#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) {
  int c = a % b;
  while (c != 0) {
    a = b;
    b = c;
    c = a % b;
  }
  return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
struct UnionFind {
  vector<int> data;
  UnionFind(int sz) { data.assign(sz, -1); }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return (false);
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }
  int find(int k) {
    if (data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
  int size(int k) { return (-data[find(k)]); }
};
long long M = 1000000007;
vector<long long> fac(2000011);
vector<long long> ifac(2000011);
long long mpow(long long x, long long n) {
  long long ans = 1;
  while (n != 0) {
    if (n & 1) ans = ans * x % M;
    x = x * x % M;
    n = n >> 1;
  }
  return ans;
}
long long mpow2(long long x, long long n, long long mod) {
  long long ans = 1;
  while (n != 0) {
    if (n & 1) ans = ans * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return ans;
}
void setcomb() {
  fac[0] = 1;
  ifac[0] = 1;
  for (long long i = 0; i < 2000010; i++) {
    fac[i + 1] = fac[i] * (i + 1) % M;
  }
  ifac[2000010] = mpow(fac[2000010], M - 2);
  for (long long i = 2000010; i > 0; i--) {
    ifac[i - 1] = ifac[i] * i % M;
  }
}
long long comb(long long a, long long b) {
  if (a == 0 && b == 0) return 1;
  if (a < b || a < 0) return 0;
  long long tmp = ifac[a - b] * ifac[b] % M;
  return tmp * fac[a] % M;
}
long long perm(long long a, long long b) {
  if (a == 0 && b == 0) return 1;
  if (a < b || a < 0) return 0;
  return fac[a] * ifac[a - b] % M;
}
long long modinv(long long a) {
  long long b = M, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= M;
  if (u < 0) u += M;
  return u;
}
long long modinv2(long long a, long long mod) {
  long long b = mod, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0) u += mod;
  return u;
}
vector<vector<long long>> mul(vector<vector<long long>> a,
                              vector<vector<long long>> b, int n) {
  int i, j, k, t;
  vector<vector<long long>> c(n);
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      t = 0;
      for (k = 0; k < n; k++) t = (t + a[i][k] * b[k][j] % M) % M;
      c[i].push_back(t);
    }
  }
  return c;
}
template <typename Monoid>
struct SegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;
  int sz;
  vector<Monoid> seg;
  const F f;
  const Monoid M1;
  SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
    sz = 1;
    while (sz < n) sz <<= 1;
    seg.assign(2 * sz, M1);
  }
  void set(int k, const Monoid &x) { seg[k + sz] = x; }
  void build() {
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  void update(int k, const Monoid &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  Monoid query(int a, int b) {
    Monoid L = M1, R = M1;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) L = f(L, seg[a++]);
      if (b & 1) R = f(seg[--b], R);
    }
    return f(L, R);
  }
  Monoid operator[](const int &k) const { return seg[k + sz]; }
  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }
  template <typename C>
  int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, seg[1]))) return find_subtree(1, check, L, false);
      return -1;
    }
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, seg[a]);
        if (check(nxt)) return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }
  template <typename C>
  int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(seg[1], R))) return find_subtree(1, check, R, true);
      return -1;
    }
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(seg[--b], R);
        if (check(nxt)) return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
};
template <unsigned mod>
struct RollingHash {
  vector<unsigned> hashed, power;
  inline unsigned mul(unsigned a, unsigned b) const {
    unsigned long long x = (unsigned long long)a * b;
    unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m;
    asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod));
    return m;
  }
  RollingHash(const string &s, unsigned base = 10007) {
    int sz = (int)s.size();
    hashed.assign(sz + 1, 0);
    power.assign(sz + 1, 0);
    power[0] = 1;
    for (int i = 0; i < sz; i++) {
      power[i + 1] = mul(power[i], base);
      hashed[i + 1] = mul(hashed[i], base) + s[i];
      if (hashed[i + 1] >= mod) hashed[i + 1] -= mod;
    }
  }
  unsigned get(int l, int r) const {
    unsigned ret = hashed[r] + mod - mul(hashed[l], power[r - l]);
    if (ret >= mod) ret -= mod;
    return ret;
  }
  unsigned connect(unsigned h1, int h2, int h2len) const {
    unsigned ret = mul(h1, power[h2len]) + h2;
    if (ret >= mod) ret -= mod;
    return ret;
  }
  int LCP(const RollingHash<mod> &b, int l1, int r1, int l2, int r2) {
    int len = min(r1 - l1, r2 - l2);
    int low = -1, high = len + 1;
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (get(l1, l1 + mid) == b.get(l2, l2 + mid))
        low = mid;
      else
        high = mid;
    }
    return (low);
  }
};
using RH = RollingHash<1000000007>;
template <typename T>
struct edge {
  int src, to;
  T cost;
  edge(int to, T cost) : src(-1), to(to), cost(cost) {}
  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T>
using Matrix = vector<vector<T>>;
template <typename G>
struct DoublingLowestCommonAncestor {
  const int LOG;
  vector<int> dep;
  const G &g;
  vector<vector<int>> table;
  DoublingLowestCommonAncestor(const G &g)
      : g(g), dep(g.size()), LOG(32 - __builtin_clz(g.size())) {
    table.assign(LOG, vector<int>(g.size(), -1));
  }
  void dfs(int idx, int par, int d) {
    table[0][idx] = par;
    dep[idx] = d;
    for (auto &to : g[idx]) {
      if (to != par) dfs(to, idx, d + 1);
    }
  }
  void build() {
    dfs(0, -1, 0);
    for (int k = 0; k + 1 < LOG; k++) {
      for (int i = 0; i < table[k].size(); i++) {
        if (table[k][i] == -1)
          table[k + 1][i] = -1;
        else
          table[k + 1][i] = table[k][table[k][i]];
      }
    }
  }
  int query(int u, int v) {
    if (dep[u] > dep[v]) swap(u, v);
    for (int i = LOG - 1; i >= 0; i--) {
      if (((dep[v] - dep[u]) >> i) & 1) v = table[i][v];
    }
    if (u == v) return u;
    for (int i = LOG - 1; i >= 0; i--) {
      if (table[i][u] != table[i][v]) {
        u = table[i][u];
        v = table[i][v];
      }
    }
    return table[0][u];
  }
};
int main() {
  int n, m, k, i, j, p, x, y;
  cin >> n >> m >> k;
  for (i = 0; i < k * 2; i++) cin >> x >> y;
  p = n + m - 2 + n * m - 1;
  cout << p << endl;
  for (i = 0; i < n - 1; i++) cout << "U";
  for (i = 0; i < m - 1; i++) cout << "L";
  for (i = 0; i < n; i++) {
    for (j = 0; j < m - 1; j++) {
      if (i % 2 == 0)
        cout << "R";
      else
        cout << "L";
    }
    if (i < n - 1) cout << "D";
  }
  cout << endl;
}

