Problem: There are n lanterns in a row. The lantern i is placed in position i and has power equal to p_i.

Each lantern can be directed to illuminate either some lanterns to the left or some lanterns to the right. If the i-th lantern is turned to the left, it illuminates all such lanterns j that j ∈ [i - p_i, i - 1]. Similarly, if it is turned to the right, it illuminates all such lanterns j that j ∈ [i + 1, i + p_i].

Your goal is to choose a direction for each lantern so each lantern is illuminated by at least one other lantern, or report that it is impossible.

Input

The first line contains one integer t (1 ≤ t ≤ 10000) — the number of test cases.

Each test case consists of two lines. The first line contains one integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of lanterns.

The second line contains n integers p_1, p_2, ..., p_n (0 ≤ p_i ≤ n) — the power of the i-th lantern.

The sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case, print the answer as follows:

If it is possible to direct all lanterns so that each lantern is illuminated, print YES in the first line and a string of n characters L and/or R (the i-th character is L if the i-th lantern is turned to the left, otherwise this character is R) in the second line. If there are multiple answers, you may print any of them.

If there is no answer, simply print NO for that test case.

Example

Input


4
8
0 0 3 1 1 1 1 2
2
1 1
2
2 2
2
0 1


Output


YES
RRLLLLRL
YES
RL
YES
RL
NO

Solution (in CPP):

Solution:
/*
    Author: Nguyen Tan Bao
    Status:
    Idea:
*/

#include <bits/stdc++.h>
#define FI first
#define SE second
#define ALL(a) a.begin(), a.end()
#define SZ(a) int((a).size())
#define MS(s, n) memset(s, n, sizeof(s))
#define FOR(i,a,b) for (int i = (a); i <= (b); i++)
#define FORE(i,a,b) for (int i = (a); i >= (b); i--)
#define FORALL(it, a) for (__typeof((a).begin()) it = (a).begin(); it != (a).end(); it++)
#define TRAV(x, a) for (auto &x : a)

using namespace std;
using ll = long long; using ld = double; 
using pi = pair<int, int>; using pl = pair<ll, ll>; using pd = pair<ld, ld>;
using cd = complex<ld>; using vcd = vector<cd>;

using vi = vector<int>; using vl = vector<ll>;
using vd = vector<ld>; using vs = vector<string>;
using vpi = vector<pi>; using vpl = vector<pl>; using vpd = vector<pd>; // vector<pair>

template<class T> using min_pq = priority_queue<T, vector<T>, greater<T> >;
template<class T> inline int ckmin(T& a, const T& val) { return val < a ? a = val, 1 : 0; }
template<class T> inline int ckmax(T& a, const T& val) { return a < val ? a = val, 1 : 0; }
template<class T> void remDup(vector<T>& v) { sort(ALL(v)); v.erase(unique(ALL(v)), end(v)); }

constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { return x == 0 ? 0 : 31-__builtin_clz(x); } // floor(log2(x)) 
constexpr int p2(int x) { return 1<<x; }
constexpr int msk2(int x) { return p2(x)-1; }

ll ceilDiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); } // divide a by b rounded up
ll floorDiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } // divide a by b rounded down
void setPrec(int x) { cout << fixed << setprecision(x); }

// TO_STRING
#define ts to_string
string ts(char c) { return string(1, c); }
string ts(const char* s) { return (string) s; }
string ts(string s) { return s; }
string ts(bool b) { return ts((int)b); }
template<class T> string ts(complex<T> c) { stringstream ss; ss << c; return ss.str(); }
template<class T> using V = vector<T>;
string ts(V<bool> v) {string res = "{"; FOR(i,0,SZ(v)-1) res += char('0'+v[i]); res += "}"; return res; }
template<size_t sz> string ts(bitset<sz> b) { string res = ""; FOR(i,0,SZ(b)-1) res += char('0'+b[i]); return res; }
template<class T, class U> string ts(pair<T,U> p);
template<class T> string ts(T v) { // containers with begin(), end()
    bool fst = 1; string res = "";
    for (const auto& x: v) { if (!fst) res += " "; fst = 0; res += ts(x); }
    return res;
}
template<class T, class U> string ts(pair<T,U> p) { return "("+ts(p.FI)+", "+ts(p.SE)+")"; }

