#include <iostream>
#include <vector>
#include <algorithm>
#include <cassert>

using namespace std;

// Aliases for common operations
#define pb push_back
#define pbk pop_back
#define mp make_pair
#define fs first
#define sc second
#define all(x) (x).begin(), (x).end()
#define foreach(i, a) for (auto i = (a).begin(); i != (a).end(); ++i)
#define len(a) ((int) (a).size())

#ifdef CUTEBMAING
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
#define eprintf(...) 42
#endif

// Type definitions
typedef long long int64;
typedef long double ld;
typedef unsigned long long lint;

const int inf = (1 << 30) - 1;
const int64 linf = (1ll << 62) - 1;
const int N = 1e6 + 100;
const int K = 20;

int n;
vector<int> g[N];
int bin[N][K], valMin[N][K], valMax[N][K];
int in[N], out[N], curTime = 0;

// Depth-First Search (DFS) function
void dfs(int v, int p = -1) {
    in[v] = curTime++;
    bin[v][0] = p;
    valMin[v][0] = min(v, p == -1 ? inf : p);
    valMax[v][0] = max(v, p);

    for (int i = 1; i < K; i++) {
        if (bin[v][i - 1] == -1) {
            bin[v][i] = -1;
            valMin[v][i] = valMin[v][i - 1];
            valMax[v][i] = valMax[v][i - 1];
        } else {
            bin[v][i] = bin[bin[v][i - 1]][i - 1];
            valMin[v][i] = min(valMin[v][i - 1], valMin[bin[v][i - 1]][i - 1]);
            valMax[v][i] = max(valMax[v][i - 1], valMax[bin[v][i - 1]][i - 1]);
        }
    }

    for (int to : g[v]) {
        if (to != p) {
            dfs(to, v);
        }
    }
    out[v] = curTime++;
}

// Check if u is an ancestor of v
inline bool anc(int u, int v) {
    return in[u] <= in[v] && out[v] <= out[u];
}

// Get the minimum value in the path from u to v
inline int smallMin(int u, int v) {
    if (anc(u, v)) return inf;
    int ans = inf;

    for (int i = K - 1; i >= 0; i--) {
        if (bin[u][i] != -1 && !anc(bin[u][i], v)) {
            ans = min(ans, valMin[u][i]);
            u = bin[u][i];
        }
    }

    ans = min(ans, valMin[u][0]);
    assert(bin[u][0] != -1);
    return ans;
}

inline int getMin(int u, int v) {
    return min(smallMin(u, v), smallMin(v, u));
}

// Get the maximum value in the path from u to v
inline int smallMax(int u, int v) {
    if (anc(u, v)) return -inf;
    int ans = -inf;

    for (int i = K - 1; i >= 0; i--) {
        if (bin[u][i] != -1 && !anc(bin[u][i], v)) {
            ans = max(ans, valMax[u][i]);
            u = bin[u][i];
        }
    }

    ans = max(ans, valMax[u][0]);
    assert(bin[u][0] != -1);
    return ans;
}

inline int getMax(int u, int v) {
    return max(smallMax(u, v), smallMax(v, u));
}

int nextL[N], nextR[N];
vector<int> rmq[N * 4];

// Build the Range Minimum Query (RMQ) structure
void make_rmq(int i, int l, int r) {
    if (l == r) {
        rmq[i].pb(nextL[l]);
        return;
    }

    make_rmq(i * 2, l, (l + r) / 2);
    make_rmq(i * 2 + 1, (l + r) / 2 + 1, r);
    rmq[i].resize(len(rmq[i * 2]) + len(rmq[i * 2 + 1]));
    merge(all(rmq[i * 2]), all(rmq[i * 2 + 1]), rmq[i].begin());
}

// Get the number of values in the range [l, r] less than v
int getValue(int i, int ll, int rr, int l, int r, int v) {
    if (ll > r || rr < l) return 0;
    if (l <= ll && rr <= r) {
        return upper_bound(all(rmq[i]), v) - rmq[i].begin();
    }
    return getValue(i * 2, ll, (ll + rr) / 2, l, r, v) + getValue(i * 2 + 1, (ll + rr) / 2 + 1, rr, l, r, v);
}

int main() {
    cin >> n;
    for (int i = 0; i < n - 1; i++) {
        int a, b;
        scanf("%d%d", &a, &b);
        a--, b--;
        g[a].pb(b);
        g[b].pb(a);
    }

    dfs(0);

    vector<int> stack;
    stack.pb(0);
    for (int i = 0; i < n; i++) {
        nextR[i] = inf;
        nextL[i] = -inf;
    }

    int64 ans = 0;
    for (int i = 1; i < n; i++) {
        while (!stack.empty() && getMin(stack.back(), i) != stack.back()) {
            nextR[stack.back()] = i;
            stack.pbk();
        }
        stack.pb(i);
    }

    stack.clear();
    stack.pb(n - 1);
    for (int i = n - 2; i >= 0; i--) {
        while (!stack.empty() && getMax(stack.back(), i) != stack.back()) {
            nextL[stack.back()] = i;
            stack.pbk();
        }
        stack.pb(i);
    }

    make_rmq(1, 0, n - 1);
    for (int i = 0; i < n; i++) {
        ans += getValue(1, 0, n - 1, i, nextR[i] - 1, i - 1);
    }

    cout << ans << endl;
    return 0;
}