### Prompt

Create a solution in cpp for the following problem:

Petya has a rectangular Board of size n × m. Initially, k chips are placed on the board, i-th chip is located in the cell at the intersection of sx_i-th row and sy_i-th column.

In one action, Petya can move all the chips to the left, right, down or up by 1 cell.

If the chip was in the (x, y) cell, then after the operation: 

  * left, its coordinates will be (x, y - 1); 
  * right, its coordinates will be (x, y + 1); 
  * down, its coordinates will be (x + 1, y); 
  * up, its coordinates will be (x - 1, y). 



If the chip is located by the wall of the board, and the action chosen by Petya moves it towards the wall, then the chip remains in its current position.

Note that several chips can be located in the same cell.

For each chip, Petya chose the position which it should visit. Note that it's not necessary for a chip to end up in this position.

Since Petya does not have a lot of free time, he is ready to do no more than 2nm actions.

You have to find out what actions Petya should do so that each chip visits the position that Petya selected for it at least once. Or determine that it is not possible to do this in 2nm actions.

Input

The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 200) — the number of rows and columns of the board and the number of chips, respectively.

The next k lines contains two integers each sx_i, sy_i ( 1 ≤ sx_i ≤ n, 1 ≤ sy_i ≤ m) — the starting position of the i-th chip.

The next k lines contains two integers each fx_i, fy_i ( 1 ≤ fx_i ≤ n, 1 ≤ fy_i ≤ m) — the position that the i-chip should visit at least once.

Output

In the first line print the number of operations so that each chip visits the position that Petya selected for it at least once.

In the second line output the sequence of operations. To indicate operations left, right, down, and up, use the characters L, R, D, U respectively.

If the required sequence does not exist, print -1 in the single line.