// OUTPUT
template<class T> void pr(T x) { cout << ts(x); }
template<class T, class ...U> void pr(const T& t, const U&... u) { pr(t); pr(u...); }
void ps() { pr("\n"); } // print w/ spaces
template<class T, class ...U> void ps(const T& t, const U&... u) { pr(t); if (sizeof...(u)) pr(" "); ps(u...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class T, class ...U> void DBG(const T& t, const U&... u) { cerr << ts(t); if (sizeof...(u)) cerr << ", "; DBG(u...); }
#define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
        << __FUNCTION__  << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);

const ld PI = acos(-1.0);
const int dx[4] = {1,0,-1,0}, dy[4] = {0,1,0,-1};
const ld EPS = 1e-9;
const ll MODBASE = 1000000007LL;
const int INF = 0x3f3f3f3f;

const int MAXN = 300010;
const int MAXM = 1000;
const int MAXK = 16;
const int MAXQ = 200010;

int n, p[MAXN], dp[MAXN], par[MAXN], lef[MAXN], rig[MAXN];

struct SegmentTree {
    public:
    int N, mx;

    // 0-indexed
    SegmentTree(int n, int mx) {
        this->mx = mx;
        t.resize(4*n);
        N = n;
        FOR(i,0,SZ(t)-1) t[i] = mx ? -INF : INF;
    }

    int get(int k, int l, int r, int u, int v) {
        if (l > r || r < u || v < l) return mx ? -INF : INF;
        if (u <= l && r <= v) return t[k];
        int m = (l + r) >> 1;
        int lef = get(k*2, l, m, u, v);
        int rig = get(k*2+1, m+1, r, u, v);
        return merge(lef, rig);
    }

    void update(int k, int l, int r, int u, int val) {
        if (l > r || r < u || u < l) return;
        if (l == r) {
            t[k] = mx ? max(t[k], val) : min(t[k], val);
            return;
        }
        int m = (l + r) >> 1;
        update(k*2, l, m, u, val);
        update(k*2+1, m+1, r, u, val);
        t[k] = merge(t[k*2], t[k*2+1]);
    }

    private:
    vi t;

    int merge(int &a, int &b) {
        return mx ? max(a, b) : min(a, b);
    }
};

int main() {
    ios::sync_with_stdio(0);
    cin.tie(nullptr);
    int te;
    cin >> te;
    while (te--) {
        cin >> n;
        FOR(i,1,n) cin >> p[i];

        dp[0] = 0;
        par[0] = -1;

        FOR(i,1,n) {
            lef[i] = max(1, i - p[i]);
            rig[i] = min(n, i + p[i]);
        }

        SegmentTree Min(n+1, 0), Max(n+1, 1);

        Min.update(1,0,n,0,0);
        FOR(i,1,n) Max.update(1,0,n,i,rig[i]);

        FOR(i,1,n) {
            dp[i] = -INF;
            par[i] = -2;
            int connect = lef[i] - 1;
            int minJ = Min.get(1,0,n,connect,n);
            // cout << i << ' ' << minJ << ' ' << connect << endl;
            if (minJ != INF) {
                int rigVal = max(i-1, Max.get(1,0,n,minJ+1,i-1));
                // cout << rigVal << "\n";
                if (rigVal > dp[i]) {
                    dp[i] = rigVal;
                    par[i] = minJ;
                }
            }

            if (dp[i-1] >= i && max(dp[i-1], rig[i]) > dp[i]) {
                dp[i] = max(dp[i-1], rig[i]);
                par[i] = -1;
            }
            if (dp[i-1] > dp[i]) {
                dp[i] = dp[i-1];
                par[i] = -1;
            }
            Min.update(1,0,n,dp[i],i);
            // int g = Min.get(1,0,n,dp[i],dp[i]);
            // dbg(g);
        }
        // FOR(i,1,n) cout << dp[i] << " "; cout << endl;
        // FOR(i,1,n) cout << par[i] << " "; cout << endl;

        if (dp[n] != n) {
            cout << "NO\n";
            continue;
        }
        cout << "YES\n";
        string res = "";
        int cur = n;
        while (cur) {
            if (par[cur] == -1) {
                cur--;
                res += "R";
            } else {
                int pcur = par[cur];
                int diff = cur - pcur;
                res += "L";
                FOR(i,1,diff-1) res += "R";
                cur = pcur;
            }
        }
        reverse(ALL(res));
        cout << res << "\n";
    }
    return 0;
}