Problem: Another dull quarantine day was going by when BThero decided to start researching matrices of size n × m. The rows are numerated 1 through n from top to bottom, and the columns are numerated 1 through m from left to right. The cell in the i-th row and j-th column is denoted as (i, j).

For each cell (i, j) BThero had two values: 

  1. The cost of the cell, which is a single positive integer. 
  2. The direction of the cell, which is one of characters L, R, D, U. Those characters correspond to transitions to adjacent cells (i, j - 1), (i, j + 1), (i + 1, j) or (i - 1, j), respectively. No transition pointed outside of the matrix. 



Let us call a cell (i_2, j_2) reachable from (i_1, j_1), if, starting from (i_1, j_1) and repeatedly moving to the adjacent cell according to our current direction, we will, sooner or later, visit (i_2, j_2). 

BThero decided to create another matrix from the existing two. For a cell (i, j), let us denote S_{i, j} as a set of all reachable cells from it (including (i, j) itself). Then, the value at the cell (i, j) in the new matrix will be equal to the sum of costs of all cells in S_{i, j}. 

After quickly computing the new matrix, BThero immediately sent it to his friends. However, he did not save any of the initial matrices! Help him to restore any two valid matrices, which produce the current one.

Input

The first line of input file contains a single integer T (1 ≤ T ≤ 100) denoting the number of test cases. The description of T test cases follows.

First line of a test case contains two integers n and m (1 ≤ n ⋅ m ≤ 10^5).

Each of the following n lines contain exactly m integers — the elements of the produced matrix. Each element belongs to the segment [2, 10^9].

It is guaranteed that ∑{(n ⋅ m)} over all test cases does not exceed 10^5.

Output

For each test case, if an answer does not exist, print a single word NO. Otherwise, print YES and both matrices in the same format as in the input.

  * The first matrix should be the cost matrix and the second matrix should be the direction matrix. 
  * All integers in the cost matrix should be positive. 
  * All characters in the direction matrix should be valid. No direction should point outside of the matrix. 