Examples

Input


3 3 2
1 2
2 1
3 3
3 2


Output


3
DRD

Input


5 4 3
3 4
3 1
3 3
5 3
1 3
1 4


Output


9
DDLUUUURR

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) {
  int c = a % b;
  while (c != 0) {
    a = b;
    b = c;
    c = a % b;
  }
  return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
struct UnionFind {
  vector<int> data;
  UnionFind(int sz) { data.assign(sz, -1); }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return (false);
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }
  int find(int k) {
    if (data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
  int size(int k) { return (-data[find(k)]); }
};
long long M = 1000000007;
vector<long long> fac(2000011);
vector<long long> ifac(2000011);
long long mpow(long long x, long long n) {
  long long ans = 1;
  while (n != 0) {
    if (n & 1) ans = ans * x % M;
    x = x * x % M;
    n = n >> 1;
  }
  return ans;
}
long long mpow2(long long x, long long n, long long mod) {
  long long ans = 1;
  while (n != 0) {
    if (n & 1) ans = ans * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return ans;
}
void setcomb() {
  fac[0] = 1;
  ifac[0] = 1;
  for (long long i = 0; i < 2000010; i++) {
    fac[i + 1] = fac[i] * (i + 1) % M;
  }
  ifac[2000010] = mpow(fac[2000010], M - 2);
  for (long long i = 2000010; i > 0; i--) {
    ifac[i - 1] = ifac[i] * i % M;
  }
}
long long comb(long long a, long long b) {
  if (a == 0 && b == 0) return 1;
  if (a < b || a < 0) return 0;
  long long tmp = ifac[a - b] * ifac[b] % M;
  return tmp * fac[a] % M;
}
long long perm(long long a, long long b) {
  if (a == 0 && b == 0) return 1;
  if (a < b || a < 0) return 0;
  return fac[a] * ifac[a - b] % M;
}
long long modinv(long long a) {
  long long b = M, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= M;
  if (u < 0) u += M;
  return u;
}
long long modinv2(long long a, long long mod) {
  long long b = mod, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0) u += mod;
  return u;
}
vector<vector<long long>> mul(vector<vector<long long>> a,
                              vector<vector<long long>> b, int n) {
  int i, j, k, t;
  vector<vector<long long>> c(n);
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      t = 0;
      for (k = 0; k < n; k++) t = (t + a[i][k] * b[k][j] % M) % M;
      c[i].push_back(t);
    }
  }
  return c;
}
template <typename Monoid>
struct SegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;
  int sz;
  vector<Monoid> seg;
  const F f;
  const Monoid M1;
  SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
    sz = 1;
    while (sz < n) sz <<= 1;
    seg.assign(2 * sz, M1);
  }
  void set(int k, const Monoid &x) { seg[k + sz] = x; }
  void build() {
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  void update(int k, const Monoid &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  Monoid query(int a, int b) {
    Monoid L = M1, R = M1;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) L = f(L, seg[a++]);
      if (b & 1) R = f(seg[--b], R);
    }
    return f(L, R);
  }
  Monoid operator[](const int &k) const { return seg[k + sz]; }
  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }
  template <typename C>
  int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, seg[1]))) return find_subtree(1, check, L, false);
      return -1;
    }
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, seg[a]);
        if (check(nxt)) return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }
