, b), thirdSide(c, d), thirdSide(e, f));
  long double denominator = sqrt(3) / 4;
  long double ans = numerator / denominator;
  long long ANS;
  if (abs(ans - ceil(ans)) <= abs(ans - floor(ans))) {
    ANS = ceil(ans);
  } else {
    ANS = floor(ans);
  }
  cout << ANS;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long test_cases;
  test_cases = 1;
  for (long long T = (0); T <= (test_cases - 1); T++) {
    solve(T);
  }
  return 0;
}

```