Example

Input


2
3 4
7 6 7 8
5 5 4 4
5 7 4 4
1 1
5


Output


YES
1 1 1 1
2 1 1 1
3 2 1 1
R D L L
D R D L
U L R U
NO

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
const int maxn = 1e5, maxm = 1e5, maxCell = 1e5;
const int maxv = maxCell + 4, maxe = maxCell * 4 + 4 * maxCell;
const int inf = std::numeric_limits<int>::max() / 2;
namespace Network {
struct GraphInfo {
  int vertex, source, sink;
};
struct Edge {
  int from, to;
  mutable int flow;
  const Edge *pre, *rev;
} ed[maxe * 2 + 10], *end = ed;
const Edge *head[maxv + 10], *cur[maxv + 10];
int exceed[maxv + 10], dep[maxv + 10];
enum class EdgeType { Normal, Required };
inline void addGraphEdge(const int from, const int to, const int flow) {
  new (end) Edge{from, to, flow, head[from], end + 1};
  head[from] = end++;
  new (end) Edge{to, from, 0, head[to], end - 1};
  head[to] = end++;
}
template <EdgeType et>
inline void addUnitEdge(const int from, const int to) {
  if constexpr (et == EdgeType::Required) {
    --exceed[from];
    ++exceed[to];
  } else
    addGraphEdge(from, to, 1);
}
bool bfs(const int V, const int newS, const int newT) {
  static int q[maxv + 10];
  std::fill(dep, dep + V, -1);
  dep[newS] = 0;
  int l = 0, r = 0;
  q[r++] = newS;
  while (l < r) {
    int v = q[l++];
    for (const Edge *i = head[v]; i; i = i->pre)
      if (i->flow) {
        int to = i->to;
        if (dep[to] == -1) {
          dep[to] = dep[v] + 1;
          q[r++] = to;
        }
      }
  }
  return dep[newT] != -1;
}
std::string ss;
void print(const int c) { ss.resize(c, ' '); }
template <class... Args>
std::string printToStr(Args... args) {
  std::ostringstream os;
  (os << ... << args);
  return os.str();
}
int dfs(const int x, const int cap, const int sink) {
  if (x == sink || !cap) {
    return cap;
  }
  int rst = cap;
  bool first = true;
  int p;
  for (const Edge *&i = cur[x]; i && rst; i = i->pre) {
    if (i->flow && dep[i->to] == dep[x] + 1) {
      const Edge *p = i;
      const int d = dfs(p->to, std::min(rst, p->flow), sink);
      assert(p == i);
      p->flow -= d;
      p->rev->flow += d;
      rst -= d;
      if (!rst) break;
    } else {
    }
  }
  return cap - rst;
}
int dinic(const GraphInfo gi) {
  int ret = 0;
  while (bfs(gi.vertex, gi.source, gi.sink)) {
    std::memcpy(cur, head, sizeof(cur[0]) * gi.vertex);
    ret += dfs(gi.source, inf, gi.sink);
  }
  return ret;
}
bool hasSolution(const int virtSource) {
  for (const Edge *i = head[virtSource]; i; i = i->pre)
    if (i->flow) return false;
  return true;
}
void init(const int n) {
  end = ed;
  std::memset(head, 0, sizeof(head[0]) * (n + 2));
  std::memset(exceed, 0, sizeof(exceed[0]) * (n + 2));
}
int findMatch(const int v, const int limit) {
  for (const Edge *i = head[v]; i; i = i->pre)
    if (!i->flow && i->to < limit) return i->to;
  return limit;
}
bool boundMaxFlow(const GraphInfo gi) {
  const int virtSource = gi.vertex, virtSink = virtSource + 1;
  addGraphEdge(gi.sink, gi.source, inf);
  for (int i = 0; i < gi.vertex; ++i)
    if (exceed[i] > 0)
      addGraphEdge(virtSource, i, exceed[i]);
    else if (exceed[i] < 0)
      addGraphEdge(i, virtSink, -exceed[i]);
  dinic(GraphInfo{virtSink + 1, virtSource, virtSink});
  return hasSolution(virtSource);
}
}  // namespace Network
int n, m;
enum Direction { Left, Right, Down, Up, None };
const Direction reverse[]{Right, Left, Up, Down, None};
struct Step {
  int dx, dy;
  inline bool operator==(const Step s) const {
    return dx == s.dx && dy == s.dy;
  }
};
const Step step[]{{0, -1}, {0, 1}, {1, 0}, {-1, 0}};
const char directionName[] = {'L', 'R', 'D', 'U'};
struct Position {
  int x, y;
  inline static Position fromId(const int id) {
    const div_t d = div(id, m);
    return Position{d.quot, d.rem};
  }
  inline Position operator+(const struct Step s) const {
    return Position{x + s.dx, y + s.dy};
  }
  inline Step operator-(const Position r) const {
    return Step{x - r.x, y - r.y};
  }
  inline bool isValid() const { return x >= 0 && y >= 0 && x < n && y < m; }
  inline int id() const { return x * m + y; }
};
struct Cell {
  Direction next;
  int sum, val;
} cell[maxCell + 10];
namespace GraphBuilder {
template <bool rev, Network::EdgeType type>
inline void linkVertex(const int from, const int to) {
  if constexpr (rev)
    Network::addUnitEdge<type>(to, from);
  else
    Network::addUnitEdge<type>(from, to);
}
template <bool toSink>
inline void linkCell(const Position pos, const int endpoint) {
  using Network::EdgeType;
  const int cid = pos.id();
  Cell &cur = cell[cid];
  cur.next = Direction::None;
  for (int k = 0; k < 4; ++k)
    if (const auto nxt = pos + step[k]; nxt.isValid()) {
      const int nextId = nxt.id();
      if (cell[nextId].sum < cur.sum)
        cur.next = static_cast<Direction>(k);
      else if (!toSink && cell[nextId].sum == cur.sum)
        Network::addUnitEdge<EdgeType::Normal>(cid, nextId);
    }
  if (cur.next == Direction::None)
    linkVertex<toSink, EdgeType::Required>(endpoint, cid);
  else
    linkVertex<toSink, EdgeType::Normal>(endpoint, cid);
}
inline bool isLinkSink(const Position &p) {
  return (p.x & 0x01) ^ (p.y & 0x01);
}
static Network::GraphInfo build(const int n, const int m) {
  const int source = n * m, sink = source + 1;
  Network::init(sink + 1);
  for (int i = 0; i < n; ++i)
    for (Position pos{i, 0}; pos.y < m; ++pos.y)
      if (isLinkSink(pos))
        linkCell<true>(pos, sink);
      else
        linkCell<false>(pos, source);
  return Network::GraphInfo{sink + 1, source, sink};
}
}  // namespace GraphBuilder
void construct(const int n, const int m) {
  const int lim = n * m;
  for (int i = 0, cid = 0; i < n; ++i)
    for (Position pos{i, 0}; pos.y < m; ++pos.y, ++cid)
      if (Cell &cur = cell[cid]; cur.next != Direction::None)
        cur.val = cur.sum - cell[(pos + step[cur.next]).id()].sum;
  for (int i = 0, cid = 0; i < n; ++i)
    for (Position pos{i, 0}; pos.y < m; ++pos.y, ++cid)
      if (!GraphBuilder::isLinkSink(pos))
        if (const int nxt = Network::findMatch(cid, lim); nxt < lim) {
          Cell &cur = cell[cid];
          const int typ =
              std::find(step, step + 4, Position::fromId(nxt) - pos) - step;
          cur.val = cur.sum - 1;
          cur.next = static_cast<Direction>(typ);
          cell[nxt].val = 1;
          cell[nxt].next = reverse[typ];
        }
}
template <class Func>
void printMatrix(const int n, const int m, Func fun) {
  const Cell *ptr = cell;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j, ++ptr) std::cout << fun(*ptr) << ' ';
    std::cout.put('\n');
  }
}
void solve() {
  std::cin >> n >> m;
  for (Cell *i = cell; i < cell + n * m; ++i) std::cin >> i->sum;
  if (!Network::boundMaxFlow(GraphBuilder::build(n, m)))
    std::cout << "NO\n";
  else {
    construct(n, m);
    std::cout << "YES\n";
    printMatrix(n, m, [](const Cell &i) { return i.val; });
    printMatrix(n, m, [](const Cell &i) { return directionName[i.next]; });
  }
}
int main() {
  std::ios::sync_with_stdio(false);
  int t;
  std::cin >> t;
  for (int i = t; i; --i) solve();
  return 0;
}