  template <typename C>
  int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(seg[1], R))) return find_subtree(1, check, R, true);
      return -1;
    }
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(seg[--b], R);
        if (check(nxt)) return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
};
template <unsigned mod>
struct RollingHash {
  vector<unsigned> hashed, power;
  inline unsigned mul(unsigned a, unsigned b) const {
    unsigned long long x = (unsigned long long)a * b;
    unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m;
    asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod));
    return m;
  }
  RollingHash(const string &s, unsigned base = 10007) {
    int sz = (int)s.size();
    hashed.assign(sz + 1, 0);
    power.assign(sz + 1, 0);
    power[0] = 1;
    for (int i = 0; i < sz; i++) {
      power[i + 1] = mul(power[i], base);
      hashed[i + 1] = mul(hashed[i], base) + s[i];
      if (hashed[i + 1] >= mod) hashed[i + 1] -= mod;
    }
  }
  unsigned get(int l, int r) const {
    unsigned ret = hashed[r] + mod - mul(hashed[l], power[r - l]);
    if (ret >= mod) ret -= mod;
    return ret;
  }
  unsigned connect(unsigned h1, int h2, int h2len) const {
    unsigned ret = mul(h1, power[h2len]) + h2;
    if (ret >= mod) ret -= mod;
    return ret;
  }
  int LCP(const RollingHash<mod> &b, int l1, int r1, int l2, int r2) {
    int len = min(r1 - l1, r2 - l2);
    int low = -1, high = len + 1;
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (get(l1, l1 + mid) == b.get(l2, l2 + mid))
        low = mid;
      else
        high = mid;
    }
    return (low);
  }
};
using RH = RollingHash<1000000007>;
template <typename T>
struct edge {
  int src, to;
  T cost;
  edge(int to, T cost) : src(-1), to(to), cost(cost) {}
  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T>
using Matrix = vector<vector<T>>;
template <typename G>
struct DoublingLowestCommonAncestor {
  const int LOG;
  vector<int> dep;
  const G &g;
  vector<vector<int>> table;
  DoublingLowestCommonAncestor(const G &g)
      : g(g), dep(g.size()), LOG(32 - __builtin_clz(g.size())) {
    table.assign(LOG, vector<int>(g.size(), -1));
  }
  void dfs(int idx, int par, int d) {
    table[0][idx] = par;
    dep[idx] = d;
    for (auto &to : g[idx]) {
      if (to != par) dfs(to, idx, d + 1);
    }
  }
  void build() {
    dfs(0, -1, 0);
    for (int k = 0; k + 1 < LOG; k++) {
      for (int i = 0; i < table[k].size(); i++) {
        if (table[k][i] == -1)
          table[k + 1][i] = -1;
        else
          table[k + 1][i] = table[k][table[k][i]];
      }
    }
  }
  int query(int u, int v) {
    if (dep[u] > dep[v]) swap(u, v);
    for (int i = LOG - 1; i >= 0; i--) {
      if (((dep[v] - dep[u]) >> i) & 1) v = table[i][v];
    }
    if (u == v) return u;
    for (int i = LOG - 1; i >= 0; i--) {
      if (table[i][u] != table[i][v]) {
        u = table[i][u];
        v = table[i][v];
      }
    }
    return table[0][u];
  }
};
int main() {
  int n, m, k, i, j, p, x, y;
  cin >> n >> m >> k;
  for (i = 0; i < k * 2; i++) cin >> x >> y;
  p = n + m - 2 + n * m - 1;
  cout << p << endl;
  for (i = 0; i < n - 1; i++) cout << "U";
  for (i = 0; i < m - 1; i++) cout << "L";
  for (i = 0; i < n; i++) {
    for (j = 0; j < m - 1; j++) {
      if (i % 2 == 0)
        cout << "R";
      else
        cout << "L";
    }
    if (i < n - 1) cout << "D";
  }
  cout << endl;
}

```