#include #include #include #include #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(i, n) for (ll i = 0; i < ll(n); ++i) #define rep2(i, s, n) for (ll i = ll(s); i < ll(n); ++i) #define rep3(i, s, n, d) for(ll i = ll(s); i < ll(n); i+=d) #define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__) #define rrep1(i, n) for (ll i = ll(n)-1; i >= 0; i--) #define rrep2(i, n, t) for (ll i = ll(n)-1; i >= (ll)t; i--) #define rrep3(i, n, t, d) for (ll i = ll(n)-1; i >= (ll)t; i-=d) #define rrep(...) overload4(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define SUM(a) accumulate(all(a),0LL) #define MIN(a) *min_element(all(a)) #define MAX(a) *max_element(all(a)) #define SORT(a) sort(all(a)); #define REV(a) reverse(all(a)); #define SZ(a) int(a.size()) #define popcount(x) __builtin_popcountll(x) #define pf push_front #define pb push_back #define ef emplace_front #define eb emplace_back #define ppf pop_front #define ppb pop_back #ifdef __LOCAL #define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; } #else #define debug(...) void(0); #endif #define INT(...) int __VA_ARGS__;scan(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__) #define STR(...) string __VA_ARGS__;scan(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__) using namespace std; using namespace __gnu_pbds; using ll = long long; using ld = long double; using P = pair; using LP = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vd = vector; using vvd = vector; using vs = vector; using vc = vector; using vvc = vector; using vb = vector; using vvb = vector; using vp = vector

; using vvp = vector; template using PQ = priority_queue, vector>, greater>>; template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << '{' << p.first << ", " << p.second << '}'; } template istream &operator>>(istream &is, tuple &t) { return is >> get<0>(t) >> get<1>(t) >> get<2>(t); } template ostream &operator<<(ostream &os, const tuple &t) { return os << '{' << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << '}'; } template istream &operator>>(istream &is, vector &v) { for (T &t: v) { is >> t; } return is; } template ostream &operator<<(ostream &os, const vector &v) { os << '['; rep(i, v.size()) os << v[i] << (i == int(v.size() - 1) ? "" : ", "); return os << ']'; } template ostream &operator<<(ostream &os, const deque &v) { os << '['; rep(i, v.size()) os << v[i] << (i == int(v.size() - 1) ? "" : ", "); return os << ']'; } template ostream &operator<<(ostream &os, const set &st) { os << '{'; auto it = st.begin(); while (it != st.end()) { os << (it == st.begin() ? "" : ", ") << *it; it++; } return os << '}'; } template ostream &operator<<(ostream &os, const multiset &st) { os << '{'; auto it = st.begin(); while (it != st.end()) { os << (it == st.begin() ? "" : ", ") << *it; it++; } return os << '}'; } template void vecout(const vector &v, char div = '\n') { rep(i, v.size()) cout << v[i] << (i == int(v.size() - 1) ? '\n' : div); } template bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } void scan() {} template void scan(Head &head, Tail &... tail) { cin >> head; scan(tail...); } template void print(const T &t) { cout << t << '\n'; } template void print(const Head &head, const Tail &... tail) { cout << head << ' '; print(tail...); } template void fin(const T &... a) { print(a...); exit(0); } template vector &operator+=(vector &v, T x) { for (T &t: v) t += x; return v; } template vector &operator-=(vector &v, T x) { for (T &t: v) t -= x; return v; } template vector &operator*=(vector &v, T x) { for (T &t: v) t *= x; return v; } template vector &operator/=(vector &v, T x) { for (T &t: v) t /= x; return v; } struct Init_io { Init_io() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cout << boolalpha << fixed << setprecision(15); cerr << boolalpha << fixed << setprecision(15); } } init_io; const string yes[] = {"no", "yes"}; const string Yes[] = {"No", "Yes"}; const string YES[] = {"NO", "YES"}; const int inf = 1001001001; const ll linf = 1001001001001001001; void rearrange(const vi &) {} template void rearrange(const vi &ord, vector &head, Tail &...tail) { assert(ord.size() == head.size()); vector ori = head; rep(i, ord.size()) head[i] = ori[ord[i]]; rearrange(ord, tail...); } template void sort_by(vector &head, Tail &... tail) { vi ord(head.size()); iota(all(ord), 0); sort(all(ord), [&](int i, int j) { return head[i] < head[j]; }); rearrange(ord, head, tail...); } template vector cumsum(const vector &v, bool shift_one = true) { int n = v.size(); vector res; if (shift_one) { res.resize(n + 1); rep(i, n) res[i + 1] = res[i] + v[i]; } else { res.resize(n); if (n) { res[0] = v[0]; rep(i, 1, n) res[i] = res[i - 1] + v[i]; } } return res; } vvi graph(int n, int m, bool directed = false, int origin = 1) { vvi G(n); rep(_, m) { INT(u, v); u -= origin, v -= origin; G[u].pb(v); if (!directed) G[v].pb(u); } return G; } template vector>> weighted_graph(int n, int m, bool directed = false, int origin = 1) { vector>> G(n); rep(_, m) { int u, v; T w; scan(u, v, w); u -= origin, v -= origin; G[u].eb(v, w); if (!directed) G[v].eb(u, w); } return G; } template class BIT { int n; vector val; public: BIT(int n) : n(n), val(n + 1, 0) {} void add(int i, T x = 1) { i++; while (i <= n) { val[i] += x; i += i & -i; } } T sum(int i) { T ret = 0; i++; while (i > 0) { ret += val[i]; i -= i & -i; } return ret; } // [l, r) T sum(int l, int r) { return sum(r - 1) - sum(l - 1); } }; template class segtree { using S = typename M::S; int _n, sz; vector d; public: constexpr segtree() : segtree(0) {} constexpr segtree(int n) : segtree(vector(n, M::e)) {} constexpr segtree(const vector &init) : _n(int(init.size())) { sz = 1; while (sz < _n) sz *= 2; d.assign(sz * 2, M::e); rep(i, _n) d[sz + i] = init[i]; rrep(i, sz, 1) d[i] = M::op(d[2 * i], d[2 * i + 1]); } void set(int p, S x) { assert(0 <= p and p < _n); p += sz; d[p] = x; while (p > 1) { p >>= 1; d[p] = M::op(d[2 * p], d[2 * p + 1]); } } template void apply(int p, const F &f) { assert(0 <= p and p < _n); p += sz; d[p] = f(d[p]); while (p > 1) { p >>= 1; d[p] = M::op(d[2 * p], d[2 * p + 1]); } } S get(int p) { assert(0 <= p and p < _n); return d[sz + p]; } S prod(int l, int r) { assert(0 <= l and l <= r and r <= _n); l += sz, r += sz; S prod_l = M::e; S prod_r = M::e; while (l < r) { if (l & 1) prod_l = M::op(prod_l, d[l++]); if (r & 1) prod_r = M::op(d[--r], prod_r); l >>= 1, r >>= 1; } return M::op(prod_l, prod_r); } S all_prod() { return d[1]; } template int max_right(int l, F f) const { assert(0 <= l && l <= _n); assert(f(M::e)); if (l == _n) return _n; l += sz; S now = M::e; do { while (~l & 1) l >>= 1; if (!f(M::op(now, d[l]))) { while (l < sz) { l *= 2; if (f(M::op(now, d[l]))) { now = M::op(now, d[l]); ++l; } } return l - sz; } now = M::op(now, d[l]); l++; } while ((l & -l) != l); return _n; } template int min_left(int r, F f) const { assert(0 <= r && r <= _n); assert(f(M::e)); if (r == 0) return 0; r += sz; S now = M::e; do { --r; while (r > 1 and (r & 1)) r >>= 1; if (!f(M::op(d[r], now))) { while (r < sz) { r = 2 * r + 1; if (f(M::op(d[r], now))) { now = M::op(d[r], now); --r; } } return r + 1 - sz; } now = M::op(d[r], now); } while ((r & -r) != r); return 0; } }; class M { public: using S = P; static constexpr S e = {inf, -inf}; static constexpr S op(const S &l, const S &r) { return {min(l.first, r.first), max(l.second, r.second)}; } }; template class lazy_segtree { using S = typename M::S; using F = typename M::F; int _n, sz, log; vector d; vector lz; void update(int k) { d[k] = M::op(d[2 * k], d[2 * k + 1]); } void all_apply(int k, F f) { d[k] = M::mapping(f, d[k]); if (k < sz) lz[k] = M::composition(f, lz[k]); } void push(int k) { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = M::id; } public: constexpr lazy_segtree() : lazy_segtree(0) {} constexpr lazy_segtree(int _n) : lazy_segtree(vector(_n, M::e)) {} constexpr lazy_segtree(const vector &init) : _n(int(init.size())) { log = 0; while (1 << log < _n) log++; sz = 1 << log; d.assign(2 * sz, M::e); lz.assign(sz, M::id); rep(i, _n) d[sz + i] = init[i]; rrep(i, sz, 1) update(i); } void set(int p, S x) { assert(0 <= p and p < _n); p += sz; rrep(i, log + 1, 1) push(p >> i); d[p] = x; rep(i, 1, log + 1) update(p >> i); } template void apply(int p, const F &f) { assert(0 <= p and p < _n); p += sz; rrep(i, log + 1, 1) push(p >> i); d[p] = f(d[p]); rep(i, 1, log + 1) update(p >> i); } S get(int p) { assert(0 <= p and p < _n); p += sz; rrep(i, log + 1, 1) push(p >> i); return d[p]; } S prod(int l, int r) { assert(0 <= l and l <= r and r <= _n); l += sz, r += sz; rrep(i, log + 1, 1) { if ((l >> i) << i != l) push(l >> i); if ((r >> i) << i != r) push(r >> i); } S sl = M::e, sr = M::e; while (l < r) { if (l & 1) sl = M::op(sl, d[l++]); if (r & 1) sr = M::op(d[--r], sr); l >>= 1, r >>= 1; } return M::op(sl, sr); } S all_prod() { return d[1]; } void apply(int l, int r, F f) { assert(0 <= l and l <= r and r <= _n); l += sz, r += sz; rrep(i, log + 1, 1) { if ((l >> i) << i != l) push(l >> i); if ((r >> i) << i != r) push(r >> i); } { int l2 = l, r2 = r; while (l < r) { if (l & 1) all_apply(l++, f); if (r & 1) all_apply(--r, f); l >>= 1, r >>= 1; } l = l2, r = r2; } rep(i, 1, log + 1) { if ((l >> i) << i != l) update(l >> i); if ((r >> i) << i != r) update(r >> i); } } template int max_right(int l, F f) { assert(0 <= l && l <= _n); assert(f(M::e)); if (l == _n) return _n; l += sz; rrep(i, log + 1, 1) push(l >> i); S now = M::e; do { while (~l & 1) l >>= 1; if (!f(M::op(now, d[l]))) { while (l < sz) { push(l); l *= 2; if (f(M::op(now, d[l]))) { now = M::op(now, d[l]); ++l; } } return l - sz; } now = M::op(now, d[l]); ++l; } while ((l & -l) != l); return _n; } template int min_left(int r, F f) { assert(0 <= r && r <= _n); assert(f(M::e)); if (r == 0) return 0; r += sz; for (int i = log; i >= 1; i--) push((r - 1) >> i); S now = M::e; do { r--; while (r > 1 && (r & 1)) r >>= 1; if (!f(M::op(d[r], now))) { while (r < sz) { push(r); r = 2 * r + 1; if (f(M::op(d[r], now))) { now = M::op(d[r], now); --r; } } return r + 1 - sz; } now = M::op(d[r], now); } while ((r & -r) != r); return 0; } }; class M_lz { public: using S = int; static constexpr S e = -1; static constexpr S op(const S &l, const S &r) { return l; } using F = int; static constexpr F id = -1; static constexpr F composition(const F &g, const F &f) { return (g == -1 ? f : g); } static constexpr S mapping(const F &f, const S &x) { return (f == -1 ? x : f); } }; int main() { INT(n); vi p(n); scan(p); vi pos(n); rep(i, n) pos[--p[i]] = i; vi x(n), y(n); BIT bt(n); rep(i, n) { x[i] = 1 - bt.sum(pos[i]) % 2; y[i] = bt.sum(pos[i]) + 1; bt.add(pos[i]); } vi sum_x = cumsum(x); vi to(n); { vp init(n); rep(i, n) init[i] = (x[i] ? P(inf, pos[i]) : P(pos[i], -inf)); segtree st(init); rep(i, n) { to[i] = st.max_right(i + 1, [&](P p) { return p.first > pos[i] and pos[i] > p.second; }); } } debug(x, y, to); vector st(2, lazy_segtree(n + 1)); vi pre(n + 1, -1); pre[0] = -2; rep(i, n + 1) { if(i) pre[i] = st[sum_x[i] % 2].get(i); if (i == n or pre[i] == -1) continue; st[1 - sum_x[i] % 2].apply(i + 1, to[i] + 1, i); } int now = n; vi v; while (now >= 0) { v.pb(now); if (pre[now] == -1) fin("No"); now = pre[now]; } print("Yes"); REV(v); rep(i, SZ(v) - 1) { int a = v[i], b = v[i + 1]; rep(j, a + 1, b) { print(j + 1, (y[j] % 2 ? y[j] : y[j] - 1)); } print(a + 1, y[a] + sum_x[b] - sum_x[a + 1]); } }